light source layout optimization strategy based on

Research ArticleLight Source Layout Optimization Strategy Based on ImprovedArtificial Bee Colony Algorithm

Bo Li Jue Wang Zijun Gao and Ning Gao

College of Information Science and Engineering Dalian Polytechnic University Dalian China

Correspondence should be addressed to Ning Gao louisgn163com

Received 29 June 2021 Revised 3 October 2021 Accepted 11 October 2021 Published 10 November 2021

Academic Editor Hao Gao

Copyright copy 2021 Bo Li et al is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In order to optimize the indoor lighting effect and reduce the energy consumption of indoor lighting the light source layout ofconventional rooms and special rooms is studied in this paper Firstly the indoor space lighting model is analyzed and theexpressions of light source output and illumination on the target plane are derived Secondly in order to improve the search abilityof the algorithm in specific areas combined with the artificial bee colony algorithm an improved artificial bee colony algorithmsuitable for indoor lighting optimization is proposed Using the average square difference of the illuminance of the target plane asthe adaptation function a penalty function is introduced and the minimum circle surrounding strategy is used to search thespecific location of the light source Finally the obtained layout is fitted by engineering standardization and the indoor lightsource layout is obtainedrough the simulation of illuminance effect in conventional room and irregular room it is proved thatthe proposed method can effectively improve the lighting effect and reduce the energy consumption of indoor lighting under thesame number of light sources and the same illuminance index

1 Introduction

In todayrsquos society the shortage of energy and the increasingenvironmental problems are becoming a serious problemthat people all over the world need to face Various energy-saving and environmental protection policies have grad-ually entered peoplersquos life In industrial development greenenergy conservation has become the main theme of thedevelopment of various industries Among them the powerresources consumed by the lighting industry account forone-fifth of the whole world every year is is a terribleresource occupation If a certain degree of energy can besaved in lighting it will greatly reduce the pressure ofenergy conservation and emission reduction in the worldIn recent years the lighting industry is also constantlyinnovating and developing for green energy conservationHowever most researchers focus on improving the lu-minous efficiency of the light source and ignore its externalenergy utilization A few scholars believe that the lightingand energy-saving methods required for green lightingshould not be limited to the traditional luminous efficiencyand the arrangement of light sources may also have a great

impact on the lighting and energy-saving effect [1ndash3]erefore it is necessary to study and strengthen the layoutof indoor light sources [4ndash6]

Aiming at the problems of indoor lighting layoutKomine et al [7] proposed a typical light source layoutwhich improved the lighting effect of indoor light source butthis layout caused a lot of energy loss of light source Yang[8] analyzed the reasonable layout of classroom lightingthrough the range value and improved the lighting envi-ronment but did not conduct in-depth research on theenergy loss of the light source Wei et al [9] proposed anoptimal coverage algorithm based on visible Voronoi dia-gram to optimize the layout of light sources e layout canconsume less energy to achieve better lighting effect but itdid not demonstrate the uniformity of illumination in detailSeo et al [10] improved the design of lighting and day-lighting system through the analysis of lighting and day-lighting environment but they lacked the planning of indoorlight source layout Guo and Guo [11] optimized the indoorspace layout by improving the small disturbance environ-ment of point light source and realized the system that canadapt to different periods and different weather but it lacks

HindawiMathematical Problems in EngineeringVolume 2021 Article ID 8099757 17 pageshttpsdoiorg10115520218099757

the specific analysis of lighting mode Wang et al [12]optimized the layout of traditional indoor lighting bystudying the standard deviation of visible light power butthey did not analyze the complex space Jin and Lee [13]proposed the layout of light source in occupied space basedon indoor lighting aesthetics and structure but it did notactually solve the problem of energy loss of light sourceWang et al [14] reduced the energy loss of light source bychanging the arrangement of near-field LEDs but ignoredthe influence of illumination uniformity

In order to solve the problem of energy loss in the lightsource layout this paper decides to optimize the indoor lightsource layout based on the basic idea of artificial bee colonyalgorithm After years of development artificial bee colonyalgorithm has been a mature optimization algorithm and aspecific application of cluster intelligence It is widely used tosolve various problems such as network traffic predictionand custom prediction [15ndash17] In order to solve the aboveproblems this paper first models and analyzes the indoorlighting and then improves the bee colony optimizationalgorithm e feasibility and practicability of the algorithmare verified by verifying the number of light sources andillumination value It is expected that the algorithm can notonly reduce the energy consumption of the light source butalso bring a better lighting experience for users

e main innovation of this paper is that by addingpenalty function and combining the idea of region seg-mentation an improved artificial bee colony algorithmsuitable for indoor lighting optimization is proposed andseveral conventional rooms and special spaces are simulatedand verified [18 19] On the basis of a large number ofexperiments it is found that the layout traversed by thealgorithm has the data characteristics of certain mathe-matical functions so the layout scheme of indoor lightsource is proposed

e main contents of this paper are as follows esecond chapter of this paper is to obtain the illuminancerelationship of indoor light source on the target plane bymodeling and analyzing LED lighting e work of Chapter3 is to improve the artificial bee swarm algorithm bycombining the illumination relationship of indoor lightsource with the idea of minimum circle area division efourth chapter is about the standardized engineering fittingof the light source layout obtained by the improved al-gorithm optimization e content of Chapter 5 is to do alarge number of optical data comparison experimentsbetween the fitted light source layout and other classicallight source layout e content of Chapter 6 is to sum-marize and analyze the new light source layout and theimproved artificial bee swarm algorithm as well as pros-pects of the future work

2 Indoor LED Lighting Model

e main purpose of this paper is to optimize the layout ofindoor light sources and the premise is to model and analyzethe indoor LED lighting model In the process of modelingthe commonly used energy-saving and environment-friendly LED light source is selected and many factors such

as brightness luminous intensity illumination uniformityand indoor glare value are comprehensively considered[20 21] Based on the indoor lighting calculation theory [22]the point by point method is used to calculate the receivingplane illuminatione schematic diagram of lighting modelis shown in Figure 1

e room size is set to L times W times H the light source isplaced at the top of the room the lower plane is the lightsource receiving plane the plane is evenly distributed as M

points and the target plane and the ground height are Hprimee luminous intensity of the light source is

I I0cosmθ (1)

Among them I is the luminous intensity emitted at angleθ I0 is the overall luminous intensity of the light source andθ is the angle between the line connecting the light sourcersquosemission point and the receiving plane and the vectorperpendicular to the ceiling m is the radiation coefficient ofthe light source which is related to the light intensity at thehalf angle and is controlled by the distance between themidpoint of the curvature of the LED light source part andthe package part Its relationship with the output half angleof the light source is

m minusln 2

cos θ12 (2)

At this time the distance Dq between the pointQ(xq yq H minus Hprime) on the receiving plane and the lightsource P(x y H) is

Dq

xq minus x1113872 11138732

+ yq minus y1113872 11138732

+ H minus Hprime( 11138572

1113970

(3)

Let H minus Hprime z and then the relationship between Dq

and z is

Dq

xq minus x1113872 11138732

+ yq minus y1113872 11138732

+ z2

1113970

(4)

