research article log-linear model based behavior selection...

Research ArticleLog-Linear Model Based Behavior Selection Method forArtificial Fish Swarm Algorithm

Zhehuang Huang12 and Yidong Chen2

1School of Mathematics Sciences Huaqiao University Quanzhou 362021 China2Cognitive Science Department Xiamen University Xiamen 361005 China

Correspondence should be addressed to Yidong Chen ydchenxmueducn

Received 31 May 2014 Accepted 15 December 2014

Academic Editor Carlos M Travieso-Gonzalez

Copyright copy 2015 Z Huang and Y Chen 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

Artificial fish swarm algorithm (AFSA) is a population based optimization technique inspired by social behavior of fishes In pastseveral years AFSA has been successfully applied inmany research and application areasThe behavior of fishes has a crucial impacton the performance of AFSA such as global exploration ability and convergence speed How to construct and select behaviors offishes are an important task To solve these problems an improved artificial fish swarm algorithm based on log-linear model isproposed and implemented in this paper There are three main works Firstly we proposed a new behavior selection algorithmbased on log-linearmodel which can enhance decisionmaking ability of behavior selection Secondly adaptivemovement behaviorbased on adaptive weight is presented which can dynamically adjust according to the diversity of fishes Finally some new behaviorsare defined and introduced into artificial fish swarm algorithm at the first time to improve global optimization capability Theexperiments on high dimensional function optimization showed that the improved algorithmhasmore powerful global explorationability and reasonable convergence speed compared with the standard artificial fish swarm algorithm

1 Introduction

Artificial fish swarm algorithm [1 2] is a new evolutionaryalgorithm proposed in 2002 to imitate the fish behaviors suchas praying swarming and following For many optimizationproblems artificial fish swarm algorithm can produce high-quality solution within a reasonable computation time andrelatively stable convergence characteristics

Compared with traditional evolutionary algorithm arti-ficial fish swarm algorithm has some attractive characteristicssuch as simple in principle good robustness and tolerance ofparameter setting [3] In recent years a series of papers havefocused on the application of AFSA such as resource leveling[4] robot task allocation [5 6] neural network [7] imagesegmentation [8] fault diagnosis in mine hoist [9] imagereconstruction [10] data clustering [11ndash13] PID controllerparameters [14] and other areas [15ndash21]

However AFSA algorithm also showed some unsatisfac-tory aspects in practical applications such as premature con-vergence and poor ability in global optimization At the same

time the experiences of group members are not used for thenextmoves To solve the problem some improved algorithms[22ndash25] have been proposed Although the methods men-tioned above can improve the performance to some extentthey still cannot get satisfactory results for some applications

At the selection of behaviors we signed by the log-linear model of thinking In statistics linear model is usedin different ways according to the context Log-linear model[26] is amathematicalmodel that takes the form of a functionwhose logarithm is a polynomial function of the parametersof the model

In this paper we proposed a behavior selection algorithmbased on log-linear model The advantages of log-linearmodel are the ability to easily blend multiple features Usingthe log-linear model can enhance decision making ability ofbehavior selection

This paper is organized as follows In Section 2 relatedwork is presented The background of artificial fish swarmalgorithm is introduced in Section 3The improved algorithmbased on log-linear model and some new behaviors of fishes

Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2015 Article ID 685404 10 pageshttpdxdoiorg1011552015685404

2 Computational Intelligence and Neuroscience

are presented in Section 4 In Section 5 some experimentaltests results and conclusions are given Section 6 concludesthe paper

2 Related Work

In recent years researchers have made some attempts toimprove the performance of artificial fish swarm algorithmIn [22] chaos optimization is first employed to initialize theposition of individual artificial fish and applied to obtain theneighborhood of the global optimum solution Gao et alreported an improved artificial fish swarm algorithm withcrossover operator based on parentsrsquo characteristics [23] In[24] the concept of ecological niche is also being intro-duced to overcome the shortcoming of traditional artificialfish swarm algorithm to obtain optimal solution Rochaet al reported an augmented Lagrangian methodology witha stochastic population based algorithm which solves asequence of simple bound global optimization subproblemsusing a fish swarm intelligent algorithm [25]

