multiobjective calibration framework for pedestrian simulation...

Research ArticleMultiobjective Calibration Framework for PedestrianSimulation Models A study on the Effect of MovementBase Cases Metrics and Density Levels

Martijn Sparnaaij Dorine C Duives Victor L Knoop and Serge P Hoogendoorn

Department of Transport amp Planning Delft University of Technology Stevinweg 1 2628 CN Delft Netherlands

Correspondence should be addressed to Martijn Sparnaaij msparnaaijtudelftnl

Received 31 January 2019 Revised 15 April 2019 Accepted 28 May 2019 Published 3 July 2019

Guest Editor Milad Haghani

Copyright copy 2019 Martijn Sparnaaij et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Ideally a multitude of steps has to be taken before a commercial implementation of a pedestrian model is used in practiceCalibration the main goal of which is to increase the accuracy of the predictions by determining the set of values for the modelparameters that allows for the best replication of reality has an important role in this process Yet up to recently calibration hasreceived relatively little attention within the field of pedestrian modelling Most studies focus only on one specific movement basecase andor use a single metric It is questionable how generally applicable a pedestrian simulationmodel is that has been calibratedusing a limited set of movement base cases and one metric The objective of this research is twofold namely to (1) determine theeffect of the choice of movement base cases metrics and density levels on the calibration results and (2) to develop a multiple-objective calibration approach to determine the aforementioned effects In this paper a multiple-objective calibration scheme ispresented for pedestrian simulation models in which multiple normalized metrics (ie flow spatial distribution effort and traveltime) are combined bymeans of weighted summethod that accounts for the stochastic nature of themodel Based on the analysis ofthe calibration results it can be concluded that (1) it is necessary to use multiple movement base cases when calibrating a model tocapture all relevant behaviours (2) the level of density influences the calibration results and (3) the choice ofmetric or combinationsof metrics influence the results severely

1 Introduction

The creation and implementation of a commercial pedestriansimulation will ideally consist of multiple steps One ofthose steps is calibrating the model whereby the goal is toincrease the accuracy of the model predictions by obtainingthe parameter set that results in the best replication of realityAs such calibration is an important step

Yet up to recently calibration has received relatively littleattentionwithin the field of pedestrianmodelling [1 2] this ismainly attributed to the lack of data [1 3ndash5] especially at highdensities Despite this issue there are many studies in whichauthors calibrate a pedestrian model (eg [6ndash10]) usually byusing a fundamental diagram [11] or trajectories However asmultiple authors mention the calibration attempts in thesestudies are limited and mostly focus on only one or a few

aspects [1 4 5 11 12] Most studies focus on one specificmovement base case (eg a bidirectional flow in a straightcorridor) use only one metric or do not look at variouspopulation compositions

It is questionable how generally applicable a pedestriansimulation model is that has been calibrated using a limitedset of movement base cases Campanella Hoogendoorn andDaamen [13] and Duives [14] show that using different flowsituations leads to different optimal parameter valuesThat isboth studies identify that for general usage (ie using a singlemodel for many different applications) one needs to calibratea pedestrian simulation model using multiple movementbases to capture all relevant behaviours The effect of usingdifferent metrics during the calibration has been investigatedby Duives [14] in relation to pedestrian dynamics and amongothers [15ndash17] in relation to vehicular traffic These studies

HindawiJournal of Advanced TransportationVolume 2019 Article ID 5874085 18 pageshttpsdoiorg10115520195874085

2 Journal of Advanced Transportation

illustrate that different combinations ofmetrics clearly lead todifferent calibration results Wolinski et al [18] also calibratea number of models using different metrics Though theydo not show the effect of using different metrics on theresulting optimal parameter set the results show clearlythat the model fit to the data depends on the metric usedFurthermore Hanseler Bierlaire Farooq and Muhlematter[19] also note differences between the optimal parameter setsobtained using different metrics or a combination of themwhen calibrating their macroscopic model

To overcome the problem of obtaining different resultswhen using different movement base cases andor metricsthree multiple-objective calibration frameworks have beenproposed in recent years which try to take a more inclusiveapproachWolinski et al [18] propose a frameworkwhich canpotentially incorporate multiple objectives However duringtheir benchmarking tests they only apply combinations ofone movement base case and one metric Campanella et al[13] show how a microscopic model can be calibrated usingmultiple movement base cases and how this compares tocalibrating the model with only one movement base caseThis study still only uses one metric during the calibrationThe work by Duives [14] uses multiple movement base caseswith multiple metrics and furthermore includes differentcombinations of weights in the objective function and isthus the most extensive of the three However except for thespatial distributionmetric the study does not show the resultsfor the other individual metrics Hence it is not possible toexactly determine the effect the different individual metricshave on the resulting optimal parameter set

So even though these works illustrate that the choice ofthe combinations of movement bases and metrics will influ-ence the optimal parameter set obtained during calibrationall three studies have their limitations For example they donot explicitly examine the effect of the level of density whichmight be a relevant factor given that work by Campanellaet al [13] shows that poorness of data can affect calibrationresults and work by [20] also shows some differences inthe obtained parameter sets for a low and high density caseof a bidirectional flow Furthermore the effects of usingdifferent metrics are also still poorly understood And aswork by Campanella Hoogendoorn and Daamen [21] showsthat using multiple objectives during the calibration willlead to a better validation score for general usage it is clearthat increased insights into which objectives to use duringcalibration can improve model validity

Given these observations the objective of this researchis twofold Firstly the objective is to determine the effectof the choice of movement base cases metrics and densitylevels on the calibration results Secondly the objective is todevelop a multiple-objective calibration method for pedes-trian simulation models to determine the aforementionedeffects taking into account the stochastic nature common tomany microscopic pedestrian models

This study aims to add value to the current body ofliterature by means of a more extensive study of the impactof calibration framework setup on the validity of a pedestriansimulation model This extension provides among otherthings novel insights into the effect of the level of density of

the movement base case and more detailed insights into theeffect of using a range of metrics in the calibration processFurthermore this study features a different type ofmodel (ievision-based model [22]) than the previous most extensivestudies (ie [13 14]) which both calibrated NOMAD Thusthis study also illustrates the replicability of their results andthe conclusions of those previous studies

The rest of the paper is organized as follows Sec-tion 2 briefly describes themicroscopic pedestrian simulationmodel Section 3 shortly introduces the methodology of thesensitivity analysis and presents the results of the analysisIn Section 4 the calibration methodology is elaborated uponThis is followed by the presentation of the results of calibrat-ing the model using a single objective in Section 5 Section 6presents the results of the multiobjective calibration Finallythis paper closes of with a discussion of the results conclu-sions and the implications of this work for practice

2 Brief Introduction to Pedestrian Dynamics

This section introduces pedestrian dynamics (PD) a micro-scopic pedestrian simulation model developed by INCON-TROL Simulation Solutions It offers a user the abilityto model the movement behaviour of pedestrians at allthree behavioural levels (strategic tactical and operational)Though in this research pedestrians only have one activitynamely to walk from their origin to their destination via asingle route and hence there is no need to model the activitychoice the activity scheduling or the route choiceThemodelfeaturing the operational walking dynamics is discussed inmore detail underneath

The operational behaviour of the INCONTROL modelconsists of two parts ie route following and collisionavoidance which together determine the acceleration of apedestrian at every time step PD determines the accelerationof a pedestrian by the combination of lsquosocial forcesrsquo and adesired velocity component The pedestrian itself is repre-sented by a circle with a radius 119903 At every time step theacceleration of a pedestrian is determined as follows

119889997888rarrV 119894119889119905 = 997888rarrV des119894 minus 997888rarrV 119894120591 + sum119895

997888rarr119891 119894119895 + sum119882

997888rarr119891 119894119882 [ms2] (1)

where 997888rarrV des119894 and997888rarrV 119894 are respectively the desired and current

velocity of pedestrian 119894 997888rarr119891 119894119895 and 997888rarr119891 119894119882 are the physical forcesthat occur on contact with another pedestrian or a staticobstacle And lastly 120591 is the relaxation time Furthermorein case the speed of the pedestrian drops below a certainthreshold (ie the minimal desired speed parameter) thepedestrian does not move until the next time step when theresulting speed is higher than the threshold

The desired velocity is determined according to themethod proposed by Moussaıd et al [22] The method usesa vision-based approach to avoid collisions This approachcombines the collision avoidance with the preferred speedand the desired destination to determine the desired velocityThedesired velocity is determined bymeans of two heuristicsnamely

Journal of Advanced Transportation 3

(1) A pedestrian chooses the direction that results in themost direct path to its desired destination given thepresence of both static and dynamic obstacles

(2) A pedestrian chooses the speed that in case there isan obstacle in the preferred direction results in thelowest time-to-collision whereby this time is alwayslarger than 120591

The pedestrian only takes into account obstacles that arewithin its field of vision ([minus120601 120601]) which is determined bythe current orientation of the pedestrian the viewing angle120601 and the viewing distance 119889max The desired direction isdetermined by minimizing (2)

119889 (120572) = 1198892max + 119891 (120572)2 minus 2119889max119891 (120572) cos (1205720 minus 120572) for 120572 isin [minus120601 120601] (2)

where 119891(120572) is the distance to the closest expected obstaclein the direction of 120572 which is equal to 119889max if there areno obstacles within the viewing range 1205720 is the angletowards the desired destination The desired speed is givenby Vdes = min(V0119894 119889ℎ120591) where V0119894 is the preferred speed ofthe pedestrian and 119889ℎ is the distance between the pedestrianand the first expected collision in the desired direction 119889ℎ isdetermined as follows

119889ℎ =

119889119894expcol minus 119889119894pers If the expected collision is with another

pedestrian travelling in the same direction

119889119894expcol Otherwise

[m] (3)

where 119889119894expcol is the distance to the first expected collisionin the desired direction 120572 of pedestrian 119894 and 119889119894pers thepersonal distance of pedestrian 119894 The personal distance isthe distance a pedestrian wants to keep between itself andanother pedestrian

There are two important notes regarding the implemen-tation of this method in PD namely (1) Regardless of thesettings for the viewing angle and viewing distance themodelwill only take into account the four closest pedestrians (whoare within the field of vision) when determining the desiredvelocity (2)Not all parameters can be adapted by the user theparameters governing the physical forces (ie

997888rarr119891 119894119895 and 997888rarr119891 119894119882)are namely not user-adaptable

The desired destination of each pedestrian is determinedusing the Indicative RouteMethod proposed by KaramouzasGeraerts and Overmars [23] This desired destination isinfluenced by two (user-adaptable) parameters which are theldquoPreferred clearancerdquo which influences the minimal distancea pedestrian wants to keep between its desired destinationand a static obstacle and the ldquoSide preference update factorrdquowhich influences the strength of the desired destinationlocation changes given the current position of the pedestrianand the current deviation from the originally planned path