Among them z is the vertical distance between the lightsource and the working surface and the cosine value of thelight source exit angle is

cos θ z

Dq

(5)

e illuminance E on the receiving plane is

E I0cos

m+1 θD

2q

(6)

e illuminance EQ at a certain point on the receivingsurface is

EQ I0z

m+1

xq minus x1113872 11138732

+ yq minus y1113872 11138732

+ z2

1113876 1113877(m+32)

(7)

Since LEDs are incoherent light sources when N LEDsare used to form an array the average light intensity E on thereceiving plane is

2 Mathematical Problems in Engineering

E 1

M1113944

N

i11113944

M

j1EQ (8)

e mean square error σ of the light intensity on thereceiving plane is

σ

1113936Mj1 EQ minus E1113872 1113873

21113969

M (9)

is section models the currently commonly used indoorlight source LED lighting methods taking into account thebrightness luminous intensity uniformity of illuminance andindoor glare values that affect indoor lighting and many otherfactors rough the analysis and calculation of the LED lightintensity and the spatial distance the illuminance relationexpression of the light source on the target plane is derived

3 Algorithm Optimization Module ofLight Source

According to the indoor lighting standard the indoor il-lumination value should be in the range 300ndash1500 lx and theillumination uniformity should be greater than 07 In orderto realize the concept of green energy-saving lighting the useof light sources should be reduced under the premise ofensuring the indoor lighting standard erefore this paperattempts to optimize the location of the light source layouton the premise of meeting the illumination and illuminationuniformity optimize the light source layout and use theleast light source to achieve the optimal lighting effect

At present the commonly used algorithms to solveoptimization problems include genetic algorithm ant colonyalgorithm particle swarm optimization artificial bee colonyand other intelligent optimization algorithms as well asmathematical optimization algorithms Artificial bee colonyalgorithm has the advantages of high accuracy strong ro-bustness and strong exploration ability and has no highrequirements for the objective and constraint function[23ndash29] Based on the optimization idea of artificial beecolony algorithm and the algorithm structure of regionsegmentation an improved artificial bee colony algorithmfor indoor light source layout optimization is proposed

e improved artificial bee colony algorithm treats thelayout of the light source as a solution in a multidimensionalspace e position of each light source has a unique corre-sponding nectar source and the position of each nectar sourcerepresents a feasible solution to the problem e number ofguide bees in the population is the same as the number offollower bees each accounting for one-half of the number ofnectar sources and each nectar source corresponds to only oneguide bee at the same time In the initialization stage thenectar source is generated by random numbers in the opti-mization interval the LED lighting function is established byequation (7) the evaluation function is constructed byequation (9) and the nectar source in the population is ini-tialized according to the number of light sources e value ineach dimension represents relative coordinates of the lightsource In the optimization stage the area is divided intouniform grids and assigned corresponding binary numbers todetermine the light source code represented by the position Inthe search stage after the bee finds a new source of nectar itshares the information source with the bee and the bee usesthe shared information to follow the bee probabilistically usingroulette In the iterative process the mean square error of thelighting function is set as the fitness value e larger the gridarea occupied by the nectar in the space the greater the fitnessand vice versa e nectar source is updated and replaced byadopting a greedy selection strategy If the new nectar sourcedoes notmeet the standard or has reached the search thresholdand no suitable nectar source is found the nectar sourcelocation is abandoned and a new nectar source is randomlygenerated and iteratively searched using the objective functionand the evaluation function When the fitness reaches the setsatisfaction the output current honey source parameters arethe current optimized relative coordinates of the light source

Under the requirement of fast convergence the pro-cessing level of artificial bee colony algorithm in specialspace decreases When the required optimization space is anirregular room at the later stage of the iteration of theconventional artificial bee colony algorithm most optimi-zation particles will repeatedly appear near the same arearesulting in some overlapping areas of light sourcesresulting in the loss of light source energy

Firstly in order to facilitate the processing of engi-neering problems the artificial bee colony algorithm isimproved and the penalty function and dynamic penaltyfactor are added to the algorithm e equations are shownas follows

minf(s)

st gi(s)ge 0 i 1 u

hj(s) 0 j 1 v

⎧⎨

⎩

minF(s λ) f(s) + λP(s)

P(s) 1113944u

i1μ gi(s)( 1113857 + 1113944

v

j1σ hj(s)1113872 1113873

(10)

Among them F(s λ) is a penalty function f(s) is anobjective function λP(s) is a penalty term λ is a dynamicpenalty factor gi(s) and hj(s) are constraint functions μ and

Light source

Ceiling

The targetplane

Y

X

ZC

B

A

Figure 1 Space lighting diagram

Mathematical Problems in Engineering 3

σ are functions of gi(s) and hj(s) In order to facilitate theimplementation of the algorithm let the constraint equationand inequality take the same dynamic penalty factor and thevalue of the dynamic penalty factor is shown in

λ 10e c2minusc15minus20 G2G1( )( )+C1+1 (11)

where c1 and c2 are fixed constants c1 4 c2 6 are selectedin this paper G1 and G2 are the maximum iteration valueand the current iteration value respectively

Firstly by adding a penalty function in the algorithm theoptimization problemof light source position is changed into an

unconstrained problem and the unconstrained optimal solu-tion of light source position is equivalent to the optimal solutionof the initial problem to reduce the difficulty of light sourceposition optimization At the same time the dynamic penaltyfactor is used to control the global convergence of the algorithmIn the initial stage of population iteration the penalty factor isvery small which makes the individual distribution and searchdimension in the population wide which is conducive to therealization of global search In the middle and late stage ofpopulation iteration with the increase of feasible solution setthe penalty factor increases exponentially which makes thealgorithm tend to converge to the optimal solution range

10-15

10-10

10-5

100

Fitn

ess

50 100 150 200 250 300 350 400 450 5000Number of iterations

Improved ABC AlgorithmABC Algorithm

PSO AlgorithmIABC Algorithm

(a)

10-10

10-8

10-6

10-4

10-2

100

102

104

Fitn

ess




(b)

Figure 2 Fitness trend chart under test functions Griewank and Rastrigin (a) Griewank function (b) Rastrigin function

10-4

10-2

100

102

104

Fitn

ess




(a)


10-15

10-10

10-5

100

Fitn

ess



(b)

Figure 3 Fitness trend chart under test functions Rosenbrock and sphere (a) Rosenbrock function (b) Sphere function


Secondly aiming at the problem of energy loss of lightsource in irregular space region segmentation is added toartificial bee colony algorithm to separate the superimposedregions In order to reduce the interaction between the lightsuperposition area and the conventional area the algorithmis set to calculate the illumination distribution of the con-ventional area first According to the light superpositionarea the minimum circle area coverage method is used tosearch the minimum light source coverage area

In view of the characteristics that the light sourceweakens continuously with distance and involves thelighting of light sources in irregular areas because the idea ofregion segmentation and minimum circle optimization al-gorithm in this paper is to use points to divide the irregularspace ZQ for the layout of light sources set ZP as the bestsolution set in region segmentation where

ZQ(a) b isin Z|(ab sub Z)1113966 1113967 (12)

If there is no intersection between points a and b in theirregular area Z in the space and outside the Z area a and b

are regarded as exactly the same visible points in the same

spaceerefore the same region of a point a in the irregularregion Z is defined as the set (ZQ) of complete intersectionsof all points starting from a and intersecting at the samepoint in the irregular region Z