Some researchers have tried to improve the performanceof AFSA by combining different algorithm with AFSA Animproved AFSO (IAFSO) [27] is proposed to train forwardneural network using a hybrid of artificial fish swarm algo-rithm and particle swarm optimization In [28] some newideas are proposed which focus on a set of movements offishes Wang and Ma reported a hybrid artificial fish swarmalgorithm which is combined with CF and artificial fishswarm algorithm to solve the Bin packing problem [29] In[30] quantum rotation gate is used to update the position ofartificial fish swarm which employs the quantum nongate tospeed up the convergenceThe experimental results show thatthe performance of AFSA is significantly improved A hybridalgorithmbased on particle swarmoptimization and artificialfish swarm algorithm [31] is reported which owns a goodglobally convergent performance with a faster convergentrate In [32] a simulated annealing artificial fish swarm algo-rithm is proposed which can obtain better optimizationprecision and convergence speed

Log-linear model is a mathematical model which iswidely used in part-of-speech tagging statistical machinetranslation and other fields Och and Ney introduced thelog-linear model for statistical machine translation (SMT) inwhich translation is considered as optimization problem Itsefficiency is comparable to the globalmethod [33] In [34] themultinomial diversity model (MDM) based on generalizedlinear models is proposed which can be used for modelselection and graphical and numerical interpretation

In this paper we proposed an improved algorithm basedon log-linear model which can transform the traditionalsingle probability model to adaptive model

3 Introduction to AFSA

Suppose 119883 is the state vector of artificial fish swarm Let119883 = (119909

1 1199092 119909

119899) where 119909

1 1199092 119909

119899is status of fishes

The action of artificial fish occurs only in the radius of a circlewith vision The artificial fish realizes external perception byits vision shown in Figure 1

Step

Xn1Xn2

X

X

Xnext

Figure 1 Vision concept of the artificial fish

Suppose 119883V is the visual position at some moment 119883V =

(119909V1 119909

V2 119909

V119899) 119883next is the new position Let Step be the

moving step length Visual represents the visual distance and120575 is the crowd factor (0 lt 120575 lt 1)Then themovement processis represented as

119883V = 119883119894 + Visual times rand () 119894 isin (0 119899]

119883next = 119883 +119883V minus 1198831003817100381710038171003817119883V minus 119883

1003817100381710038171003817

times Step times rand () (1)

where rand() produces random numbers between 0 and 1The basic behaviors of artificial fish are defined as follows

31 Prey Behavior Prey behavior is a basic biological behav-ior to find food Suppose 119883

119894is the current state of artificial

fish and 119883119895is a random state in its visual distance and 119884 is

the food concentration

119883119895= 119883119894+ Visual times rand () (2)

If 119884119894lt 119884119895 it goes forward a step in this direction

119883119905+1

119894= 119883119905

119894+

119883119895minus 119883119905

119894

10038171003817100381710038171003817119883119895minus 119883119905

119894

10038171003817100381710038171003817


32 Swarm Behavior Suppose 119883119888is the center position and

the number of artificial fish is 119899119891 If 119899119891119899 lt 120575 and 119884

119888gt 119884119894 it

goes forward a step to the companion center otherwise per-form prey behavior

119883119905+1

119894= 119883119905

119894+119883119888minus 119883119905

119894

1003817100381710038171003817119883119888 minus 119883119905

119894

1003817100381710038171003817


33 Follow Behavior Suppose119883max is the optimal state fromvisual neighbors and the number of partners of119883max is 119899119891 If

Computational Intelligence and Neuroscience 3

119899119891119899 lt 120575 and119884

119895gt 119884119894 it goes forward a step to the companion

119883119895 otherwise perform prey behavior

119883119905+1

119894= 119883119905

119894+119883max minus 119883

119905

119894

1003817100381710038171003817119883max minus 119883119905

119894

1003817100381710038171003817


34Move Behavior Move behavior is a basic behavior to seekfood or companions in larger ranges They can choose a statein the vision and then move towards this state

119883119905+1

119894= 119883119905

119894+ Visual times rand () (6)

35 Leap Behavior If the fitness function is almost the sameor the difference is smaller than a proportion during the given(119898minus119899) iterations leap behavior canmove to new state to avoidthe local extreme values