As is the case for many pedestrian models PD isstochastic by nature (ie two simulations with exactly thesame parameters and input but with different seeds resultin different outcomes) In this study there are three maincauses for this stochasticity namely the preferred speedthe initial destination point and the exact point of originThe first contributes to the stochasticity due to the fact thatevery pedestrian is randomly assigned a preferred speed froma given distribution The latter two causes of stochasticityare points whose location influences the desired destinationand whose exact position is a randomly determined locationwithin a respective origin or destination area The fact thatthe model is stochastic by nature has to be taken into account

during the calibration and is discussed in more detail in thenext section

3 Sensitivity Analysis

A sensitivity analysis is performed to determine to whichparticular parameters the model is sensitive This sectiondescribes the methodology of the sensitivity analysis andpresents the results of this analysisThe results of the sensitiv-ity analysis are used to determine which parameters shouldbe incorporated in the calibration process as recalibratingall model parameters is not feasible within the time frameof this study How the results are used to determine thecalibration search space andwhy it is not feasible to include allparameters is explained in more detail in Section 45 SearchSpace Definition

31 Methodology of the Sensitivity Analysis The goal of thesensitivity analysis is to determine which of the 7 modelparameters of the INCONTROL model (see Table 1) thatinfluence the operational behaviour most affect the modelrsquosresults The authors expect that the sensitivity depends onthe scenario Thus the analysis is performed for all sevenscenarios used in the calibration These scenarios are asfollows A high density bidirectional flow a high densitycorner flow a high density t-junction flow a bottleneck flowand low density variants of the bidirectional corner and t-junction flows For a detailed description of the scenarios seeSection 41

The distribution of the instantaneous speeds of all pedes-trians is used as the sole metricThis distribution contains allinstantaneous speeds of all pedestrians and all replicationsThis metric is chosen because the distribution of the speedsis able to give insight into both the efficiency of the flow (ahigher mean speed indicates a more efficient flow) and intothe underlying behaviour (eg a high variance can indicate


Obtain speed distribution for default value

Obtain speed distribution for plusmn25 deviation

Obtain speed distributions for all points in between

Significantly different

compared to default

Yes

No Model not sensitive to the

parameter

Curve describing

model sensitivity

Figure 1 Overview of the sensitivity analysis methodology The process depicted in the figure is performed for all combinations of the 7scenarios and 7 parameters

Table 1 The seven parameters included in the sensitivity analysis

Route following Preferred clearanceSide pref update factor

Collision avoidance Relaxation timeViewing angle

Viewing distanceMin desired speedPersonal distance

that interactions are not solved efficiently causing pedestriansto change their speed a lot)

The Anderson-Darling test [24] is used to determine ifenough replications have been performed to allow for thecomparison of two distributions of the instantaneous speedThis statistical test determines whether a distribution hasconverged (for more details see Section 46)

To limit the amount of simulations only first-order effectsare investigated Note that the number of replications isalready extensive due to the incorporation of seven scenariosand a vast number of replications to account for modelstochasticity Figure 1 depicts the process which is appliedto every combination of a scenario and a parameter Theremaining text in this subsection describes the process andits steps in more detail For every scenario the first step isto obtain the speed distribution using the defaults valuesThis distribution serves as the base line Accordingly for allcombinations of the 7 parameters and 7 scenarios the valueof the parameter in question is increased by 25 After whichthe distribution of the speeds is again obtained The sameprocedure is followed for a decrease of the parameter valuesby 25 The limit of 25 is chosen as the INCONTROLmodel already has undergone some basic calibration andhence it is assumed that the optimal values will not deviatemuch from the current default values

For all these new distributions of speeds accordingly thefollowing two checks are identified (a) is the new distributionsignificantly different from the default distribution accordingto the Anderson-Darling test and (b) are the differencesbetween the means and standard deviations of the distribu-tions larger than one would expect based on the influence

of the stochasticity (for more details see [25]) The secondcheck provides insight into the magnitude of the differenceand thus the degree of the sensitivity of the model tochanges in this parameter If both these conditions hold (iesignificant differences are found between the new and olddistributions) all distributions between the 25 boundaryand the default value using a precision of 1 point areobtained to gain insight into how the modelrsquos sensitivitychanges as the deviation from the default value increases

For a more detailed description of the methodology thereader is referred to [25]

32 Results of the Sensitivity Analysis Based on the method-ology described above the following results are obtainedFirstly the model is not sensitive to changes in the ldquoPreferredclearancerdquo parameter and changes in the ldquoViewing distancerdquoparameter Even in high density cases the model is notsensitive to changes in the viewing distance parameter Thisis most likely the result of the fact that PD only takes intoaccount the four closest pedestrians within the viewing fieldwhich might all reside well within this radius

In general the model is not sensitive to changes in theldquoPersonal distancerdquo the ldquoSide pref update factorrdquo and theldquoMin desired speedrdquo In the case of the ldquoPersonal distancerdquothe model is slightly sensitive to changes in this parameter inthe case of the bottleneck scenario In the case of the ldquoSidepref update factorrdquo the model is slightly sensitive to the t-junction high density scenario The model is also slightlysensitive to changes in the ldquoPersonal distancerdquo for bothscenarios However as the maximum differences betweenthe means and the standard deviations are at most 2we conclude that within the plusmn25 range changes in theseparameters will not affect the model results much

The only parameter to which the model is sensitive inall seven scenarios is the relaxation time The model isfurthermore sensitive to the viewing angle in all four highdensity scenarios Figure 2 presents that for both parametersand the seven scenarios the differences between the meanand the standard deviation of the distributions are obtainedusing an increased or decreased parameter value Fromthis figure a number of observations can be made Firstlythe figure clearly shows that the model is more sensitiveto changes in the relaxation time than to the changes in


minus20

0

20

40

60D

iffer

ence

com

pare

d to

def

ault

[]

minus20 minus10 0 10 20Deviation from default parameter value []

Bidirectional - high Bidirectional - lowCorner - highCorner - low

T-junction - highT-junction - lowBottleneck

(a) Relaxation time-mean

minus20

0

20

40

60

Diff

eren

ce co

mpa

red

to d

efau

lt [

]




(b) Viewing angle-mean


minus10

0

10

20

Diff

eren

ce co

mpa

red

to d

efau

lt [

]



(c) Relaxation time-std


minus10

0

10

20

Diff

eren

ce co

mpa

red

to d

efau

lt [

]



(d) Viewing angle-std

Figure 2 Results of the sensitivity analysis

the viewing angle Secondly clear differences between thescenarios can be identified For example the model is moresensitive to changes in the parameters when simulating highdensity scenarios And thirdly in many cases an asymmetrycan be observed between the slope and shape of the curve leftfrom the default value (ie the decreased parameter values)and the one on the right Overall we conclude that the effectof changing a parameterrsquos value differs a lot between the twoparameters and the seven scenarios

In conclusion overall the INCONTROLmodel is not verysensitive to changes in many of the parameters given theplusmn25boundariesThemodel is primarily sensitive to changesin the relaxation time whose value influences the outcome ofthe simulation in all seven scenarios and the viewing anglein the case of the high density scenarios

4 MethodologyThis section presents the reasoning behind the newly devel-oped calibration methodology Figure 3 depicts the multiple-objective calibration methodology and its parts In line with

previous research the methodology uses multiple scenariosand multiple metrics For every combination of a scenarioand a metric an objective value is obtained which representsthe difference between the simulation and the reference datafor the given parameter set These objective values are thencombined into a single objective value which in turn is usedby the optimization method to determine if the currentparameter set is optimal In case the current parameter set isdeemedoptimal the calibration stops and the next stepwouldbe to validate the model (which is not part of this study)Alternatively in case the parameter set is not deemed optimala new parameter set is created and the calibration processcontinues

All of these parts are discussed in more detail in thissection First the scenarios are identified Accordingly themetrics and the objective function are presentedThis sectionfurthermore elaborates on the optimization method and themanner that the stochasticities of the pedestrian simulationmodel are handled


Multiple objectives

Single objective

Optimization algorithm

Validation

If not optimal

If optimal

Referencedata

Simulation model

S1

S2

Sn

E

Ei

Ei = [1 2 k]

E = [E1 E2 En]

1

2

k

M1

M2

Mk

darr

Si

Figure 3 Overview of the multiple-objective methodology where 1198781 to 119878119899 are the used scenarios 1198721 to 119872119896 the used metrics 1205981 to 120598119896 theindividual errors and 119864119894 the combined error for scenario 119894 120598 the combined error and 120579 the parameter set

41 Scenarios Contemporary several datasets are availablethat feature the movement of pedestrians in multiple move-ment base cases and a similar population of pedestriansamong others [26ndash28] Since the experiments within theHERMES project represent the most comprehensive set ofmovement base cases featuring a similar population anddifferent levels of density this dataset will be used in thiscalibration procedure Based on this dataset seven scenariosare constructed whereby every scenario contains a singlemovement base case and a single density level Four move-ment base cases are studied these are a bidirectional flowa unidirectional corner flow a merging flow at a t-junctionand a bottleneck flow All base cases have both a low andhigh density variant except for the bottleneck which onlyhas a high density variant Figure 4 shows the layout of thefour simulated movement base cases For a more detailedoverview of the experimental setup within the HERMESproject the reader is referred to [27] Care is taken to ensure asimilar flow pattern over time speed distribution and routechoice details on the exact simulation setup of the sevenscenarios in PD are mentioned in [25]

42 Metrics In this multiple-objective framework four dif-ferent metrics are used to identify how different metricsimpact the calibration results In this research the choice ismade to use twometrics at themacroscopic level the flow andthe spatial distribution and two at the mesoscopic level thetravel timedistribution and the effort distributionThesemet-rics are chosen because on both levels they describe differentaspects of the walking behaviour Microscopic metrics ietrajectories are not used for three reasons Firstly calibrationbased on trajectories requires a different approach thancalibrating based on macroscopic and mesoscopic metricsIt would require many more simulations to use both micro-scopic and mesoscopic andor macroscopic metrics and due

to time limits this was not considered to be viable withinthis study Secondly the current approaches for calibratingbased on trajectories do not deal with the stochastic natureof the model Lastly since pedestrian simulation modelsare mostly used to approximate the macroscopic propertiesof the infrastructure (eg capacity density distribution)[21] and given that calibrating based on microscopic met-rics does not necessarily result in a macroscopically validmodel [11]macroscopic andmesoscopicmetrics take priorityover microscopic metrics The four metrics adopted in thisresearch to calibrate PD are discussed in more detail below

Flow The flow is chosen as a macroscopic metric to checkto what extent the model can reproduce the throughput indifferent situations In all seven scenarios the average flow ismeasured along a certain cross-section (see Figure 4) duringa certain measurement period The average flow is calculatedas follows

119902119894 = 119873119894Δ119905 times 119897 [pedsm] (4)

where 119873119894 is the number of unique pedestrians with maintravel direction 119894 that passed the line in the direction equalto the main travel direction and during the measurementperiod (Δ119905) The flow is normalized to a flow per meter ofmeasurement line whereby 119897 is the length of themeasurementline in order to allow for comparisons between scenarios

Distribution over Space Reference [14] showed that micro-scopic models might not always be able to accurately repro-duce the spatial distribution patterns Hence it is essentialto check whether a model performs well with respect tothis property The distribution over space measures howthe pedestrians are distributed over the measurement areaA grid of 04 x 04 m which is approximately the size ofone pedestrian during a high density situation overlays the


8m

36m

(a)24m 32m

24m

32m

(b)

24m

32m

2m2m 24m(c)

36m

9m 4m1m(d)