ZP(A) cupn

i1ZR ai( 1113857 (13)

where A is a set of n points the positions between the n

points are completely independent andZR is the completelyirregular region (ZP) of point of A at is

ZR ai( 1113857 b isin Z| b minus ai

le b minus aj

foralljne i ai aj isin A1113882 1113883

(14)

b minus ai represents the Euclidean distance between the b

point and the point a in the irregular area

ZD(A) cupn

i1ZX ai( 1113857 (15)

ZD is the same visible figure of the whole set of A where

ZX ai( 1113857 b isin ZQ ai( 1113857| b minus ai

le b minus aj

foralljne i b isin ZQ ai( 11138571113882 1113883

(16)

is point ai exactly the same as that of the visible area (ZX)erefore when calculating the visible area illuminated

by the light source based on the environmental conditionsconstructed in Chapter 2 the relationship between thedistances of points a and b in the irregular area Z is asfollows

f(a b) b a b isin ZQ(a)

infin b notin ZQ(a)1113896 (17)

e minimum distance between adjacent iterative par-ticles is constrained by the distance formula to ensure theaccuracy of the final result

Light source under improved ABC algorithm

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Figure 4 8times 6times 3m room light source layout

X

Y

Figure 5 Bernoulli line

Fitted light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Figure 6 8times 6times 3m room fitting layout


After combining the penalty function and region seg-mentation the execution steps of the improved artificial beecolony algorithm in the search space are as follows

(i) Step 1 Judge whether the target space is a regulararea If it is a regular area go to step 3 When thetarget space is a complex area go to step 2

(ii) Step 2 Divide the complex area detect the overlaparea of the light source calculate the minimumcoverage area f the overlap area and step into Step3

(iii) Step 3 Discrete precalculated area light sourceinitial position iteration number

(iv) Step 4 Establish the objective function and fitnessfunction according to equations (7) and (9)

(v) Step 5 Calculate the respective density of the bi-nary numbers of the light source code and es-tablish the relative coordinates of the light sourcein the space corresponding to the value in eachdimension of the nectar source

(vi) Step 6 Iteratively solve the fitness value of the lightsource position represented by the nectar adoptthe strategy of greedy selection compare with thefitness value of the best light source position of theprevious generation decide to eliminate or selectthe better solution and calculate the followprobability at the same time

(vii) Step 7 Update the optimal position and followingprobability of the light source in the population

(viii) Step 8 Iteratively replace the dimension value ofthe light source position

(ix) Step 9 If the expected conditions are met or themaximum number of iterations is reached stop thesearch and judge whether the standard is met Ifthe expected condition is not reached and thesearch threshold is reached step 3 is executed ifthe condition is met the light source position isoutput

In order to visually compare the performance of thealgorithm four different functions Sphere RastriginRosenbrock and Griewank are used to test the improvedartificial bee swarm algorithm the original artificial beeswarm algorithm the particle swarm algorithm and theIABC algorithm improved in document [30]

e simulation experiment uses MATLAB 2019a as theexperimental platform the operating system is Windows 10the memory is 16G the CPU is Intel(R) Core(TM) i5-9400and the main frequency is 29GHz To avoid the randomnessof the optimization algorithm this experiment will use theaverage value of the results obtained by running the program30 times as the final fitness curve result e expression andvalue range of each test function are shown in Table 1 efitness change trend of the standard test function of eachalgorithm is shown in Figures 2 and 3

In Figures 2 and 3 the improved artificial bee swarmalgorithm uses a new fitness function and a region search

scheme compared with the original artificial bee swarmalgorithm particle swarm algorithm and IABC algorithmmentioned in document [30] which can not only search forthe optimal location more quickly but also avoid the localoptimum caused by multiple particle overlap at the end ofiteration

4 Optimization Results EngineeringStandardized Position Fitting

In this paper 8 times 6 times 3m general specification room iscalculated After optimization by improved artificial beecolony algorithm the relative coordinates of light source areshown in Table 2 and its spatial layout is shown in Figure 4

In Figure 4 the left half of the space is mainly illuminatedby No 3 No 4 No 5 and No 6 light sources the right half ofthe space is mainly illuminated by No 7 No 8 No 9 and No10 light sources and the central area is mainly illuminated byNo 1 and No 2 main light sources and edge light sourcesAmong them the x-axis coordinates of No 1 and No 2 lightsources No 3 and No 6 light sources No 4 and No 5 lightsources No 7 and No 10 light sources and No 8 and No 9light sources are inconsistent in the spatial coordinate systemwhile the y-axis coordinates of No 6 and No 7 light sourcesNo 5 and No 8 light sources No 4 and No 9 light sourcesand No 3 and No 10 light sources are inconsistent in thespatial coordinate system and there are some differences

e analysis of the optimized light source layout positionshows that although the lighting effect achieved by thislayout can meet the actual lighting requirements it hasrelatively random characteristics and the coordinates of thelight source layout are asymmetrical which lacks aestheticsin the actual layout In this paper the regular curve equationis used to further study the optimization results so as toachieve the beauty symmetry and engineering practicabilityof the layout rough a large number of experimentalanalysis it is found that the shape formed by the actualcoordinate position of the light source is similar to the shapeof Bernoulli Line in mathematics erefore this paper usesthe Bernoulli Line to fit the indoor light source layout inengineering standardization

e Bernoulli Line is a curve in the plane rectangularcoordinate system It is the inversion figure of hyperbolaabout the circle whose center is in the hyperbolic center Itsmathematical expression is shown in equation (18)

x2

+ y2

1113872 11138732

2a2

x2

minus y2

1113872 1113873 (18)

e mathematical graph is shown in Figure 5In the case of a limited number of interpolations this

paper uses the principle of least squares to perform fittingoperations [31ndash33] e least square method matches thebest function of the data byminimizing the sum of squares oferrors e fitting function is as follows

αx4

+ βy4

+ δx2y2

+ cx2

minus ηy2

+ φ (19)

In combination with the least square method equation(20) is as follows


R1 [α β δ c ηφ]T

R2 x4 y

4 x

2y2 x

2 y 11113960 1113961

T

⎧⎪⎨

⎪⎩(20)

e optimization goal is as follows

min RT1 R2

2

RT1 R2R

T2 R1

st RT1 UR1 lt 0

⎧⎪⎨

⎪⎩(21)

where RT1 UR1 lt 0 is constrained by the properties of the

double helix ac minus b2 lt 0e layout of engineering standardized fitting light

source after smoothing is shown in Figure 6 ComparingFigure 6 with Figure 4 it can be seen that the layout positionof the light source has not changed greatly but its symmetryand aesthetics are greatly enhanced

In this section on the premise of aesthetics and engi-neering practicability through the analysis of the optimallight source layout position optimized by improved artificialbee colony algorithm and using the mathematical curveequation to carry out the standardized fitting of the lightsource position the engineering standardized fitting lightsource layout is obtained