If (119884119898max minus 119884119899

max lt 119890119901119904)

119883119905+1

119894= 119883119905

119894+ 120573 times Visual times rand () (7)

where 119890119901119904 is a smaller constant and 120573 is a parameter that canmake some fishes have other actions

The artificial fish swarm algorithm mainly includes thefollowing steps

Step 1 Initialize the parameters of artificial fish such as StepVisual the number of exploratory and maximum number ofiterations

Step 2 Select the optimal value and recorded in the bulletin

Step 3 Perform prey behavior swarm behavior followbehavior move behavior and leap behavior

Step 4 If individual optimum is better than bulletin boardupdate the optimal value in bulletin board

Step 5 If the termination condition is satisfied output theresult otherwise return to Step 2

4 The Improved Fish Swarm AlgorithmBased on Log-Linear Model (LAFSA)

In this section we proposed a behavior selection algorithmbased on log-linear model Firstly log-linear model is usedto implement a multiprobability adaptive model A varietyof knowledge sources are added to the model in the form ofa feature function to enhance decision making ability Sec-ondly some new behaviors are proposed to improve theperformance of fish swarm algorithm

41 Log-Linear Model Suppose that the state vector of fishesis 119883 = (119909

1 1199092 119909

119899) where 119909

1 1199092 119909

119899is status of the

fishes The basic form of the behavior selection algorithmbased on log-linear model can be defined as

119875119903(119905) =

sum119898exp [120573

119898ℎ119898(119905)]

sum119905sum119898exp [120573

119898ℎ119898(119905)] (8)

where ℎ119898(119905) (119898 = 1 2 119872) are feature functions and

120582119898(119898 = 1 2 119872) are the weight of feature function

42 The Selection of Feature Function The selections of fea-ture functions have a crucial impact on the optimization per-formance how to construct feature functions is an importanttask In this paper we choose diversity function dimensionaldistribution function and average distance metrics functionas feature function in the experiment

(1) Diversity Function Diversity function is used to describethe degree of dispersion of the fishes Diversity function ℎ

1(119905)

describes adaptive diversity of 119905th iteration

ℎ1(119905) =

sum119873

119894=1

10038161003816100381610038161003816119891 (119909119894) minus 119891119905

avg10038161003816100381610038161003816

119873 lowastmax1le119895le119873

(10038161003816100381610038161003816119891 (119909119895) minus 119891119905avg

10038161003816100381610038161003816)

(9)

where 119891119905avg means the average fitness value of 119905th iterative and119891 is the fitness value of the current fishes119883

119894 Consider ℎ

1(119905) isin

(0 1] ℎ1(119905) = 1means the diversity is poor ℎ

1(119905) ≪ 1means

the diversity is good

(2)DimensionalDistribution FunctionWe select dimensionaldistribution function as feature function

ℎ2(119905) =

sum119873

119894=1radicsum119863

119889(119909119894119889minus 119909119889)2

119873 timesmax1le119895le119873

(radicsum119863

119889(119909119895119889minus 119909119889)2

)

(10)

where 119873 means the number of particles and 119909119889means the

average value of the 119863 dimension component of particlesWhen ℎ

2(119905) is less than a threshold we must employ some

strategies to improve the diversity of population

(3) Average Distance Metrics Function We select averagedistance metrics function as feature function Suppose thatthe distance between the fishes is 119889

119894119895= 119883119894minus 119883119895 and 119894 and

119895 are the number of random fishes Diversity function ℎ3(119905)

describes average distance of 119894th fishes119883119894

ℎ3(119905) =

sum119873

119895=1119889119894119895

119873 timesmax1le119894119895le119873

(119889119894119895)

119894 = 1 2 119873 (11)

Additionally we can choose other functions such ascontraction expansion measure as feature function

43 New Behaviors

431 Adaptive Movement Behavior Suppose that inertiaweight vector is119908 = [119908

1 1199082 119908

119899] here119908

119894(119894 = 1 2 119899)

is inertia weight of the 119894th dimension and its value dynam-ically adjusts according to diversity of fishes When thediversity of fishes is good the inertiaweight can be set smallerWhen the diversity of fishes is good the inertia weight can beset larger The inertia weight of 119894th dimension can be set as