Figure 4 Overview of the layout of the four movement base cases used during the calibration (a) Bidirectional flow (b) Unidirectionalcorner flow (c) Merging t-junction flow (d) Bottleneck In the figure the hatched areas indicate the measurement areas the dashed lines thelocation where the flow is measured and in the case of the bottleneck the grey area indicates the waiting area at the start of the simulation

measurement area and for every cell the percentage of thetime it is occupied is determined by (5)

119865119895 = 119873occ119895

119873steps[minus] (5)

where 119873occ119895 is the number of time steps cell 119895 is occupiedby one or more pedestrians (based on the centre point of thepedestrians) and 119873steps is the number of time steps taken intoaccount

Travel Time The travel time is the time it takes a pedestrianto traverse the measurement area as determined by (5)

119879119879119896 = 119905end minus 119905start119897ref [sm] (6)

where 119905start and 119905end are respectively the time pedestrian 119896first which entered the measurement area and time pedes-trian 119896 which left the area 119897ref is the average length of thepath in themeasurement area as obtained from the referencedata The travel time is normalized in order to simplifythe comparison of the goodness-of-fit of different scenarioswith different average path lengths Note that this metricapproximates the realized pace of each individual That is if

an individual makes a detour at a very high speed it will notaffect its travel time but it will influence the effort required toget to its destination

Only the travel times of those pedestrians who suc-cessfully traversed the whole measurement area during themeasurement period are included in the distribution of thetravel times

Effort Several studies have identified the difficulty of smoothinteractions between simulated pedestrians in bidirectionalflows In order to ensure realistic interaction behaviour theeffort metric is introduced which captures how much effortit takes a pedestrian to traverse the measurement area Theeffort for pedestrian k is defined as the average change invelocity per time step (see (7))

119890119896 = sum119899minus1 (1003816100381610038161003816V119909 (119905) minus V119909 (119905 minus 1)1003816100381610038161003816 + 10038161003816100381610038161003816V119910 (119905) minus V119910 (119905 minus 1)10038161003816100381610038161003816)119899 minus 1 [ms]

(7)

V119909 (119905) = 119909 (119905) minus 119909 (119905 minus 1)Δ119905 [ms]

V119910 (119905) = 119910 (119905) minus 119910 (119905 minus 1)Δ119905 [ms]

(8)


Table 2 Normalization values

MnormFlow 10Spatial distribution 018994Travel time-mean 099107Travel time-std 020728Effort-mean 004345Effort-std 000953

where V119909(119905) and V119910(119905) are respectively the speed in the x andy-direction at time step 119905 and 119899 the number of time stepsThe speeds are obtained by differentiating the current andprevious positions of pedestrian 119896 (see (8)) where 119909(119905) and119910(119905) are respectively the x and y-position at time step 119905 andΔ119905 is the duration of the time step The effort measurementsof all pedestrians are combined into one distribution

43 Objectives In this research multiple objectives are com-bined into a single objective using the weighted sum method[29] This is in line with research by Duives [14] theonly example in literature using both multiple metrics andscenarios to calibrate a pedestrian model

In order to make a fair comparison between objectivesnormalization is necessary as the metrics have differentunits and different orders of magnitude Table 2 shows thenormalization values used during calibration The adoptednormalization method is based on two main assumptionsFirstly it is assumed that for a single metric a deviationof 1 unit (for example 1 pedms is case of the flow) inone scenario is equally wrong as a deviation of 1 unit inanother scenario (ie an absolute error is used instead ofa relative error) Secondly it is assumed that for everymetric a deviation of 1 pedms in the flow is equal to adeviation equal to the average ratio between the values offlow and the respective metric in the reference data (ie(1119878119899) sum119904isin119878(119910119898119904119902119904) where 119878 is the set of scenarios 119878119899 isthe number of scenarios 119902119904 is the average flow of scenario119904 and 119910119898119904 is the value for metric 119898 for scenario 119904) Thismethod is chosen because it does not explicitly assume abias towards any of the metrics or scenarios which is deemedappropriate for this study given its goal However this mightnot necessarily be the case if one intends to calibrate a modelfor a specific intended use For amore detailed explanation ofthis method and an underpinning of the choice to specificallyuse this method the reader is referred to [25]

The objective function for a given metric and scenariois given by the normalized Squared Error (SE) which forthe macroscopic metrics is determined by (9) and for themesoscopic metrics is determined by (10)

119878119864norm (120579) = 1119898sum119895

(sum119894119872sim119894119895 (120579) 119899 minus 119872ref 119895

119872norm)2

(9)

119878119864normmeso (120579) = 12 (119872sim120583 (120579) minus 119872ref 120583

119872norm120583)2

+ 12 (119872sim120590 (120579) minus 119872ref 120590119872norm120590

)2

(10)

where 119872sim is the metricrsquos value according to the simulation119872ref the reference value according to the data 119872norm thevalue used for the normalization and 120579 the vector of modelparameters In the case of (9) 119899 is the number of replicationsand 119898 is the number of travel directions in case of the flowand the number of cells in case of the spatial distributionIn the case of the mesoscopic metrics (10) shows that thedifference between the distributions is approximated bytaking both the error in the mean (120583) and the standarddeviation (120590) These distributions contain the measurementsof all replications

The objective functions for a given set of metrics andscenarios are combined into a single objective function asfollows

119874 (120579) = 1119873119904 lowast 119873119898sum

119904

sum119898

119878119864norm119904119898 (120579) (11)

where 119878119864norm119904119898(120579) is the value of the objective function ofscenario 119904 and metric 119898 for the parameter set 120579 and 119873119904 and119873119898 are respectively the number of scenarios and metrics inthe set A likelihood method which multiplies probabilitiesmight not work in this case as this method will alwaysattempt to fix the worst parameter first In an additive schemeweights can be applied to prioritize certain combinations ofscenarios and metrics over other combinations However asthis research studies the effects of the different choices ofscenarios and metrics in this research all combinations areconsidered to be of equal importance andhence equalweightsare used

44 Optimization Method In this research a grid search isused to obtain the optimal parameter set as it provides theresearcher with more insight into the shape of the surfaceof objective space The disadvantage of using a grid searchis that other optimization methods eg Greedy and Geneticalgorithms can potentially be faster However thesemethodsdo run the risk of getting stuck in a localminimumanddo notnecessarily give a good insight into the shape of surface of theobjective space As can be derived from (11) smaller valuesof the objective function represent a better goodness-of-fit(GoF) and hence the goal of the optimization is to minimizethe objective value

45 Search Space Definition Rudimentary calibration ofPD has already been performed by the company Thusinstead of calibrating all model parameters the presentedcalibration method will be used in this research to identifythe correctness of the variables with respect to which thismodel is most sensitive namely the relaxation time and theviewing angle Even though the model is less sensitive withrespect to the radius this parameter will also be included inthe calibration as initial tests of the implementation of thescenarios illustrated that in the case of the bidirectional highdensity scenario the default radius of this model producedproblematic results The search space is defined as follows

(i) The upper and lower boundaries of the relaxationtime and viewing angle are determined by a deviationof minus024 lowast 120579def lt 120579 lt 024 lowast 120579def with respect to the


default parameters The step size is 3 of the defaultvalue The resulting ranges are [0380sminus1-0620sminus1]for the relaxation time and [5700∘-9200∘] for theviewing angle

(ii) For the radius the upper boundary is equal to thedefault value the lower bound has a deviation ofminus040lowast120579def and the step size is 4 of the default valueThis results in a range of [014340m-023900m]

As this research focuses on the effect of density levels themetrics that are part of the objective function and movementbase cases the search space is not continuous and has beenrestricted in order to create reasonable computation timesand a reasonably good insight into the shape of the objectivefunction

46 Dealing with Stochasticity in Pedestrian Simulation Mod-els Similar to most pedestrian simulation models PD isstochastic in natureTherefore it is essential to determine theminimum amount of replications one would need in orderto assure that statistical differences are due to differencesin model parameters instead of stochasticity in the modelrealization

In this research the required number of replications isdetermined using a convergence method similar to [30]whereby the distribution of speeds is used as the solemetric To determine if two subsequent distributions can beconsidered to be samples drawn from the same distributionthe Anderson-Darling test is used [24] Equation (12) showsthat if b subsequent distributions are considered to besimilar according to the Anderson-Darling test (ie the testreturn a p-value greater than 119901threshold indicating that thenull hypothesis that the two samples come from the samedistribution can be rejected at the 119901threshold significance level)the distribution has converged

119860119863 (119878119899 119878119899minus1) gt 119901threshold

forall 119899 isin [119898 minus 119887 + 1 119898 minus 119887 + 2 119898] (12)

whereby 119878119899 is the speed distribution containing all instan-taneous speed measurements of all pedestrians for all timesteps they spent within the infrastructure for all 119899 subsequentreplications

Tests showed that regardless of the chosen values for 119887and 119901threshold the required number of replications dependson the exact seeds that are used and their order Thereforea predefined seed set was used during the calibration ofPD to ensure that any differences between simulations usingdifferent parameter sets were not caused by the stochasticnature of the model Using this predefined set a value of10 for 119887 and a value of 025 for 119901threshold it was determinedthat the required number of replications was a 100 forthe bidirectional scenarios 50 for the corner high densityscenarios 40 for the t-junctions and corner low densityscenarios and 30 for the bottleneck scenario For a moredetailed discussion of the method and the choice for thevalues of 119887 and 119901threshold the reader is referred to [25]

5 Calibration Results Based onSingle Objectives

In this section the results of the individual objectives (acombination of a single scenario and a single metric) arediscussed Figures 5(a)ndash5(d) show boxplots of the objectivevalues determined by (11) per individual objective con-taining the objective values of all 3179 points of the searchspace These plots provide insight into the distribution ofthe objective values More importantly these figures showthe order of magnitude of the minimal objective value if themodel would be calibrated using a single metricobjectiveHere smaller objective values represent a better fit of themodel results to the reference data

These plots provide insight into how the objective valuesare distributed but primarily show the order of magnitude ofthe minimal objective value if the model would be calibratedusing only a single objective The smaller the objective valuesthe better the model results fit the reference data By usinga logarithmic scale the figure clearly illustrates how well themodel fits to the data (when the optimal parameter set isused) and how this differs between the different scenarios andmetrics

Figures 5(e)ndash5(j) show boxplots of the nonnormalizednonsquared errors and these provide insight into the size ofthe errors and how they are distributed Here it is the case thecloser to zero the values are the smaller the error between thesimulation and the reference data is Due to the linear scalethese plot provide a better insight into how the value of theparameters influences the error and therefore the objectivevalue

Figures 5(a) and 5(e) show that for all scenarios themodelcan reproduce the flows well given both the small errorsand the low minimal objective values Furthermore one canobserve that on average the lowdensity scenarios have a lowerobjective value but that theminimal objective value is smallerfor the high density scenarios

Figures 5(b) and 5(f) show that the model cannot repro-duce the spatial patterns very well given the high errors andthe large minimal objective values The low density scenariosboth have a lower objective value on average and a lowerminimal objective value Furthermore especially for the highdensity case of the t-junction scenario the performance isrelatively bad compared to the other scenarios