5 Simulation Experiment

In order to verify the rationality and superiority of theindoor space lighting layout proposed in this paper fouraspects of simulation experiments are carried out Simula-tion experiment 1 is used to verify the difference of lightingeffect between the engineering standard fitting light sourcelayout and the optimal light source layout optimized byimproved artificial bee colony algorithm Simulation ex-periment 2 is used to verify the difference between the in-door light source layout finally given by this method and theindoor light source layout lighting effect given by otherdocuments Simulation experiment 3 is used to verify theenergy consumption comparison between the final lightsource layout given by this method and the indoor lightsource layout given by other documents at the same illu-minance effect Simulation experiment 4 is used to verify the

application effect of this method in irregular rooms Insimulation experiments 1 2 and 3 in order to reflect thegenerality of the method standard square room mediumrectangular room and large rectangular room are selectedree room sizes of 5m times 5m times 3m 8m times 6m times 3m and12m times 9m times 3m are selected as examples In SimulationExperiment 4 an irregular space of L-shaped room is se-lected as an example

51 Simulation Experiment 1 In order to verify the dif-ference of lighting effect between the engineering standardfitting light source layout and the optimal light sourcelayout optimized by improved artificial bee colony algo-rithm this experiment compares and analyzes the fittingaccuracy and illumination distribution In terms of fittingaccuracy the least square fitting method of boundary [34]is used to calculate the fitting layout accuracy of rooms withvarious specifications In terms of illuminance distributionthe same number of light sources is used in the same roomto compare the illuminance distribution of multiple groupsof different room specifications e layout comparisondiagram and illuminance distribution diagram are shownin Figures 7ndash9

In Figures 7ndash9 the layout of engineering standardizedfitting light source deviates slightly from the layout directlyoptimized by using the improved artificial bee colony al-gorithm e boundary difference is obtained by traversingthe sampling coordinates of the fitting layout and the resultsoptimized by the algorithm It can be proved that the errorrate of the two layouts is very small which meets the re-quirements of boundary fitting threshold rough thecomparative analysis of indoor illuminance under the sameroom standard and the same number of light sources al-though the lighting effect of the optimized light sourcelayout using the improved artificial bee colony algorithm isslightly better the illuminance deviation from the engi-neering standardized fitting light source layout is very smallwhich can be ignored e lighting effects of the two areconsistent and the light source layout of engineeringstandardized fitting is more symmetrical and beautiful

Table 1 Expression and range of test function

Function name Function expression Search scopeGriewank f1(x) 1113936

ni1 x2

i [minus600600]Rastrigin f2(x) 1113936

ni1(x2

i minus 10(cos(2πxi)) + 10) [minus512512]Rosenbrock f3(x) 1113936

ni1 100(xi+1 minus x2

i )2 + (1 minus xi)2 [minus100100]

Sphere f4(x) (14000) 1113936ni0 x2

i minus 1113937ni1 cos(xi

i

radic) + 1 [minus100100]

Table 2 Relative coordinates of 8 times 6 times 3m room light source

Light source number Coordinate X(m) Coordinate Y(m) Light source number Coordinate X(m) Coordinate Y(m)1 399 405 6 223 5452 401 200 7 558 5653 234 048 8 725 4664 083 167 9 733 1655 081 459 10 575 050


which is convenient for construction It verifies the prac-ticability of the improved artificial bee colony algorithm inthis paper and the rationality of its optimization results afterengineering standardized fitting

52 SimulationExperiment 2 is simulation experiment isused to verify the difference between the indoor lightsource layout finally given by this method and the lightingeffect of the indoor light source layout given by other


0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

Fitted light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(b)

Light source under improved ABC algorithmFitted light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(d)

400

200

02

0-2

2

0

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(e)

Figure 7 5mtimes 5mtimes 3m room layout and illumination diagram (a) Optimized layout (b) Fitted layout (c) Layout comparison (d) Fittinglayout illumination map (e) Optimized layout illumination map


documents According to the light source layout and pa-rameters given in reference [35] the lighting effects ofrectangular and circular light source layouts are simulatedby using the same number of light sources in the sameroom e layout of the light source and its illuminance areshown in Figure 10 8m times 6m times 3m is shown in Figure 11

and 12m times 9m times 3m is shown in Figure 12 e indoorlight source layout and lighting effects finally given by themethod in this paper are shown in Figures 7ndash9 in Section51 respectively

Take a 5m times 5m times 3m room as an example to analyzethe experimental results In Figure 10 the maximum


0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(b)


0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(c)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

360

340

320

300

(d)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

340

320

300

(e)

Figure 8 8mtimes 6mtimes 3 m room layout and illumination diagram (a) Optimized layout (b) Fitted layout (c) Layout comparison (d) Fittinglayout illumination map (e) Optimized layout illumination map


indoor illuminance value of the rectangular layout is555164 lx the minimum is 288548 lx the average roomilluminance is 388879 lx and the uniformity of illumi-nance is 742 Although the rectangular layout can meet

the indoor lighting requirements in terms of illuminancevalue there is a great difference between the maximum andminimum values of illuminance In terms of lighting effectthere is a big gap between the central part and the edge part


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

7

8

9

y (m

)

0 4 6 8 10 122x (m)

(b)


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(c)

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

450

400

350

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

(e)

Figure 9 12mtimes 9mtimes 3m room layout and illumination diagram (a) Optimized layout (b) Fitted layout (c) Layout comparison(d) Fitting layout illumination map (e) Optimized layout illumination map


of the rectangular light source layout e illuminationvalue changes obviously from the center to the edge andthe room illumination distribution is unbalanced whichleads to the characteristics of high central illumination andlow edge illumination which affects the overall lightingeffect

In Figure 10(d) the light source is arranged in a tra-ditional circular layout the maximum illumination is5967869 lx the minimum is 2993843 lx the average illu-mination in the room is 395488 lx the difference betweenthe maximum and minimum illumination is 2974026 lxand the illumination uniformity is 757 In the layout ofcircular light source the central illumination value is toohigh and the edge illumination value is too low whichshows a cliff like downward trend at the corner of the spaceso that the uniformity of room illumination is at a low levelresulting in the uneven distribution of indoor illuminationCircular layout exposes the problem of sharp decrease ofillumination value at the edge of space which has a greatimpact on personnel activities

In Figure 7 the maximum illuminance value of the spacesimulated by the method in this paper is 4388067 lx theminimum illuminance value is 3552899 lx the average in-door illuminance is 410953 lx and the difference betweenthe maximum and minimum illuminance is 835168 lx euniformity is 864 which is higher than the lightingstandard In terms of illuminance value the fitting layout issmaller in illuminance difference the illuminance changefrom the central area to the edge area is more gentle theoverall illuminance value decreases less and there is nosharp decrease in the edge illuminance value which reducesthe local high illuminance uniformity andmakes the lightingeffect more uniform

In rooms of different specifications the illuminancedistribution changes with the change of the light sourcelayout e uniformity of the illuminance of each layoutunder the same number of light sources is shown in Table 3

In Table 3 under the same room standard with the samenumber of light sources compared with rectangular andcircular light source layouts the layout given in this paper

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)

Figure 10 5mtimes 5mtimes 3m room layout and illumination diagram (a) Layout of rectangular light source (b) Rectangular layout illu-mination map (c) Layout of circular light source (d) Circular layout illumination map


has the highest illumination uniformity while meeting thelighting standard

In this section combined with the illuminance and il-luminance uniformity standards it is proved that the illu-minance and illuminance uniformity of the indoor lightsource layout given by this method is better than therectangular and circular light source layout given in thecurrent literature