120596119894= 06 lowast 119890

(minus120572lowast(1minus119875119903(119905)))+ 03 119894 = 1 2 119899 (12)

where diversity function 119875119903(119905) describes adaptive diversity of

119905th iteration 120572 is a constant we set 120572 = 10 in the experiment


0 02 04 06 08 1

04

05

06

07

08

09

1

x

120572 = 2

120572 = 6

120572 = 10

Figure 2 The image of function 119891(119909) = 06 lowast 119890(minus120572lowast(1minus119909)) + 03

The image of function 119891(119909) = 06 lowast 119890(minus120572lowast(1minus119909))

+ 03

is shown in Figure 2 It can be used to describe the changetendency of parameters 120596

119894

So the traditional prey behavior swarm behavior and fol-low behavior can be redefined as adaptive movement behav-ior based on inertia weightThe adaptive movement behaviorincludes three behaviors new prey behavior new swarmbehavior and new follow behavior which is shown as (13) to(15)

New prey behavior is

119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)

119883119895minus 119883119905

119894

10038171003817100381710038171003817119883119895minus 119883119905

119894

10038171003817100381710038171003817


New swarm behavior is

119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)119883119888minus 119883119905

119894

1003817100381710038171003817119883119888 minus 119883119905

119894

1003817100381710038171003817


New follow behavior is

119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)119883max minus 119883

119905

119894

1003817100381710038171003817119883max minus 119883119905

119894

1003817100381710038171003817

times Step times rand ()

(15)

If (119875119903(119905) gt 119877

1) perform adaptive movement behavior else

perform traditional prey behavior swarm behavior and fol-low behavior where 119877

1is diversity threshold value and we

set 1198771= 06 in the experiment

432 Population Inhibition Behavior In artificial fish swarmalgorithm the convergence speed of later stages is too slow alot of fishes perform invalid search which wastes much timeSo we introduce population inhibition behavior to acceleratethe convergence speed

After a period of evolution the big fishes will eat smallfishes and the occupied space of small fishes will be cleared

Released the space of invalid fishes

Raw fishes

After a certain number of iterations

Move one step to the center of subclass of fishes

Yes

NoPr(t) gt R2

Figure 3 The population inhibition behavior of artificial fishswarm

The population inhibition behavior of artificial fishswarm is shown in Figure 3 where 119877

2is diversity threshold

value and we set 1198772= 085 in the experiment

433 Population Expansion Behavior Population inhibitionbehavior can improve the convergence speed but it may leadto poor global exploration ability So we introduce populationexpansion behavior to maintain a certain population size

For fish 119894 it can generate subswarm which is in line withthe normal distribution The generation of new fishes can beset as

119883new119894= 119883119894+ random (minus119897 lowast Step 119897 lowast Step) (16)

where 119897 is an integer constant The population expansionbehavior of artificial fish swarm is shown in Figure 4 where1198773is diversity threshold value and we set 119877

3= 02 in the

experimentFor the new artificial fishes firstly find 119883max with the

largest objective function value and if 119884119894lt 119884max then move

one step to the center of subclass119883119888 otherwisemove one step

to the largest fish of subclass119883max

44 The Behavior Selection Algorithm Based on Log-LinearModel The improved algorithm is shown in Algorithm 1

The overall structure of the improved algorithm is shownin Figure 5

5 Experiment

A set of unconstrained benchmark functions was used toinvestigate the effect of the improved algorithm which isshown in Table 1

Sphere function is a single-peak function we can findthe optimal value to be 0 through the analysis for functionexpression and the function image is shown in Figure 6

Rastrigin function is a multipeak function we can findthe optimal value to be 0 through the analysis for functionexpression and the function image is shown in Figure 7

Griewank function is a multipeak function we can findthe optimal value to be 0 through the analysis for functionexpression and the function image is shown in Figure 8


(1) Initialize variables(2) Construct the log-linear model by (8)(3) Each fishes update their location(a) If 119875

119903(119905) gt 119877

1 perform adaptive movement behavior by (13) to (15)

else perform traditional prey behavior swarm behavior and follow behavior(b) If 119875

119903(119905) gt 119877

2 perform population inhibition behavior

(c) If 119875119903(119905) lt 119877

3 then perform population expansion behavior by (16)