Figures 5(d) 5(h) and 5(j) show that except for thebidirectional high and t-junction high density scenariosthe travel time distribution can be reproduced well by themodel In the case of the bidirectional high and t-junctionhigh density scenarios the figures show that the model canreproduce the mean and the standard deviation of the traveltime distribution well individually but apparently not whenthey are combined Also similar to the spatial distributionthe low density scenarios have a lower objective value onaverage as well as a lower minimum objective value

In the case of the effort metric Figures 5(c) 5(g) and5(i) show that for most scenario the model cannot reproducethe effort distribution very well The two exceptions are thebottleneck and t-junction high density scenarios In thesecases the model can reproduce the effort distributions well


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Figure 5 Results of calibrating the model using a single objective Graphs (a)-(d) show per combination of metric and scenario how theobjective values (calculated according to (11)) are distributed Graphs (e)-(j) show the nonnormalized nonsquared errors (ie119872sim(120579)minus119872ref )which give insight into size and the distribution of the errors The flow scenarios are identified by their acronyms (ie B-H = bidirectionalhigh B-L = bidirectional low B = bottleneck C-H = corner high C-L = corner low T ndashH = T-junction high and T-L = T-junction low)

Generally the same pattern can be observed as the flowregarding the difference between the high and low densityscenarios That is the high density scenarios generally have alower minimum objective value but the low density scenariosgenerally have a lower objective value on average

All figures show that both the size of the minimal objec-tive value and the distribution of the errors depend on the

particular combination of scenario and metric Furthermorethe figure illustrates that the model can generally reproducethe metrics related to the performance of the infrastructure(the flow and travel time) better than those more relatedto the underlying microscopic and macroscopic pedestriandynamics (spatial distribution and the effort) Howeverregarding the difference between the performances of the


model on the different metrics three things have to benoted

Firstly as Liao Zhang Zheng and Zhao [31] show eventhough the flow of their calibrated model is similar to theflow in the data the underlying fundamental diagrams differslightly Regarding the results of this study a quick reviewof the average velocities and average densities illustrates thatdifferences exist between the reference data and the dataobtained during the calibration This finding suggests thatthe model and the data have slightly different underlyingfundamental diagrams Furthermore it also suggests thatwithin the given search space there does not seem to exista parameter set that aligns the modelrsquos fundamental diagramto the data This may in part explain why especially for thespatial distribution and effort metrics the model fit is worsethan compared to the flow

Secondly as pointed out by Benner Kretz Lohmillerand Sukennik [32] also a lack of detailed information aboutthe boundary conditions (eg the exact distribution of thedesired speeds and the order in which pedestrians enter theinfrastructure) might negatively influence a modelrsquos capabil-ity to fit the data Again this lack of detailed information islikely to have the smallest impact on the flow as this is themost aggregated metrics of the four

Lastly some metrics might be more sensitive to changesin parameters of the pedestrian simulationmodel that are nottaken into account in this study than the parameters includedin the search space of the calibration The sensitivity to theselsquootherrsquo parameters is due to two things First the sensitivityanalysis was performed before the choice of metrics for thiscalibration Second the speed distribution was used in thesensitivity analysis to determine significant differences inmodel result Thus this suggests that it is not only importantto include multiple scenarios in the sensitivity analysis butalso multiple metrics This would ensure enhanced insightinto the modelrsquos sensitivity and hence also better insight intowhich are the most important parameters to include in thesearch space during calibration

This research aims to determine how different choicesregarding scenarios andmetrics influence the calibration andnot calibration of the InControl modelTherefore differencesbetween the simulation model results and the data are notinvestigated in more detail in this paper

6 Differences in Performance betweenCalibration Strategies

In this section the results of different calibration strategiesare discussed First a general analysis of the results isperformed based on the obtained optimal parameter setsfor all of the 16 combinations Afterwards the results ofdifferent strategies are compared to determine the influenceof movement base cases density levels and metrics Table 3identifies 16 different calibration strategies whereby the tableindicateswhich scenarios andmetrics are included during thecalibration according to a certain strategy

Table 4 presents the optimal parameter sets for all 16strategies The results in the table show three notable thingsFirstly given the large variance in optimal parameter sets it

is clear that the choice of scenarios and metrics does affectthe results of the calibration Secondly the optimal objectivevalues in Table 4 are notably higher than those found inFigure 5 which indicates that a combination of objectivesdecreases the fit of the model with respect to the data Next tothat for all 16 strategies the optimal viewing angle is smallerthan the default and in many cases equal to the lower limit(57 degrees) Given that PD only takes into account the fourclosest pedestrians the results of the calibration indicate thatit is more important to take those pedestrians into accountwho are in front rather than those who are more to the sideFurthermore in the case of the relaxation time the parametervalue also frequently lies on the boundary of the search spaceDue to time constraints it was not possible to extent the searchspace However an analysis is performed to ascertain thelikely effects changing the search space this includes bothextending it and increasing the precision would have on thelocation of the optimal parameter sets

61 Precision of the Grid Search and the Values on the SearchSpace Boundaries The search space is limited both by itsboundaries and by its precision To obtain insight into thelikelihood that the results would change significantly (ie thelocation of the optimal parameter set changes significantly)an analysis is performed The analysis is based on visualinspection of two types of graphs

Figure 6 provides insight into how likely it is that thelocation of the optimal parameter changes significantly if theprecision of the search space in increased It is consideredlikely that the location of the optimal parameter set canchange significantly if the search space contains points witha very similar objective value compared to the minimalobjective value which are located in a significant differentpart of the search spaceThegraphs show the relation betweenthe decrease in GoF and the distance from the optimalparameter set The decrease in GoF is calculated by (14)whereby a small decrease in the GoF equals a small differencebetween the objective value of a given parameter set and theminimal objective value The distance is calculated by

119863 (120579 120579lowast) = radic119873120591 (120579 120579lowast)2 + 119873120601 (120579 120579lowast)2 + 119873119903 (120579 120579lowast)2 (13)

where 119873120591(120579 120579lowast) 119873120601(120579 120579lowast) and 119873119903(120579 120579lowast) are respectivelythe number of step-sizes between the optimal parameterset 120579lowast and the parameter set 120579 for the relaxation time theviewing angle and the radius So 119873120591(120579 120579lowast) = 2 meansthat the relaxation time of parameter set 120579 is 2 step-sizesremoved from the relaxation time of the optimal parametersetThemaximumdistance is 2474 (radic162 + 162 + 102) whichis the distance between one corner of the search space to theopposite corner of the search space

Figure 6(a) shows that for the bidirectional low case thereare many points that have a fairly similar GoF and that manyof them are in significantly different parts of the search space(ie are at a large distance from the optimal parameter set)Hence it could be likely that a change in the precision of thesearch space would lead to a significant different location ofthe optimal parameter set


Table 3 Tested combination of scenarios and metrics where the acronyms identify the metrics (ie Q = flow SD = spatial distribution Eff= effort and TT = travel time) and the scenarios (ie B-H = bidirectional high B-L = bidirectional low B = bottleneck C-H = corner highC-L = corner low T-H = T-junction high and T-L = T-junction low)

Combination Metrics ScenariosQ SD TT Eff B-H B-L C-H C-L T-H T-L B

1 Bidirectional high (B-H) x x x x x2 Bidirectional low (B-L) x x x x x3 Corner high (C-H) x x x x x4 Corner low (C-L) x x x x x5 T-junction high (T-H) x x x x x6 T-junction low (T-L) x x x x x7 Bottleneck (B) x x x x x8 Flow (Q) x x x x x x x x9 Spatial distribution (SD) x x x x x x x x10 Travel time (TT) x x x x x x x x11 Effort (Eff) x x x x x x x x12 High density scenarios (HD) x x x x x x x x13 Low density scenarios (LD) x x x x x x x14 All scenarios - Macro (Macro) x x x x x x x x x15 All scenarios - Meso (Meso) x x x x x x x x x16 All combined (All) x x x x x x x x x x x

Table 4 Calibration results where 119874(120579) represents the optimal value of the objective function The cells in italic font indicate that the valueis at the upper or lower boundary of the search space

Combination O(120579)[-] Relaxationtime [1s] Viewing angle[degree] Radius[m]

1 Bidirectional high 01329 0620 5700 0152962 Bidirectional low 00588 0620 5700 0191203 Corner high 00561 0395 5700 0239004 Corner low 00742 0380 6150 0239005 T-junction high 01190 0590 5700 0219986 T-junction low 00468 0380 6825 0239007 Bottleneck 01093 0395 6825 0200768 Flow 00146 0380 5925 0200769 Spatial distribution 02015 0575 5925 02198810 Travel time 01814 0620 5925 01529611 Effort 01798 0500 5700 02390012 High density scenarios 02647 0575 5700 02103213 Low density scenarios 00722 0500 5700 02390014 All scenarios - Macro 01444 0545 5925 02198815 All scenarios - Meso 02012 0620 5925 01529616 All combined 01814 0575 5700 021032

Figure 6(b) shows that this is not the case for the bot-tleneck case Figures 6(c) and 6(d) show a few points whoseGoF is similar to that of the optimal point but whose distanceto the optimal point is rather large (see the red rectangles)For these cases it is determined which parameter(s) isarethe main contributor to this large distance In both exampleshere it is found that primarily the viewing angle changes Soin these cases it is likely that even if the precision of the searchspace is increased the location of the optimal parameter set

will not change significantly in relation to both the relaxationtime and the radiusThe location regarding the viewing angleis less certain though

The main conclusion of the visual inspection of thesegraphs for all 16 combinations is that for most of the lowdensity cases the exception is theT-junction low case and theflow case it is likely that the location of the optimal parameterset could change significantly if the precision of the searchspace in increased For all other cases this is not the case


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Figure 6 The deviation from optimal GoF versus the distance to the optimal parameter set

Figure 7 shows how the objective value changes over thesearch space for two examples These graphs provide insightinto the question if it is likely that an extension of the searchspace would cause the optimal parameter to be located in asignificantly different part of the search space in relation tothe parameter whose value is on the search space boundary

For example Figures 7(a)ndash7(c) show no discernible pat-tern Hence one cannot state with a high degree of certaintythat if the search space is extended the relaxation time will beequal to or larger than the current value and that the viewingangle will be equal to or smaller than its current value

Figures 7(d)ndash7(f) on the other hand do show a clearpattern In this case it is likely that an extension of the searchspace will result in an optimal parameter set whose viewingangle is equal to or smaller than the current optimal viewingangle The patterns shown in the graphs also make it likelythat the optimal radius and relaxation time will be fairlysimilar to the current optimal values

Performing this analysis for all 16 combinations yieldsthe conclusion that for all cases where the previous analysisdid conclude that an increase in the precision is unlikelyto change the results an extension of the search space islikely to increase the differences between the cases instead ofdecreasing it

Overall the analysis shows that for some cases the loca-tion of the optimal parameter set could change significantlyif the search space if changed However it also shows thatthe large differences between the optimal parameter setscurrently found are also likely to be found if the search space

is adapted Hence the authors expect that an extension of thesearch space results in even larger differences in the optimalparameter sets than the differences identified in this paper

62 Identification of Differences in Performance betweenCalibration Procedures In order to illustrate the differencesbetween the optimal parameter sets a cross-comparison of thegoodness-of-fit is performed These comparisons are basedon the difference between the optimal GoF of combination Aand the GoF of combination A when the optimal parameterset of combination B is used (see (14))