53 Simulation Experiment 3 In order to verify the energyconsumption comparison between the light source layoutgiven by this method and the indoor light source layoutgiven by other literatures in the same illumination effect therectangular layout circular layout and this method canachieve the average illumination effect of 450 lx 550 lx and700 lx in the same room e number of light sources re-quired for each layout is shown in Tables 4 5 and 6

In the table in the same room to achieve the same il-lumination requirements the number of light sources

required for this layout is less than that for rectangular andcircular layout In different rooms to achieve the same il-lumination the number of additional light sources requiredfor this layout is less than that for rectangular and circularlayout which proves that this layout can effectively reducethe number of light sources used which is in line with theenvironmental protection concept of high efficiency andenergy saving

54 Simulation Experiment 4 In order to verify the versa-tility of the method in this paper a complex L-shaped roomis selected for verification and its space model and size areshown in Figure 13 Since there is no other relevant literatureto design the layout of the light source in a complex roomsimulation experiment 4 only analyzes and explains theeffect of the layout of the light source in this paper

e lighting layout design of complex room is differentfrom the traditional rectangular room which is limited bythe conditions such as the superposition of regional light

Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)


Table 3 Illumination uniformity table of different room layout

Room size (m) Rectangular layout () Circular layout () Layout of this paper ()5 times 5 times 3 742 757 8648 times 6 times 3 725 712 82112 times 9 times 3 683 684 796

Table 4 e number of light sources required for each layout in a 5 times 5 times 3m room

Illumination value(lx)

Number of light sources in rectangularlayout

Number of light sources in circularlayout

Number of light sources laid outin

this paper450 9 10 9550 12 12 11700 14 16 13


sources and the loss of illumination For the optimizationof light source layout in irregular rooms the room layout isfirst cut into regular areas for calculation As shown inFigure 13 the L-shaped room in this paper is divided intothree areas S1 S2 and S3 Since the S3 area light source willaffect the S1 and S2 areas and it will be superimposed bythe illuminance of the S1 and S2 area light sources whencalculating the illuminance value of the room the S1 andS2 areas are prioritized for layout optimization Whencalculating the light source superposition region S3 re-stricted by the illumination of S1 and S2 regions thecontour detection and matching of the search region arecarried out e minimum coverage problem [36] is usedto solve the problem and the improved artificial beecolony algorithm is combined to optimize the light sourcelayout of L-shaped complex space e light source layoutand illumination distribution of complex space are shownin Figure 14

In Figure 14(d) the illuminance distribution of theL-type room is characterized by regional fluctuations due tothe division calculation of the space In S1 S2 and S3 areas

the total coverage of illumination is achieved and theoverlapping area of illumination has a little higher illumi-nation e maximum illumination is 4926214 lx theminimum is 3023994 lx and the illumination uniformity is827 e illumination is within the illumination standardrange the illumination uniformity is much higher than thestandard and the feasibility of the algorithm in indoorcomplex area is verified

To sum up in terms of average illumination and uni-formity of illumination the lighting effect achieved by thelayout proposed in this paper meets the lighting standardsCompared with rectangular and circular light source layout[35] the illumination uniformity is higher the overall il-lumination difference is lower and the spatial illuminationdistribution is more balanced so less light sources are usedto achieve the required illumination e layout optimizedby improved artificial bee colony algorithm not only hasmore advantages in the effect of indoor lighting but also canmeet the requirements of standard lighting layout for ir-regular rooms without general light source layout achievinglighting effect and saving energy






this paper450 12 13 11550 15 16 14700 16 18 15





Number of light sources laid out inthis paper

450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2

Figure 13 Schematic diagram of L-shaped room


6 Conclusion

In order to enhance the indoor lighting effect and reduce theenergy loss of excess light source this paper focuses on thelayout of indoor light source e general LED lightingmodel is selected and analyzed and its mathematical modelis constructed In order to find the specific lighting positionof the light source under the optimal lighting effect theoptimization mechanism of artificial bee colony algorithm isused for reference and the improved artificial bee colonyalgorithm combined with region segmentation is proposedto optimize the location and layout of the light sourceAccording to the rationality of light source construction thespecific location of standardized light source is obtained bynumerical fitting en in the simulation experiment thelighting effect of different specifications of the room iscompared In the case of the same illumination and the samenumber of light sources it is proved that the advantage ofuniform distribution of illumination after the standardized

fitting is fully in line with and better than the indoor lightingstandardrough the above experiments the overall idea ofimproved artificial bee colony algorithm is proved to beeffective which reduces the energy loss of indoor lightsource and provides a new choice for indoor light sourcelayout Although the improved artificial bee colony algo-rithm has advantages due to the introduction of the idea ofregion segmentation algorithm the algorithm focuses moreon region search which weakens its development ability andconsumes too much global search time How to improve thedevelopment ability of the improved artificial bee colonyalgorithm and reduce its time loss will be the work content inthe future At the same time based on the experience ofusing the improved artificial bee colony algorithm to studythe light source layout in this paper in the development ofartificial bee colony algorithm I think the following prob-lems are worth exploring In the future work the artificialbee colony algorithm can be combined with more swarmintelligence algorithms Under the new constrained

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

Figure 14 L-type room light source layout and illumination diagram (a) Optimized layout (b) Fitted layout (c) Layout comparison (d) L-type room illumination diagram


multiobjective optimization problem to develop a hybridswarm intelligence algorithm can solve practical problems

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare that there are no conflicts of interest

Acknowledgments

is work was supported in part by the Natural ScienceFoundation Program of Liaoning Province of China underGrants J2020109 and 2019-ZD-0289

References

[1] L Carpenter ldquoGreen lights blue skiesrdquo Sewanee Reviewvol 128 no 2 pp 189ndash200 2020

[2] D Vn and K Va ldquoEnergy saving and LED lamp lighting andhuman healthrdquo Gigiena i Sanitaria vol 81 2013

[3] A M Moram ldquoLight-emitting diodes and their applicationsin energy-saving lightingrdquo Proceedings of the Institution ofCivil EngineersmdashEnergy vol 164 no 1 2011

[4] N Kumar and N R Lourenco ldquoLed-based visible lightcommunication system a brief survey and investigationrdquoJournal of Engineering and Applied Sciences vol 5 no 4pp 296ndash307 2012

[5] T Komine and M Nakagawa ldquoFundamental analysis forvisible-light communication system using LED lightsrdquo IEEETransactions on Consumer Electronics vol 50 no 1pp 100ndash107 2004

[6] S Hann J Kim S Jung and C Park ldquoWhite LED ceilinglights positioning systems for optical wireless indoor appli-cationsrdquo in Proceedings of the 36th European Conference andExhibition on Optical Communication pp 1ndash3 Turin ItalySeptember 2010

[7] T Komine S Haruyama and M Nakagawa ldquoA study ofshadowing on indoor visible-light wireless communicationutilizing plural white LED lightingsrdquo Wireless PersonalCommunications vol 34 no 1-2 pp 211ndash225 2005

[8] H Z Yang ldquoResearch on the design strategy of childrenrsquosinterior lightingrdquo Light and Lighting vol 43 no 04pp 47ndash50 2019