(4) The threshold gradually reduced which can lead to the dispersion of fishes(5) Update the optimal value(6) If the termination condition is satisfied output the optimal value otherwise return to Step 2

Algorithm 1 Improved AFSA based on log-linear model

Table 1 Functions used to test the effects of improved algorithm

Function Function expression Optimal value

Sphere function 1198911(119909) =

119899

sum

119905=1

1199092

119905 0

Rastrigin function 1198912(119909) =

119899

sum

119905=1

(1199092

119905minus 10 cos (2120587119909

119905) + 10) 0

Griewank function 1198913(119909) =

1

4000

119899

sum

119905=1

(119909119905minus 100)

2minus

119899

prod

119905=1

cos(119909119905minus 100

radic119905) + 1 0

Ackley function1198914(119909) = 20 + 119890 minus 20119890

minus02radicsum119899

119905=1119909119905

2119899minus 119890sum119899

119905=1cos (2120587119909

119905)119899 0

Shafferrsquos function 1198915(119909) = 05 +

(sinradic1199091

2 + 1199092

2)2

minus 05

(1 + 0001 (1199091

2 + 1199092

2))2

0

Raw fishes

Generated new artificial fish

Yes

No

Yes

Move one step to the largest fishof subclass Xmax

Move one step to the center ofsubclass Xc

Yi gt Ymax

Through the traverse find the artificial fishXmax and Xc

Pr(t) lt R3

Figure 4 The population expansion behavior of artificial fishswarm

Table 2 The parameter setting of test algorithm

Algorithm Fish number Visual Delta Step Number of iterationsAFSA 100 285 9 1 60LAFSA 100 285 9 1 60

Ackley function is a multipeak function we can find theoptimal value to be 0 through the analysis for function expres-sion and the function image is shown in Figure 9

Shaffer function is a multipeak function we can find theoptimal value to be 0 through the analysis for function expres-sion and the function image is shown in Figure 10

The parameter setting of test algorithm is shown inTable 2

For comparison we use five strategies

(1) AFSA basic artificial fish swarm algorithm(2) AFSA + AMB artificial fish swarm algorithm with

adaptive movement behavior based on log-linearmodel

(3) AFSA + PIB artificial fish swarm algorithm withpopulation inhibition behavior based on log-linearmodel

(4) AFSA + PEB artificial fish swarm algorithm withpopulation expansion behavior based on log-linearmodel


Yes Yes Yes

Start

Yes

No

Output the optimal value

Iteration termination

End

No

Log-linear model

Preyswam followbehavior

Population inhibition behavior

Population expansionbehavior

Pr(t) gtR3Pr(t) gt R2Pr(t) gt R1

Variableinitialization

Adaptivemove

behavior

Figure 5 Log-linear model based artificial fish swarm algorithm

minus10minus5

05

10

minus10

minus5

0

510

minus150

minus100

minus50

0

Figure 6 The image of Sphere function

(5) LAFSA improved artificial fish swarmalgorithmwithhybrid behavior (adaptivemovement behavior popu-lation inhibition behavior and population expansionbehavior) based on log-linear model

We used mean (average optimal value) times (executiontime) SD (standard deviation) and iterations (average con-vergence iterations number) as evaluation indicators

minus10 minus8 minus6 minus4 minus2 0 2 4 6 8 10

minus10minus5

05

10minus200minus180minus160minus140minus120minus100

minus80minus60minus40minus20

0

Figure 7 The image of Rastrigin function

minus10minus5

05

10

minus10minus5

05

10minus25

minus2

minus15

minus1

minus05

0

Figure 8 The image of Griewank function

minus10minus5

05

10

minus10minus5

05

10minus20

minus15

minus10

minus5

0

5

Figure 9 The image of Ackley function

The comparison of different methods is shown in Table 3to Table 5 Each point is made from average values of over30 repetitions The dimension of Sphere function Rastriginfunction Griewank function and Ackley function is taken as10 dimensions Shaffer function is taken as 2 dimensions


minus1

minus08

minus06

minus04

minus02

0

minus10minus5

05

10

minus10minus5

05

10

5

Figure 10 The image of Shaffer function

Table 3 The performances of AFSA and AFSA + AMB

Algorithm AFSA AFSA + AMBMean Time (s) Mean Time (s)