Δ119866119900119865AB = minus (119874A (120579lowastB) minus 119874A (120579lowastA)) (14)

where 119874A(120579lowastA) is the value of the objective function ofcombination A when its optimal parameter set 120579lowastA is used119874A(120579lowastB) is the value of the objective function of combinationA if the optimal parameter set of combination B is used Asstated in the methodology section an increase in the valueof the objective function equals a decrease in the GoF hencethe minus value equation (14) Thus the larger the decreasein GoF the worse the fit of the model to the data is if thegiven parameter set is used instead of the optimal parameterset In the remainder of this section the effects the choice ofmovement base case the density level andmetrics on theGoFare discussed in more detail

63 Effect of Movement Base Case on Multiple-Objective Cali-bration Results Figure 8 presents the results of a comparison


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Figure 7 Examples of surface plots showing how the objective value changes over the search space The green dot identifies the location ofthe optimal parameter set

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Figure 8 The distribution of the objective values per movement base case combination is displayed by the boxplots The markers indicateper used parameter set how much the objective value would deviate from its optimum if the optimal parameter set obtained using another(combination of) movement base case(s) would be used The combinations are identified by their acronyms as found in Table 3


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allUsed parameter set

Figure 9 The distribution of the objective values per density level combination is displayed by the boxplots The markers indicate perused parameter set how much the objective value would deviate from its optimum if the optimal parameter set obtained using the same(combination of) movement base case(s) but a different density level would be used The combinations are identified by their acronyms asfound in Table 3

between different calibration strategies in which the differ-ence in goodness-of-fit is depicted All comparisons aremadebetween (combinations of) scenarios of the same densitylevel in order to exclude the possibility that differences arecaused by a difference in the level of density and not by adifference in movement base case

The figure shows the distribution of the objective valuesfor the differentmovement base casesThemarkers depict theobjective value if the optimal parameter set obtained usinganother movement base case is used The difference betweenthe location of the marker and the minimal objective valueas indicated by the boxplot indicates the difference in GoF

The boxplots show that generally the low density caseshave a higherGoF and that they are less sensitive to changes inthe parameter set regarding their fit to the data Furthermorefor both the low and high density cases the corner scenariosseem least sensitive to changes in the parameter setThe datamoreover illustrates that in all cases theGoF of the individualmovement base cases decreases when the parameter setbased on another movement base case or a set of movementbase cases is used However the size of the decrease clearlydepends on the scenario as well as which scenariorsquos optimalparameter set is used A few notable observations can bemade regarding the decreases in GoF

Firstly in the case of the high density bidirectionalscenario (B-H) all other optimal parameter sets from theother high density combinations lead to a similar decreasein GoF This is also the case for the low density bidirectionalscenario (B-L) However in this case the optimal parameterset obtained when combining all three low density scenariosresults in a far smaller decrease in GoF indicating that thebidirectional scenario has a strong influence on the objectivefunction of this combination Overall both observationsindicate that the bidirectional movement base case containsbehaviours which are not well captured by other movementbase cases

Secondly the high density t-junction scenario (T-H) alsoseems to contain behaviours which are not captured wellby other high density movement base cases Furthermoreas the decrease of GoF is clearly smallest for the optimalparameter set obtained using a combination of all four highdensity scenarios it is clear that the objective function of thiscombination is strongly influenced by the t-junction scenario

Thirdly in the cases of the low density corner (C-L) andt-junction scenarios (T-H T-L) the decrease in GoF is verysmall when the optimal parameter set of the other scenariois used Table 4 furthermore identifies that the optimalparameter sets for these two scenarios are very similar Thisindicates that at low densities the t-junction movement basecase effectively reduces to a corner movement base case asthe densities are so low that there is probably little mergingbehaviour

Overall based on this analysis we conclude that differentmovement base cases contain different behaviours which arenot necessarily captured when the model is calibrated usingother movement base cases The exceptions are the cornerand t-junction base cases at low densities (C-L T-L) Usingan optimal parameter set obtained by combining multiplemovement base cases mitigates this problem somewhatHowever this still results in clear decreases in the GoF forall movement base cases

64 Effect of Density Level on Multiple-Objective CalibrationResults In Figure 9 the results of the comparison betweenthe GoFrsquos for different density levels are presented The datashows that in all three cases the decrease in the GoF is smallerwhen the optimal parameter set of the high density case isused in the low density case than vice versa However thereare clear differences to be observed between the movementbase cases In the case of the corner movement base casethe level of density does not have a clear effect as using theoptimal parameter set of the other density level only leads to


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]

Predicted combinationUsed parameter set

08

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06

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00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all

Figure 10 The distribution of the objective values per metric combination is displayed by the boxplots The markers indicate per usedparameter set how much the objective value would deviate from its optimum if the optimal parameter set obtained using another(combination of) metrics(s) would be used The combinations are identified by their acronyms as found in Table 3

a very small decrease in the GoF This is also the case whenthe optimal parameter set of the high density bidirectionalscenario is used for the low density bidirectional scenarioHowever vice versa it is not the case For the t-junctionscenarios the figure clearly shows that in both cases using theoptimal parameter set of the other density level results in alarge decrease in the GoF

The data also illustrates that the decrease in GoF of thecombination of high density scenarios is larger when theoptimal parameter set of the combination of low densityis used than vice versa This remains the case even if thebottleneck scenario is omitted from the high density set suchthat the high density set contains exactly the samemovementbase case as the low density set In this case the decrease inGoF for the high density set becomes even larger

Overall it can be concluded that the level of density of thescenario does influence the calibration resultsTherefore it isconcluded that it is more important to include the high den-sity scenarios than the low density scenarios Furthermoredepending on themovement base case it can even be the casethat the low density variant can be omitted as it will not addany value

65 Effect of the Metrics on the Multiple-Objective CalibrationResults In Figure 10 a comparison is visualised between theinfluences of the different parameter sets on the performanceof the metrics There seems to be a correlation between thedistribution of the effort and the spatial distribution (ieSD Eff Meso and all) When the model is calibrated usingonly one of them the decrease in the GoF of the other issmall Besides that both the use of the spatial distributionand the use of the distribution of the effort result in a farworse prediction of the flow compared to the distributionof the travel times That is the decrease in GoF of theflow is far larger in case the optimal parameter set of thespatial distribution or the use of the distribution of theeffort is used Lastly the optimal parameter sets obtainedusing combinations of metrics are more heavily influenced

by certain metrics When only the macroscopic metrics areapplied the spatial distribution clearly has a larger impacton the location of the optimal parameter set given thelower decrease in GoF When solely using the mesoscopicmetrics the distribution of the travel time has a larger impactcompared to the distribution of the effort

These results show that the choice of metrics doesinfluence the results of the calibration Depending on thechoice of metric or combination of metrics different optimalparameter sets are found which in turn lead to differentresults regarding the GoF

7 Conclusions Discussion andImplications for Practice

The findings of this research regarding the influence of themovement base cases are found to be consistent with both[13 14] Similar to those studies this research finds that (1)it is necessary to use multiple movement base cases whencalibrating a model to capture all relevant behaviours and(2) the GoF of the individual movement base cases decreaseswhen the parameter set based on multiple movement basecases is used

Hence this research confirms that one needs to usemultiple movement base cases when calibrating a modelintended for general usage However when the intendeduse of the model is more limited (ie it does not need toaccurately replicate all movement base cases and or metrics)it might be preferred to use a limited set of movement basecases during the calibration in particular given the fact thatthe GoF of the individual movement base case decreaseswhen multiple movement base cases are used during thecalibration

The level of density also influences the calibration resultsThus depending on the intended use of the model differentdensity levels should be taken into account during thecalibration Furthermore this study concludes that it is more


important to incorporate high density scenarios As a resultone can omit some of low density scenarios in particular thebidirectional and corner low density scenarios

This study also finds that the calibration results depend onthe choice of metric or combinations of metrics Dependingon the combination of metrics also the choice of objectivefunction and normalization method influences the resultsConsequently depending on the usage of the model oneshould decide which metric or metrics are most importantand how to reflect the difference in importance of thesemetrics when combining multiple objectives into one

The results also show that the relaxation time is the onlyparameter to which the model is sensitive to in all scenariosIts exact value thus has a large impact on how well thesimulations fit the data Reference [33] found similar resultsfor a different model though they only studied a bottleneckFurthermore it is also the only parameter where the optimalvalue can lie on both sides of the search space dependingon the used combination of scenarios and metrics This canpossibly be explained by the fact that the relaxation parameterhas multiple roles as is described in [34] As Johansson etal [34] conclude this indicates that the models may be toosimplistic

A number of things have to be noted when reflecting onthe method of handling the multiple objectives In light ofthe goal of this study the method presented in this study waschosen to assure as little as possible bias towards any of themetrics or scenarios However if one calibrates amodel givena certain type ofmodel usage onemight use different weightsor even different optimization method For example onecan search for the Pareto optimal solution [29] or combinemultiple objectives using the 120598-constraint method [29] Boththe choice of the optimization method and its influence onthe calibration results are relevant topics for future research

Though this study is more extensive than previousstudies it still has a number of limitations Firstly dueto limitations of the available dataset this study did notinclude a crossing movement base case So it is unclearwhether and to what extent the crossing movement basecase contains behaviours which are not captured by othermovement base cases More research in which also effects ofthe intersecting movement base cases are included is neededto create a comprehensive overview of the effect the choice ofmovement base cases has on the calibration Secondly onlyone microscopic model was used in this study Therefore assuch it is unclear to what extent the current findings can begeneralized and whether the conclusions of this study alsohold for other microscopic models The fact that the resultsare consistent with [13 14] and the fact that these studiesused another microscopic model does indicate that this isthe case Lastly as already reflected upon this study did notlook into the effects of the chosen calibration methodologyInsights into these effects could be relevant when deciding onthe calibration methodology for a microscopic model with acertain intended use

All in all the results show two important things Firstlythe optimal parameter set obtained using a single or limitedamount of objectives does not always provide an accurate fitof the model to the data for other combinations of scenarios

and metrics Besides that using multiple objectives (egusing multiple high density scenarios) to calibrate the modeldecreases the GoF of the model to the data for all theindividual objectives These two conclusions imply that theintended use of the model should be taken into accountwhen deciding which scenarios metrics objective functionsand method for combining multiple objectives one shoulduse These results also raise an important question Is theimplicit assumption that the behaviour of the pedestrians isindependent of the flow situation which is at the foundationof most pedestrian simulation models valid This researchcannot answer this question because of among other itslimitations on the number of parameters included in thesearch space Hence it is an interesting topic for futureresearch

Lastly these results show that a model only providesaccurate results for scenarios and metrics that the modelhas been calibrated and validated on Using the model forpredictions of other scenarios and metrics is likely to resultin large inaccuracies Hence it is essential that calibration orvalidation attempts include multiple scenarios and multiplemetrics

Data Availability

The empirical data used in this study can be found at httppedfz-juelichdeda

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

The research presented in this paper is part of the researchprogram ldquoAllegro Unravelling slow mode traveling andtraffic with innovative data to a new transportation andtraffic theory for pedestrians and bicyclesrdquo (ERC GrantAgreement no 669792) a Horizon 2020 project which isfunded by the European Research Council Additionally theresearch presented in this paper has been presented at theTransportation Research Board 97th Annual Meeting (2018Washington DC United States)