[9] R J Wei L Lv and L C Yang ldquoA lighting design algorithmin complex regionsrdquo Journal of Computer-Aided Design ampComputer Graphics vol 27 no 10 pp 1944ndash1949 2015

[10] D Seo L Park P Ihm and M Krarti ldquoOptimal electricalcircuiting layout and desk location for day lighting con-trolled spacesrdquo Energy and Buildings vol 51 pp 122ndash1302012

[11] B W Guo and Y X Guo ldquoOptimization design of spatiallayout interior environment in point source small distur-bancerdquo Bulletin of Science and Technology vol 32 no 01pp 128ndash132 2016

[12] A J Wang Y Che Y L Guo and L X Wang ldquoLED layoutoptimization and performance analysis of indoor visible lightcommunication systemrdquo Chinese Journal of Lasers vol 45no 05 pp 172ndash183 2018

[13] S Jin and S H Lee ldquoLighting layout optimization for 3Dindoor scenesrdquo Computer Graphics Forum vol 38 no 7pp 733ndash743 2019

[14] H Wang H Q Zhang H H Wang and F X ZhangldquoDesign of LED arrays for uniform near-field illumina-tionrdquo Optics amp Optoelectronic Technology vol 7 no 05pp 78ndash83 2009

[15] D Z Tian J S Li H Y Wang and D X Wang ldquoNetworktraffic prediction method based on improved ABC algorithmoptimized EM-ELMrdquo e Journal of China Universities ofPosts and Telecommunications vol 25 no 03 pp 33ndash442018

[16] Z Tian G Wang S Li Y Wang and X Wang ldquoArtificial beecolony algorithm-optimized error minimized extremelearningmachine and its application in short-termwind speedpredictionrdquo Wind Engineering vol 43 no 3 pp 263ndash2762019

[17] Z Tian G Wang Y Ren S Li and Y Wang ldquoAn adaptiveonline sequential extreme learning machine for short-termwind speed prediction based on improved artificial bee colonyalgorithmrdquo Neural NetworkWorld vol 28 no 3 pp 191ndash2122018

[18] C K Cowan and A Bergman ldquoDetermining the camera andlight source location for a visual taskrdquo in Proceedings of theInternational Conference on Robotics and Automation vol 1pp 509ndash514 Scottsdale AZ USA May 1989

[19] K R Konda and N Conci ldquoIllumination modelling andoptimization for indoor video surveillancerdquo ComputationalImaging XII vol 9020 2013

[20] C Cuttle ldquoMaking the switch from task illumination toambient illumination standards principles and practicalitiesincluding energy implicationsrdquo Lighting Research amp Tech-nology vol 52 no 4 pp 455ndash471 2020

[21] J Vitasek T Stratil J Latal J Kolar and Z WilcekldquoIndoor illumination imitating optical parameters of sunnysummer daylightrdquo Optics and Laser Technology vol 1242020

[22] M B Kosfic and F V Topalis ldquoInterior lighting calculationssurvey of theoretical methodsrdquo Lighting Research and Tech-nology vol 30 no 4 pp 151ndash157 1998

[23] D Karaboga and B Basturk ldquoOn the performance of artificialbee colony (ABC) algorithmrdquo Applied Soft ComputingJournal vol 8 no 1 pp 687ndash697 2007

[24] B Akay and D Karaboga ldquoA modified artificial bee colonyalgorithm for real-parameter optimizationrdquo InformationSciences vol 192 pp 120ndash142 2012

[25] B Zhang T T Liu S C Zhang and P Wang ldquoArtificial beecolony algorithm with strategy and parameter adaptation forglobal optimizationrdquo Neural Computing and Applicationsvol 28 no 1 pp 349ndash364 2017

[26] W Ma Z Sun J Li M Song and X Lang ldquoAn improvedartificial bee colony algorithm based on the strategy of globalreconnaissancerdquo Soft Computing vol 20 no 12pp 4825ndash4857 2016

[27] S Babaeizadeh and R Ahmad ldquoPerformance comparison ofconstrained artificial bee colony algorithmrdquo Research Journalof Applied Sciences Engineering and Technology vol 10 no 5pp 537ndash546 2015

[28] A Yurtkuran and E Emel ldquoAn enhanced artificial bee colonyalgorithm with solution acceptance rule and probabilisticmultisearchrdquo Computational Intelligence and Neurosciencevol 2016 Article ID 8085953 13 pages 2016

[29] J Liu H Zhu Q Ma L Zhang and H Xu ldquoAn artificial beecolony algorithm with guide of global and local optima and


asynchronous scaling factors for numerical optimizationrdquoApplied Soft Computing vol 37 pp 608ndash618 2015

[30] J X Bi and J R Gong ldquoHybrid clustering algorithm based onartificial bee colony and K-means algorithmrdquo ApplicationResearch of Computers vol 29 no 6 pp 2040ndash2042 2012

[31] L L Long T P Lee and S Y Whar ldquoDirect least squaresfitting of ellipses segmentation and prioritized rules classifi-cation for curve-shaped chart patternsrdquo Applied Soft Com-puting Journal vol 107 2021

[32] M Zic ldquoAn alternative approach to solve complex nonlinearleast-squares problemsrdquo Journal of Electroanalytical Chem-istry vol 760 pp 85ndash96 2016

[33] A Amiri-Simkooei and S Jazaeri ldquoWeighted total leastsquares formulated by standard least squares theoryrdquo Journalof Geodetic Science vol 2 no 2 pp 113ndash124 2012

[34] W Wanguo W Shirong X Zhengfei Y Wenbo W Zhenliand L Li ldquoImproved least squares ellipse fitting algorithmbased on boundaryrdquo Computer Technology and Developmentvol 23 no 4 pp 67ndash70 2013

[35] T H Do J Hwang and M Yoo ldquoAnalysis of the effects ofLED direction on the performance of visible light commu-nication systemrdquo Photonic Network Communications vol 25no 1 2013

[36] H M Li Algorithm Research on Minimum Power PartialCover Problem Zhejiang Normal University Jinhua China2020


the specific analysis of lighting mode Wang et al [12]optimized the layout of traditional indoor lighting bystudying the standard deviation of visible light power butthey did not analyze the complex space Jin and Lee [13]proposed the layout of light source in occupied space basedon indoor lighting aesthetics and structure but it did notactually solve the problem of energy loss of light sourceWang et al [14] reduced the energy loss of light source bychanging the arrangement of near-field LEDs but ignoredthe influence of illumination uniformity

In order to solve the problem of energy loss in the lightsource layout this paper decides to optimize the indoor lightsource layout based on the basic idea of artificial bee colonyalgorithm After years of development artificial bee colonyalgorithm has been a mature optimization algorithm and aspecific application of cluster intelligence It is widely used tosolve various problems such as network traffic predictionand custom prediction [15ndash17] In order to solve the aboveproblems this paper first models and analyzes the indoorlighting and then improves the bee colony optimizationalgorithm e feasibility and practicability of the algorithmare verified by verifying the number of light sources andillumination value It is expected that the algorithm can notonly reduce the energy consumption of the light source butalso bring a better lighting experience for users

e main innovation of this paper is that by addingpenalty function and combining the idea of region seg-mentation an improved artificial bee colony algorithmsuitable for indoor lighting optimization is proposed andseveral conventional rooms and special spaces are simulatedand verified [18 19] On the basis of a large number ofexperiments it is found that the layout traversed by thealgorithm has the data characteristics of certain mathe-matical functions so the layout scheme of indoor lightsource is proposed

e main contents of this paper are as follows esecond chapter of this paper is to obtain the illuminancerelationship of indoor light source on the target plane bymodeling and analyzing LED lighting e work of Chapter3 is to improve the artificial bee swarm algorithm bycombining the illumination relationship of indoor lightsource with the idea of minimum circle area division efourth chapter is about the standardized engineering fittingof the light source layout obtained by the improved al-gorithm optimization e content of Chapter 5 is to do alarge number of optical data comparison experimentsbetween the fitted light source layout and other classicallight source layout e content of Chapter 6 is to sum-marize and analyze the new light source layout and theimproved artificial bee swarm algorithm as well as pros-pects of the future work

2 Indoor LED Lighting Model

e main purpose of this paper is to optimize the layout ofindoor light sources and the premise is to model and analyzethe indoor LED lighting model In the process of modelingthe commonly used energy-saving and environment-friendly LED light source is selected and many factors such

as brightness luminous intensity illumination uniformityand indoor glare value are comprehensively considered[20 21] Based on the indoor lighting calculation theory [22]the point by point method is used to calculate the receivingplane illuminatione schematic diagram of lighting modelis shown in Figure 1

e room size is set to L times W times H the light source isplaced at the top of the room the lower plane is the lightsource receiving plane the plane is evenly distributed as M

points and the target plane and the ground height are Hprimee luminous intensity of the light source is

I I0cosmθ (1)

Among them I is the luminous intensity emitted at angleθ I0 is the overall luminous intensity of the light source andθ is the angle between the line connecting the light sourcersquosemission point and the receiving plane and the vectorperpendicular to the ceiling m is the radiation coefficient ofthe light source which is related to the light intensity at thehalf angle and is controlled by the distance between themidpoint of the curvature of the LED light source part andthe package part Its relationship with the output half angleof the light source is

m minusln 2

cos θ12 (2)

At this time the distance Dq between the pointQ(xq yq H minus Hprime) on the receiving plane and the lightsource P(x y H) is

Dq

xq minus x1113872 11138732

+ yq minus y1113872 11138732

+ H minus Hprime( 11138572

1113970

(3)

Let H minus Hprime z and then the relationship between Dq

and z is

Dq

xq minus x1113872 11138732

+ yq minus y1113872 11138732

+ z2

1113970

(4)

Among them z is the vertical distance between the lightsource and the working surface and the cosine value of thelight source exit angle is

cos θ z

Dq

(5)

e illuminance E on the receiving plane is

E I0cos

m+1 θD

2q

(6)

e illuminance EQ at a certain point on the receivingsurface is

EQ I0z

m+1

xq minus x1113872 11138732

+ yq minus y1113872 11138732

+ z2

1113876 1113877(m+32)

(7)

Since LEDs are incoherent light sources when N LEDsare used to form an array the average light intensity E on thereceiving plane is


E 1

M1113944

N

i11113944

M

j1EQ (8)


σ

1113936Mj1 EQ minus E1113872 1113873

21113969

M (9)








minf(s)

st gi(s)ge 0 i 1 u

hj(s) 0 j 1 v

⎧⎨

⎩


P(s) 1113944u

i1μ gi(s)( 1113857 + 1113944

v

j1σ hj(s)1113872 1113873

(10)


Light source

Ceiling

The targetplane

Y

X

ZC

B

A








10-15

10-10

10-5

100

Fitn

ess




(a)

10-10

10-8

10-6

10-4

10-2

100

102

104

Fitn

ess




(b)


10-4

10-2

100

102

104

Fitn

ess




(a)


10-15

10-10

10-5

100

Fitn

ess



(b)









ZP(A) cupn

i1ZR ai( 1113857 (13)




le b minus aj


(14)



ZD(A) cupn

i1ZX ai( 1113857 (15)



le b minus aj


(16)







0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)


X

Y


Fitted light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)






















x2

+ y2

1113872 11138732

2a2

x2

minus y2

1113872 1113873 (18)



αx4

+ βy4

+ δx2y2

+ cx2

minus ηy2

+ φ (19)




R2 x4 y

4 x

2y2 x

2 y 11113960 1113961

T

⎧⎪⎨

⎪⎩(20)


min RT1 R2

2

RT1 R2R

T2 R1

st RT1 UR1 lt 0

⎧⎪⎨

⎪⎩(21)












ni1 x2


ni1(x2



i )2 + (1 minus xi)2 [minus100100]

Sphere f4(x) (14000) 1113936ni0 x2


i








0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

Fitted light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(b)


0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(d)

400

200

02

0-2

2

0

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(e)







0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(b)


0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(c)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

360

340

320

300

(d)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

340

320

300

(e)






0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

7

8

9

y (m

)

0 4 6 8 10 122x (m)

(b)


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(c)

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

450

400

350

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

(e)








Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)










Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References








































E 1

M1113944

N

i11113944

M

j1EQ (8)


σ

1113936Mj1 EQ minus E1113872 1113873

21113969

M (9)








minf(s)

st gi(s)ge 0 i 1 u

hj(s) 0 j 1 v

⎧⎨

⎩


P(s) 1113944u

i1μ gi(s)( 1113857 + 1113944

v

j1σ hj(s)1113872 1113873

(10)


Light source

Ceiling

The targetplane

Y

X

ZC

B

A








10-15

10-10

10-5

100

Fitn

ess




(a)

10-10

10-8

10-6

10-4

10-2

100

102

104

Fitn

ess




(b)


10-4

10-2

100

102

104

Fitn

ess




(a)


10-15

10-10

10-5

100

Fitn

ess



(b)









ZP(A) cupn

i1ZR ai( 1113857 (13)




le b minus aj


(14)



ZD(A) cupn

i1ZX ai( 1113857 (15)



le b minus aj


(16)







0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)


X

Y


Fitted light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)






















x2

+ y2

1113872 11138732

2a2

x2

minus y2

1113872 1113873 (18)



αx4

+ βy4

+ δx2y2

+ cx2

minus ηy2

+ φ (19)




R2 x4 y

4 x

2y2 x

2 y 11113960 1113961

T

⎧⎪⎨

⎪⎩(20)


min RT1 R2

2

RT1 R2R

T2 R1

st RT1 UR1 lt 0

⎧⎪⎨

⎪⎩(21)












ni1 x2


ni1(x2



i )2 + (1 minus xi)2 [minus100100]

Sphere f4(x) (14000) 1113936ni0 x2


i








0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

Fitted light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(b)


0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(d)

400

200

02

0-2

2

0

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(e)







0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(b)


0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(c)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

360

340

320

300

(d)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

340

320

300

(e)






0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

7

8

9

y (m

)

0 4 6 8 10 122x (m)

(b)


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(c)

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

450

400

350

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

(e)








Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)










Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References













































10-15

10-10

10-5

100

Fitn

ess




(a)

10-10

10-8

10-6

10-4

10-2

100

102

104

Fitn

ess




(b)