References

[1] C Rudloff T Matyus S Seer and D Bauer ldquoCan walkingbehavior be predicted Analysis of calibration and fit of pedes-trian modelsrdquo Transportation Research Record no 2264 pp101ndash109 2011

[2] S Seer N Brandle andC Ratti ldquoKinects and human kinetics Anew approach for studying pedestrian behaviorrdquo Transporta-tion Research Part C Emerging Technologies vol 48 pp 212ndash228 2014

[3] A Abdelghany K Abdelghany and H Mahmassani ldquoA hybridsimulation-assignmentmodeling framework for crowd dynam-ics in large-scale pedestrian facilitiesrdquo Transportation ResearchPart A Policy and Practice vol 86 pp 159ndash176 2016


[4] J L Berrou J Beecham P Quaglia M A Kagarlis and AGerodimos ldquoCalibration and validation of the legion simula-tion model using empirical datardquo in Pedestrian and evacuationdynamics 2005 N Waldau P Gattermann H Knoflacher andM Schreckenberg Eds pp 167ndash181 2007

[5] M Davidich and G Koster ldquoPredicting pedestrian flow Amethodology and a proof of concept based on real-life datardquoPLoS ONE vol 8 no 12 Article ID e83355 2013

[6] W Klein G Koster and A Meister ldquoTowards the calibration ofpedestrian stream modelsrdquo in Proceedings of the Internationalconference on parallel processing and applied mathematics RWyrzykowski J Dongarra K Karczewski and J WasniewskiEds pp 521ndash528 2010

[7] R Lovreglio E Ronchi and D Nilsson ldquoCalibrating floorfield cellular automaton models for pedestrian dynamics byusing likelihood function optimizationrdquo Physica A StatisticalMechanics and its Applications vol 438 pp 308ndash320 2015

[8] T Robin G Antonini M Bierlaire and J Cruz ldquoSpecificationestimation and validation of a pedestrian walking behaviormodelrdquo Transportation Research Part B Methodological vol 43no 1 pp 36ndash56 2009

[9] A Schadschneider C Eilhardt SNowak andRWill ldquoTowardsa calibration of the floor field cellular automatonrdquo in Pedestrianand evacuation dynamics pp 557ndash566 2011

[10] M Davidich and G Koster ldquoTowards automatic and robustadjustment of human behavioral parameters in a pedestrianstream model to measured datardquo Safety Science vol 50 no 5pp 1253ndash1260 2012

[11] M C Campanella S P Hoogendoorn and W DaamenldquoImproving the nomad microscopic walker modelrdquo IFAC Pro-ceedings Volumes vol 42 no 15 pp 12ndash18 2009

[12] S P Hoogendoorn and W Daamen ldquoMicroscopic calibrationand validation of pedestrian models Cross-comparison ofmodels using experimental datardquo inTraffic and granular flowrsquo05A Schadschneider T Poschel R Kuhne M Schreckenbergand D E Wolf Eds pp 329ndash340 Springer Berlin Germany2007

[13] M C Campanella S P Hoogendoorn and W DaamenldquoA methodology to calibrate pedestrian walker models usingmultiple-objectivesrdquo in Pedestrian and evacuation dynamics pp755ndash759 2011

[14] D C Duives Analysis and modelling of pedestrian movementdynamics at large-scale events [Doctoral thesis] 2016

[15] A Duret C Buisson and N Chiabaut ldquoEstimating individualspeed-spacing relationship and assessing ability of newellrsquoscar-following model to reproduce trajectoriesrdquo TransportationResearch Record no 2088 pp 188ndash197 2008

[16] S Ossen and S P Hoogendoorn ldquoValidity of trajectory-basedcalibration approach of car-following models in presence ofmeasurement errorsrdquoTransportation Research Record no 2088pp 117ndash125 2008

[17] V Punzo B Ciuffo and M Montanino ldquoCan results ofcar-following model calibration based on trajectory data betrustedrdquo Journal of the Transportation Research Board vol 2315pp 11ndash24 2012

[18] D Wolinski S J Guy A-H Olivier M Lin D Manocha andJ Pettre ldquoParameter estimation and comparative evaluation ofcrowd simulationsrdquoComputerGraphics Forum vol 33 no 2 pp303ndash312 2014

[19] F S Hanseler M Bierlaire B Farooq and T MuhlematterldquoA macroscopic loading model for time- varying pedestrian

flows in public walking areasrdquo Transportation Research Part BMethodological vol 69 pp 60ndash80 2014

[20] M Ko T Kim and K Sohn ldquoCalibrating a social-force-based pedestrian walkingmodel based onmaximum likelihoodestimationrdquo Transportation vol 40 no 1 pp 91ndash107 2013

[21] M C Campanella S Hoogendoorn and W Daamen ldquoQuan-titative and qualitative validation procedure for general useof pedestrian modelsrdquo in Pedestrian and evacuation dynamics2012 U Weidmann U Kirsch andM Schreckenberg Eds pp891ndash905 2014

[22] M Moussaid D Helbing and G Theraulaz ldquoHow simplerules determine pedestrian behavior and crowd disastersrdquoProceedings of the National Acadamy of Sciences of the UnitedStates of America vol 108 no 17 pp 6884ndash6888 2011

[23] I Karamouzas R Geraerts and M Overmars ldquoIndicativeroutes for path planning and crowd simulationrdquo in Proceedingsof the 4th International Conference on the Foundations of DigitalGames ICFDG 2009 pp 113ndash120 USA April 2009

[24] T W Anderson and D A Darling ldquoAsymptotic theory ofcertain ldquogoodness of fitrdquo criteria based on stochastic processesrdquoAnnals of Mathematical Statistics vol 23 no 2 pp 193ndash2121952

[25] M Sparnaaij How to calibrate a pedestrian simulation model[MasterrsquosThesis] 2017 httpsrepositorytudelftnlislandorasearchcollection=education

[26] W Daamen Modelling Passenger Flows in Public TransportFacilities 2004 httpresolvertudelftnluuide65fb66c-1e55-4e63-8c49-5199d40f60e1

[27] C Keip and K Ries Dokumentation Von Versuchen Zur Per-sonenstromdynamik - Projekt rdquoHermesldquo Ber- gische UniversitatWuppertal 2009 httppedfz-juelichdeexperiments20090512Duesseldorf Messe HermesdocuVersuchsdokumentationHERMESpdf

[28] S C Wong W L Leung S H Chan et al ldquoBidirectionalpedestrian stream model with oblique intersecting anglerdquoJournal of Transportation Engineering vol 136 no 3 pp 234ndash242 2010

[29] S H Zak and E K P Chong ldquoMultiobjective optimizationrdquo inAn Introduction to Optimization vol 24 pp 577ndash598 2013

[30] E Ronchi E D Kuligowski P A Reneke R D Peacock and DNilsson ldquoThe process of verification and validation of buildingfire evacuationmodelsrdquo Technical Note (NIST TN) - 1822 2013

[31] W Liao J Zhang X Zheng and Y Zhao ldquoA generalized vali-dation procedure for pedestrian modelsrdquo Simulation ModellingPractice andTheory vol 77 pp 20ndash31 2017

[32] H Benner T Kretz J Lohmiller and P Sukennik ldquoIs calibrationa straight-forward task if detailed trajectory data is availablerdquoin Transportation Research Board 96th Annual Meeting 2017

[33] M Haghani and M Sarvi ldquoSimulating pedestrian flow throughnarrow exitsrdquo Physics Letters A vol 383 no 2 pp 110ndash120 2019

[34] F Johansson D Duives W Daamen and S HoogendoornldquoThe many roles of the relaxation time parameter in forcebased models of pedestrian dynamicsrdquo Transportation ResearchProcedia pp 300ndash308 2014

International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom


illustrate that different combinations ofmetrics clearly lead todifferent calibration results Wolinski et al [18] also calibratea number of models using different metrics Though theydo not show the effect of using different metrics on theresulting optimal parameter set the results show clearlythat the model fit to the data depends on the metric usedFurthermore Hanseler Bierlaire Farooq and Muhlematter[19] also note differences between the optimal parameter setsobtained using different metrics or a combination of themwhen calibrating their macroscopic model

To overcome the problem of obtaining different resultswhen using different movement base cases andor metricsthree multiple-objective calibration frameworks have beenproposed in recent years which try to take a more inclusiveapproachWolinski et al [18] propose a frameworkwhich canpotentially incorporate multiple objectives However duringtheir benchmarking tests they only apply combinations ofone movement base case and one metric Campanella et al[13] show how a microscopic model can be calibrated usingmultiple movement base cases and how this compares tocalibrating the model with only one movement base caseThis study still only uses one metric during the calibrationThe work by Duives [14] uses multiple movement base caseswith multiple metrics and furthermore includes differentcombinations of weights in the objective function and isthus the most extensive of the three However except for thespatial distributionmetric the study does not show the resultsfor the other individual metrics Hence it is not possible toexactly determine the effect the different individual metricshave on the resulting optimal parameter set

So even though these works illustrate that the choice ofthe combinations of movement bases and metrics will influ-ence the optimal parameter set obtained during calibrationall three studies have their limitations For example they donot explicitly examine the effect of the level of density whichmight be a relevant factor given that work by Campanellaet al [13] shows that poorness of data can affect calibrationresults and work by [20] also shows some differences inthe obtained parameter sets for a low and high density caseof a bidirectional flow Furthermore the effects of usingdifferent metrics are also still poorly understood And aswork by Campanella Hoogendoorn and Daamen [21] showsthat using multiple objectives during the calibration willlead to a better validation score for general usage it is clearthat increased insights into which objectives to use duringcalibration can improve model validity

Given these observations the objective of this researchis twofold Firstly the objective is to determine the effectof the choice of movement base cases metrics and densitylevels on the calibration results Secondly the objective is todevelop a multiple-objective calibration method for pedes-trian simulation models to determine the aforementionedeffects taking into account the stochastic nature common tomany microscopic pedestrian models

This study aims to add value to the current body ofliterature by means of a more extensive study of the impactof calibration framework setup on the validity of a pedestriansimulation model This extension provides among otherthings novel insights into the effect of the level of density of

the movement base case and more detailed insights into theeffect of using a range of metrics in the calibration processFurthermore this study features a different type ofmodel (ievision-based model [22]) than the previous most extensivestudies (ie [13 14]) which both calibrated NOMAD Thusthis study also illustrates the replicability of their results andthe conclusions of those previous studies

The rest of the paper is organized as follows Sec-tion 2 briefly describes themicroscopic pedestrian simulationmodel Section 3 shortly introduces the methodology of thesensitivity analysis and presents the results of the analysisIn Section 4 the calibration methodology is elaborated uponThis is followed by the presentation of the results of calibrat-ing the model using a single objective in Section 5 Section 6presents the results of the multiobjective calibration Finallythis paper closes of with a discussion of the results conclu-sions and the implications of this work for practice