10-4

10-2

100

102

104

Fitn

ess




(a)


10-15

10-10

10-5

100

Fitn

ess



(b)









ZP(A) cupn

i1ZR ai( 1113857 (13)




le b minus aj


(14)



ZD(A) cupn

i1ZX ai( 1113857 (15)



le b minus aj


(16)







0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)


X

Y


Fitted light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)






















x2

+ y2

1113872 11138732

2a2

x2

minus y2

1113872 1113873 (18)



αx4

+ βy4

+ δx2y2

+ cx2

minus ηy2

+ φ (19)




R2 x4 y

4 x

2y2 x

2 y 11113960 1113961

T

⎧⎪⎨

⎪⎩(20)


min RT1 R2

2

RT1 R2R

T2 R1

st RT1 UR1 lt 0

⎧⎪⎨

⎪⎩(21)












ni1 x2


ni1(x2



i )2 + (1 minus xi)2 [minus100100]

Sphere f4(x) (14000) 1113936ni0 x2


i








0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

Fitted light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(b)


0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(d)

400

200

02

0-2

2

0

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(e)







0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(b)


0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(c)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

360

340

320

300

(d)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

340

320

300

(e)






0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

7

8

9

y (m

)

0 4 6 8 10 122x (m)

(b)


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(c)

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

450

400

350

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

(e)








Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)










Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References














































ZP(A) cupn

i1ZR ai( 1113857 (13)




le b minus aj


(14)



ZD(A) cupn

i1ZX ai( 1113857 (15)



le b minus aj


(16)







0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)


X

Y


Fitted light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)






















x2

+ y2

1113872 11138732

2a2

x2

minus y2

1113872 1113873 (18)



αx4

+ βy4

+ δx2y2

+ cx2

minus ηy2

+ φ (19)




R2 x4 y

4 x

2y2 x

2 y 11113960 1113961

T

⎧⎪⎨

⎪⎩(20)


min RT1 R2

2

RT1 R2R

T2 R1

st RT1 UR1 lt 0

⎧⎪⎨

⎪⎩(21)












ni1 x2


ni1(x2



i )2 + (1 minus xi)2 [minus100100]

Sphere f4(x) (14000) 1113936ni0 x2


i








0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

Fitted light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(b)


0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(d)

400

200

02

0-2

2

0

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(e)







0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(b)


0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(c)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

360

340

320

300

(d)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

340

320

300

(e)






0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

7

8

9

y (m

)

0 4 6 8 10 122x (m)

(b)


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(c)

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

450

400

350

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

(e)








Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)










Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References



























































x2

+ y2

1113872 11138732

2a2

x2

minus y2

1113872 1113873 (18)



αx4

+ βy4

+ δx2y2

+ cx2

minus ηy2

+ φ (19)




R2 x4 y

4 x

2y2 x

2 y 11113960 1113961

T

⎧⎪⎨

⎪⎩(20)


min RT1 R2

2

RT1 R2R

T2 R1

st RT1 UR1 lt 0

⎧⎪⎨

⎪⎩(21)












ni1 x2


ni1(x2



i )2 + (1 minus xi)2 [minus100100]

Sphere f4(x) (14000) 1113936ni0 x2


i








0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

Fitted light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(b)


0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(d)

400

200

02

0-2

2

0

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(e)







0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(b)


0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(c)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

360

340

320

300

(d)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

340

320

300

(e)






0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

7

8

9

y (m

)

0 4 6 8 10 122x (m)

(b)


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(c)

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

450

400

350

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

(e)








Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)










Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References









































R2 x4 y

4 x

2y2 x

2 y 11113960 1113961

T

⎧⎪⎨

⎪⎩(20)


min RT1 R2

2

RT1 R2R

T2 R1

st RT1 UR1 lt 0

⎧⎪⎨

⎪⎩(21)












ni1 x2


ni1(x2



i )2 + (1 minus xi)2 [minus100100]

Sphere f4(x) (14000) 1113936ni0 x2


i








0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

Fitted light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(b)


0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(d)

400

200

02

0-2

2

0

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(e)







0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(b)


0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(c)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

360

340

320

300

(d)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

340

320

300

(e)






0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

7

8

9

y (m

)

0 4 6 8 10 122x (m)

(b)


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(c)

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

450

400

350

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

(e)








Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)










Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References











































0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

Fitted light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(b)


0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(d)

400

200

02

0-2

2

0

-2

Illum

inan

ce (l

x)

y (m) x( m)

460

440

420

400

380

360

(e)







0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(b)


0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(c)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

360

340

320

300

(d)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

340

320

300

(e)






0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

7

8

9

y (m

)

0 4 6 8 10 122x (m)

(b)


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(c)

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

450

400

350

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

(e)








Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)










Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References












































0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(b)


0

1

2

3

4

5

6

y (m

)

1 2 3 4 5 6 7 80x (m)

(c)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

360

340

320

300

(d)

300

0

100

200

20

-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

340

320

300

(e)






0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

7

8

9

y (m

)

0 4 6 8 10 122x (m)

(b)


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(c)

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

450

400

350

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

(e)








Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)










Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References











































0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(a)

Fitted light source

0

1

2

3

4

5

6

7

8

9

y (m

)

0 4 6 8 10 122x (m)

(b)


0

1

2

3

4

5

6

7

8

9

y (m

)

2 4 6 8 10 120x (m)

(c)

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)

450

400

350

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

(e)








Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)










Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References













































Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(a)

400

200

02

0

-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(b)

Light source

0

05

1

15

2

25

3

35

4

45

5

y (m

)

05 1 15 2 25 3 35 4 45 50x (m)

(c)

400

200

02

0-2

20

-2

Illum

inan

ce (l

x)

y (m) x( m)

550

500

450

400

350

300

(d)










Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References















































Light source

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

(a)

600

400

200

02

10

-2-1

42

0-4

-2

Illum

inan

ce (l

x)

y (m)x( m)

600

500

400

300

(b)

0

1

2

3

4

5

6

y (m

)

63 80 521 4 7x (m)

Light source

(c)

400

200

02

0-2

42

0-4

-2

Illum

inan

ce (l

x)

y (m) x( m)

500

450

550

400

350

(d)



Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References








































Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(a)

600

400

200

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m)x( m)

600

400

500

300

(b)

Light source

0

1

2

3

4

5

6

7

8

9

y (m

)

86 100 2 124x (m)

(c)

600500400300200100

04

20

-4-2

50

-5

Illum

inan

ce (l

x)

y (m) x( m)

600

700

400

500

300

(d)









this paper450 9 10 9550 12 12 11700 14 16 13











this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References

















































this paper450 12 13 11550 15 16 14700 16 18 15






450 14 15 12550 16 17 15700 18 20 17

3 m

8 m

5 m

5 m

3 m

3 m

8 m

S1 S3

S2



6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References








































6 Conclusion



Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(a)

Light source

0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(b)


0

1

2

3

4

5

6

7

8

y (m

)

63 80 521 4 7x (m)

(c)

400

200

04

20

-4-2

42

0

-4-2

Illum

inan

ce (l

x)

y (m) x( m)

450

400

350

(d)




Data Availability




Acknowledgments


References









































Data Availability




Acknowledgments


References








































light source layout optimization strategy based on

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