2 Brief Introduction to Pedestrian Dynamics

This section introduces pedestrian dynamics (PD) a micro-scopic pedestrian simulation model developed by INCON-TROL Simulation Solutions It offers a user the abilityto model the movement behaviour of pedestrians at allthree behavioural levels (strategic tactical and operational)Though in this research pedestrians only have one activitynamely to walk from their origin to their destination via asingle route and hence there is no need to model the activitychoice the activity scheduling or the route choiceThemodelfeaturing the operational walking dynamics is discussed inmore detail underneath

The operational behaviour of the INCONTROL modelconsists of two parts ie route following and collisionavoidance which together determine the acceleration of apedestrian at every time step PD determines the accelerationof a pedestrian by the combination of lsquosocial forcesrsquo and adesired velocity component The pedestrian itself is repre-sented by a circle with a radius 119903 At every time step theacceleration of a pedestrian is determined as follows

119889997888rarrV 119894119889119905 = 997888rarrV des119894 minus 997888rarrV 119894120591 + sum119895

997888rarr119891 119894119895 + sum119882

997888rarr119891 119894119882 [ms2] (1)

where 997888rarrV des119894 and997888rarrV 119894 are respectively the desired and current

velocity of pedestrian 119894 997888rarr119891 119894119895 and 997888rarr119891 119894119882 are the physical forcesthat occur on contact with another pedestrian or a staticobstacle And lastly 120591 is the relaxation time Furthermorein case the speed of the pedestrian drops below a certainthreshold (ie the minimal desired speed parameter) thepedestrian does not move until the next time step when theresulting speed is higher than the threshold

The desired velocity is determined according to themethod proposed by Moussaıd et al [22] The method usesa vision-based approach to avoid collisions This approachcombines the collision avoidance with the preferred speedand the desired destination to determine the desired velocityThedesired velocity is determined bymeans of two heuristicsnamely







119889ℎ =




[m] (3)
















compared to default

Yes


parameter

Curve describing

model sensitivity
















minus20

0

20

40

60D

iffer

ence

com

pare

d to

def

ault

[]





minus20

0

20

40

60

Diff

eren

ce co

mpa

red

to d

efau

lt [

]






minus10

0

10

20

Diff

eren

ce co

mpa

red

to d

efau

lt [

]





minus10

0

10

20

Diff

eren

ce co

mpa

red

to d

efau

lt [

]











Multiple objectives

Single objective


Validation

If not optimal

If optimal

Referencedata

Simulation model

S1

S2

Sn

E

Ei

Ei = [1 2 k]

E = [E1 E2 En]

1

2

k

M1

M2

Mk

darr

Si






119902119894 = 119873119894Δ119905 times 119897 [pedsm] (4)




8m

36m

(a)24m 32m

24m

32m

(b)

24m

32m

2m2m 24m(c)

36m

9m 4m1m(d)



119865119895 = 119873occ119895










(7)

V119909 (119905) = 119909 (119905) minus 119909 (119905 minus 1)Δ119905 [ms]

V119910 (119905) = 119910 (119905) minus 119910 (119905 minus 1)Δ119905 [ms]

(8)








119878119864norm (120579) = 1119898sum119895

(sum119894119872sim119894119895 (120579) 119899 minus 119872ref 119895

119872norm)2

(9)


119872norm120583)2


)2

(10)



119874 (120579) = 1119873119904 lowast 119873119898sum

119904

sum119898

119878119864norm119904119898 (120579) (11)
























B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(a) Flow

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]


B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(c) Travel time

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(d) Effort

B-H

B-L

C-H

C-L

T-H

T-L B

minus10

minus05

00

05

10

Erro

r [pe

ds

m]

(e) Flow

B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [-]

022502000175015001250100007500500025


B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [s

m]

050

075

025

000

minus025

minus050

minus075

minus100


HB-

LC-

HC-

LT-

HT-

L B

minus002

000

002

004

006

Erro

r [m

s]

(h) Effort-mean

B-H

B-L

C-H

C-L

T-H

T-L B

minus04

minus02

00

02

04

Erro

r [s

m]

(i) Travel time-std

B-H

B-L

C-H

C-L

T-H

T-L B

minus0005

0000

0005

0010

Erro

r [m

s]

(j) Effort-std































20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(b) Bottleneck

20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(d) Travel time













060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

10

08

06

04

02

00O

bjec

tive v

alue

[-]

[1

s]

(a) 120601 = 5700

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(b) 120601 = 7500

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(c) 120601 = 9300

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(d) 120601 = 5700

T-ju

nctio

n hi

gh

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

060

055

050

045

040

015 020

r [m]

[1

s]

(e) 120601 = 7500

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(f) 120601 = 9300


10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]


B-H

C-H

T-H B

B-L

C-L

T-L


HDLD all

Used parameter set



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








119889ℎ =




[m] (3)
















compared to default

Yes


parameter

Curve describing

model sensitivity
















minus20

0

20

40

60D

iffer

ence

com

pare

d to

def

ault

[]





minus20

0

20

40

60

Diff

eren

ce co

mpa

red

to d

efau

lt [

]






minus10

0

10

20

Diff

eren

ce co

mpa

red

to d

efau

lt [

]





minus10

0

10

20

Diff

eren

ce co

mpa

red

to d

efau

lt [

]











Multiple objectives

Single objective


Validation

If not optimal

If optimal

Referencedata

Simulation model

S1

S2

Sn

E

Ei

Ei = [1 2 k]

E = [E1 E2 En]

1

2

k

M1

M2

Mk

darr

Si






119902119894 = 119873119894Δ119905 times 119897 [pedsm] (4)




8m

36m

(a)24m 32m

24m

32m

(b)

24m

32m

2m2m 24m(c)

36m

9m 4m1m(d)



119865119895 = 119873occ119895










(7)

V119909 (119905) = 119909 (119905) minus 119909 (119905 minus 1)Δ119905 [ms]

V119910 (119905) = 119910 (119905) minus 119910 (119905 minus 1)Δ119905 [ms]

(8)








119878119864norm (120579) = 1119898sum119895

(sum119894119872sim119894119895 (120579) 119899 minus 119872ref 119895

119872norm)2

(9)


119872norm120583)2


)2

(10)



119874 (120579) = 1119873119904 lowast 119873119898sum

119904

sum119898

119878119864norm119904119898 (120579) (11)
























B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(a) Flow

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]


B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(c) Travel time

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(d) Effort

B-H

B-L

C-H

C-L

T-H

T-L B

minus10

minus05

00

05

10

Erro

r [pe

ds

m]

(e) Flow

B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [-]

022502000175015001250100007500500025


B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [s

m]

050

075

025

000

minus025

minus050

minus075

minus100


HB-

LC-

HC-

LT-

HT-

L B

minus002

000

002

004

006

Erro

r [m

s]

(h) Effort-mean

B-H

B-L

C-H

C-L

T-H

T-L B

minus04

minus02

00

02

04

Erro

r [s

m]

(i) Travel time-std

B-H

B-L

C-H

C-L

T-H

T-L B

minus0005

0000

0005

0010

Erro

r [m

s]

(j) Effort-std































20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(b) Bottleneck

20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(d) Travel time













060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

10

08

06

04

02

00O

bjec

tive v

alue

[-]

[1

s]

(a) 120601 = 5700

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(b) 120601 = 7500

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(c) 120601 = 9300

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(d) 120601 = 5700

T-ju

nctio

n hi

gh

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

060

055

050

045

040

015 020

r [m]

[1

s]

(e) 120601 = 7500

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(f) 120601 = 9300


10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]


B-H

C-H

T-H B

B-L

C-L

T-L


HDLD all

Used parameter set



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







compared to default

Yes


parameter

Curve describing

model sensitivity
















minus20

0

20

40

60D

iffer

ence

com

pare

d to

def

ault

[]





minus20

0

20

40

60

Diff

eren

ce co

mpa

red

to d

efau

lt [

]






minus10

0

10

20

Diff

eren

ce co

mpa

red

to d

efau

lt [

]





minus10

0

10

20

Diff

eren

ce co

mpa

red

to d

efau

lt [

]











Multiple objectives

Single objective


Validation

If not optimal

If optimal

Referencedata

Simulation model

S1

S2

Sn

E

Ei

Ei = [1 2 k]

E = [E1 E2 En]

1

2

k

M1

M2

Mk

darr

Si






119902119894 = 119873119894Δ119905 times 119897 [pedsm] (4)




8m

36m

(a)24m 32m

24m

32m

(b)

24m

32m

2m2m 24m(c)

36m

9m 4m1m(d)



119865119895 = 119873occ119895










(7)

V119909 (119905) = 119909 (119905) minus 119909 (119905 minus 1)Δ119905 [ms]

V119910 (119905) = 119910 (119905) minus 119910 (119905 minus 1)Δ119905 [ms]

(8)








119878119864norm (120579) = 1119898sum119895

(sum119894119872sim119894119895 (120579) 119899 minus 119872ref 119895

119872norm)2

(9)


119872norm120583)2


)2

(10)



119874 (120579) = 1119873119904 lowast 119873119898sum

119904

sum119898

119878119864norm119904119898 (120579) (11)
























B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(a) Flow

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]


B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(c) Travel time

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(d) Effort

B-H

B-L

C-H

C-L

T-H

T-L B

minus10

minus05

00

05

10

Erro

r [pe

ds

m]

(e) Flow

B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [-]

022502000175015001250100007500500025


B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [s

m]

050

075

025

000

minus025

minus050

minus075

minus100


HB-

LC-

HC-

LT-

HT-

L B

minus002

000

002

004

006

Erro

r [m

s]

(h) Effort-mean

B-H

B-L

C-H

C-L

T-H

T-L B

minus04

minus02

00

02

04

Erro

r [s

m]

(i) Travel time-std

B-H

B-L

C-H

C-L

T-H

T-L B

minus0005

0000

0005

0010

Erro

r [m

s]

(j) Effort-std































20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(b) Bottleneck

20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(d) Travel time













060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

10

08

06

04

02

00O

bjec

tive v

alue

[-]

[1

s]

(a) 120601 = 5700

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(b) 120601 = 7500

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(c) 120601 = 9300

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(d) 120601 = 5700

T-ju

nctio

n hi

gh

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

060

055

050

045

040

015 020

r [m]

[1

s]

(e) 120601 = 7500

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(f) 120601 = 9300


10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]


B-H

C-H

T-H B

B-L

C-L

T-L


HDLD all

Used parameter set



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



minus20

0

20

40

60D

iffer

ence

com

pare

d to

def

ault

[]





minus20

0

20

40

60

Diff

eren

ce co

mpa

red

to d

efau

lt [

]






minus10

0

10

20

Diff

eren

ce co

mpa

red

to d

efau

lt [

]





minus10

0

10

20

Diff

eren

ce co

mpa

red

to d

efau

lt [

]











Multiple objectives

Single objective


Validation

If not optimal

If optimal

Referencedata

Simulation model

S1

S2

Sn

E

Ei

Ei = [1 2 k]

E = [E1 E2 En]

1

2

k

M1

M2

Mk

darr

Si






119902119894 = 119873119894Δ119905 times 119897 [pedsm] (4)




8m

36m

(a)24m 32m

24m

32m

(b)

24m

32m

2m2m 24m(c)

36m

9m 4m1m(d)



119865119895 = 119873occ119895










(7)

V119909 (119905) = 119909 (119905) minus 119909 (119905 minus 1)Δ119905 [ms]

V119910 (119905) = 119910 (119905) minus 119910 (119905 minus 1)Δ119905 [ms]

(8)








119878119864norm (120579) = 1119898sum119895

(sum119894119872sim119894119895 (120579) 119899 minus 119872ref 119895

119872norm)2

(9)


119872norm120583)2


)2

(10)



119874 (120579) = 1119873119904 lowast 119873119898sum

119904

sum119898

119878119864norm119904119898 (120579) (11)
























B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(a) Flow

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]


B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(c) Travel time

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(d) Effort

B-H

B-L

C-H

C-L

T-H

T-L B

minus10

minus05

00

05

10

Erro

r [pe

ds

m]

(e) Flow

B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [-]

022502000175015001250100007500500025


B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [s

m]

050

075

025

000

minus025

minus050

minus075

minus100


HB-

LC-

HC-

LT-

HT-

L B

minus002

000

002

004

006

Erro

r [m

s]

(h) Effort-mean

B-H

B-L

C-H

C-L

T-H

T-L B

minus04

minus02

00

02

04

Erro

r [s

m]

(i) Travel time-std

B-H

B-L

C-H

C-L

T-H

T-L B

minus0005

0000

0005

0010

Erro

r [m

s]

(j) Effort-std































20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(b) Bottleneck

20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(d) Travel time













060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

10

08

06

04

02

00O

bjec

tive v

alue

[-]

[1

s]

(a) 120601 = 5700

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(b) 120601 = 7500

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(c) 120601 = 9300

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(d) 120601 = 5700

T-ju

nctio

n hi

gh

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

060

055

050

045

040

015 020

r [m]

[1

s]

(e) 120601 = 7500

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(f) 120601 = 9300


10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]


B-H

C-H

T-H B

B-L

C-L

T-L


HDLD all

Used parameter set



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Multiple objectives

Single objective


Validation

If not optimal

If optimal

Referencedata

Simulation model

S1

S2

Sn

E

Ei

Ei = [1 2 k]

E = [E1 E2 En]

1

2

k

M1

M2

Mk

darr

Si






119902119894 = 119873119894Δ119905 times 119897 [pedsm] (4)




8m

36m

(a)24m 32m

24m

32m

(b)

24m

32m

2m2m 24m(c)

36m

9m 4m1m(d)



119865119895 = 119873occ119895










(7)

V119909 (119905) = 119909 (119905) minus 119909 (119905 minus 1)Δ119905 [ms]

V119910 (119905) = 119910 (119905) minus 119910 (119905 minus 1)Δ119905 [ms]

(8)








119878119864norm (120579) = 1119898sum119895

(sum119894119872sim119894119895 (120579) 119899 minus 119872ref 119895

119872norm)2

(9)


119872norm120583)2


)2

(10)



119874 (120579) = 1119873119904 lowast 119873119898sum

119904

sum119898

119878119864norm119904119898 (120579) (11)
























B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(a) Flow

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]


B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(c) Travel time

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(d) Effort

B-H

B-L

C-H

C-L

T-H

T-L B

minus10

minus05

00

05

10

Erro

r [pe

ds

m]

(e) Flow

B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [-]

022502000175015001250100007500500025


B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [s

m]

050

075

025

000

minus025

minus050

minus075

minus100


HB-

LC-

HC-

LT-

HT-

L B

minus002

000

002

004

006

Erro

r [m

s]

(h) Effort-mean

B-H

B-L

C-H

C-L

T-H

T-L B

minus04

minus02

00

02

04

Erro

r [s

m]

(i) Travel time-std

B-H

B-L

C-H

C-L

T-H

T-L B

minus0005

0000

0005

0010

Erro

r [m

s]

(j) Effort-std































20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(b) Bottleneck

20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(d) Travel time













060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

10

08

06

04

02

00O

bjec

tive v

alue

[-]

[1

s]

(a) 120601 = 5700

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(b) 120601 = 7500

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(c) 120601 = 9300

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(d) 120601 = 5700

T-ju

nctio

n hi

gh

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

060

055

050

045

040

015 020

r [m]

[1

s]

(e) 120601 = 7500

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(f) 120601 = 9300


10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]


B-H

C-H

T-H B

B-L

C-L

T-L


HDLD all

Used parameter set



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



8m

36m

(a)24m 32m

24m

32m

(b)

24m

32m

2m2m 24m(c)

36m

9m 4m1m(d)



119865119895 = 119873occ119895










(7)

V119909 (119905) = 119909 (119905) minus 119909 (119905 minus 1)Δ119905 [ms]

V119910 (119905) = 119910 (119905) minus 119910 (119905 minus 1)Δ119905 [ms]

(8)








119878119864norm (120579) = 1119898sum119895

(sum119894119872sim119894119895 (120579) 119899 minus 119872ref 119895

119872norm)2

(9)


119872norm120583)2


)2

(10)



119874 (120579) = 1119873119904 lowast 119873119898sum

119904

sum119898

119878119864norm119904119898 (120579) (11)
























B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(a) Flow

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]


B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(c) Travel time

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(d) Effort

B-H

B-L

C-H

C-L

T-H

T-L B

minus10

minus05

00

05

10

Erro

r [pe

ds

m]

(e) Flow

B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [-]

022502000175015001250100007500500025


B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [s

m]

050

075

025

000

minus025

minus050

minus075

minus100


HB-

LC-

HC-

LT-

HT-

L B

minus002

000

002

004

006

Erro

r [m

s]

(h) Effort-mean

B-H

B-L

C-H

C-L

T-H

T-L B

minus04

minus02

00

02

04

Erro

r [s

m]

(i) Travel time-std

B-H

B-L

C-H

C-L

T-H

T-L B

minus0005

0000

0005

0010

Erro

r [m

s]

(j) Effort-std































20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(b) Bottleneck

20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(d) Travel time













060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

10

08

06

04

02

00O

bjec

tive v

alue

[-]

[1

s]

(a) 120601 = 5700

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(b) 120601 = 7500

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(c) 120601 = 9300

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(d) 120601 = 5700

T-ju

nctio

n hi

gh

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

060

055

050

045

040

015 020

r [m]

[1

s]

(e) 120601 = 7500

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(f) 120601 = 9300


10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]


B-H

C-H

T-H B

B-L

C-L

T-L


HDLD all

Used parameter set



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









119878119864norm (120579) = 1119898sum119895

(sum119894119872sim119894119895 (120579) 119899 minus 119872ref 119895

119872norm)2

(9)


119872norm120583)2


)2

(10)



119874 (120579) = 1119873119904 lowast 119873119898sum

119904

sum119898

119878119864norm119904119898 (120579) (11)
























B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(a) Flow

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]


B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(c) Travel time

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(d) Effort

B-H

B-L

C-H

C-L

T-H

T-L B

minus10

minus05

00

05

10

Erro

r [pe

ds

m]

(e) Flow

B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [-]

022502000175015001250100007500500025


B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [s

m]

050

075

025

000

minus025

minus050

minus075

minus100


HB-

LC-

HC-

LT-

HT-

L B

minus002

000

002

004

006

Erro

r [m

s]

(h) Effort-mean

B-H

B-L

C-H

C-L

T-H

T-L B

minus04

minus02

00

02

04

Erro

r [s

m]

(i) Travel time-std

B-H

B-L

C-H

C-L

T-H

T-L B

minus0005

0000

0005

0010

Erro

r [m

s]

(j) Effort-std































20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(b) Bottleneck

20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(d) Travel time













060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

10

08

06

04

02

00O

bjec

tive v

alue

[-]

[1

s]

(a) 120601 = 5700

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(b) 120601 = 7500

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(c) 120601 = 9300

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(d) 120601 = 5700

T-ju

nctio

n hi

gh

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

060

055

050

045

040

015 020

r [m]

[1

s]

(e) 120601 = 7500

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(f) 120601 = 9300


10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]


B-H

C-H

T-H B

B-L

C-L

T-L


HDLD all

Used parameter set



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





















B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(a) Flow

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]


B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(c) Travel time

B-H

B-L

C-H

C-L

T-H

T-L B


Obj

ectiv

e val

ue [-

]

(d) Effort

B-H

B-L

C-H

C-L

T-H

T-L B

minus10

minus05

00

05

10

Erro

r [pe

ds

m]

(e) Flow

B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [-]

022502000175015001250100007500500025


B-H

B-L

C-H

C-L

T-H

T-L B

Erro

r [s

m]

050

075

025

000

minus025

minus050

minus075

minus100


HB-

LC-

HC-

LT-

HT-

L B

minus002

000

002

004

006

Erro

r [m

s]

(h) Effort-mean

B-H

B-L

C-H

C-L

T-H

T-L B

minus04

minus02

00

02

04

Erro

r [s

m]

(i) Travel time-std

B-H

B-L

C-H

C-L

T-H

T-L B

minus0005

0000

0005

0010

Erro

r [m

s]

(j) Effort-std































20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(b) Bottleneck

20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(d) Travel time













060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

10

08

06

04

02

00O

bjec

tive v

alue

[-]

[1

s]

(a) 120601 = 5700

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(b) 120601 = 7500

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(c) 120601 = 9300

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(d) 120601 = 5700

T-ju

nctio

n hi

gh

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

060

055

050

045

040

015 020

r [m]

[1

s]

(e) 120601 = 7500

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(f) 120601 = 9300


10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]


B-H

C-H

T-H B

B-L

C-L

T-L


HDLD all

Used parameter set



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




























20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(b) Bottleneck

20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]


20

15

10

5

0


Dist

ance

from

opt

imal

par

amet

er se

t [-]

Decrease in GoF [-]

(d) Travel time













060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

10

08

06

04

02

00O

bjec

tive v

alue

[-]

[1

s]

(a) 120601 = 5700

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(b) 120601 = 7500

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(c) 120601 = 9300

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(d) 120601 = 5700

T-ju

nctio

n hi

gh

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

060

055

050

045

040

015 020

r [m]

[1

s]

(e) 120601 = 7500

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(f) 120601 = 9300


10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]


B-H

C-H

T-H B

B-L

C-L

T-L


HDLD all

Used parameter set



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

10

08

06

04

02

00O

bjec

tive v

alue

[-]

[1

s]

(a) 120601 = 5700

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(b) 120601 = 7500

060

055

050

045

040

Bidi

rect

iona

l low

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(c) 120601 = 9300

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1

s]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(d) 120601 = 5700

T-ju

nctio

n hi

gh

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

060

055

050

045

040

015 020

r [m]

[1

s]

(e) 120601 = 7500

T-ju

nctio

n hi

gh

060

055

050

045

040

015 020

r [m]

[1s

]

10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]

(f) 120601 = 9300


10

08

06

04

02

00

Obj

ectiv

e val

ue [-

]


B-H

C-H

T-H B

B-L

C-L

T-L


HDLD all

Used parameter set



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



10

08

06

04

02

00O

bjec

tive v

alue

[-]

B-H

C-H

T-H

B-L

C-L

T-L


HD LD


HDLD












Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Obj

ectiv

e val

ue [-

]


08

07

06

05

04

03

02

01

00

QQ

SD

SD

TT

TT

Eff

Eff macro meso all





















Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











Data Availability




Acknowledgments


References







































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


multiobjective calibration framework for pedestrian simulation...

Documents