Sphere 0017 302 0016 313Rastrigin 427 352 346 343Griewank 2456 221 2456 256Ackley 025 393 014 318Shaffer 00097 179 00097 172

We can see from Table 3 for Sphere function Rastriginfunction and Ackey function that we can improve the opti-mal value compared with the standard AFSA For Griewankfunction and Shaffer function the optimal value of the twoalgorithms is the same

So the adaptive inertia weight can effectively reflect thediversity of fish swarm Adaptive movement behavior withreasonable setting according to diversity of fish swarm canimprove the performance

From Table 4 we can find out that the convergence timeof AFSA + PIB is greatly reduced as expected for all the fivefunctions The number of fishes is gradually reduced whichcan avoid useless search so the time can be reduced But wecan see that optimal value is slightly inferior to the standardalgorithm

For all the five functions the accuracy obtained inAFSA + PEB is significantly improved because the introduc-tion of population expansion behavior can improve globaloptimization capability But at the same time the executiontime inevitably increases compared with the standard AFSAalgorithm

So different behavior has both advantages and disadvan-tages from an overall point of view and we must selectdifferent behaviors according to different condition

From Table 5 for Sphere function Rastrigin functionGriewank function and Ackley function LAFSA algorithmcan effectively improve the accuracy such that the optimalvalue obtained is much closer to the theoretical one andthe accuracy is improved compared with the standard AFSA

0 10 20 30 40 50 600

2

4

6

8

10

12

14

The number of iterations

Opt

imal

val

ue

Iterative process of the fish swarm algorithm

AFSALAFSA

Figure 11 Sphere function

AFSALAFSA

0 10 20 30 40 50 6025

30

35

40

45

50

55

60

65

70

75


Opt

imal

val

ue


Figure 12 Rastrigin function

algorithm On the convergence speed and algorithm execu-tion time there is a significant improvement as expected forall the five functions

So the new behaviors of fish presented in this paperare essential for better performance At the same time thebehavior selection based on log-linear model can enhancedecision making ability of behavior selection

The comparison of the two methods with convergentcurves is shown in Figures 11 12 13 14 and 15 Comparingwith AFSA the LAFSA algorithm has both global searchability and fast convergence speed


Table 4 The testing performance comparison among of AFSA AFSA + PIB and AFSA + PEB

Algorithm AFSA AFSA + PIB AFSA + PEBMean Time (s) Mean Time (s) Mean Time (s)

Sphere 0017 302 0036 149 0013 459Rastrigin 427 352 453 155 223 458Griewank 2456 221 2625 133 1863 351Ackley 025 393 033 196 016 519Shaffer 00097 179 0051 138 0 322

Table 5 The performances of AFSA and LAFSA

Algorithm AFSA LAFSAMean SD Time (s) Iterations Mean SD Time (s) Iterations

Sphere 0017 00048 302 21 0014 00023 188 15Rastrigin 427 754 352 55 296 531 223 28Griewank 2456 491 221 57 2445 304 135 32Ackley 025 0072 393 45 018 0054 2456 31Shaffer 00097 000013 179 8 00097 000011 151 8

0 10 20 30 40 50 60244

246

248

25

252

254

256


Opt

imal

val

ue


AFSALAFSA

Figure 13 Griewank function

6 Conclusions

In this paper we present an improved artificial fish swarmalgorithm based on log-linear model This is the first effortto introduce log-linear model and some new behavior toartificial fish swarm algorithm Experiments show that theimproved algorithm has more powerful global explorationability with reasonable convergence speed

We got the following conclusions

(1) Using the log-linear model the traditional singleprobability model can be transformed into multi-probability adaptive model which can efficiently usethe advantages of a variety of probabilistic models

0 10 20 30 40 50 600

1

2

3

4

5

6


Opt

imal

val

ueIterative process of the fish swarm algorithm

AFSALAFSA

Figure 14 Ackley function

and enhance decision making ability of behaviorselection

(2) Adaptive movement behavior with reasonable settingaccording to diversity of fish swarm can improve theperformance of basic artificial fish swarm algorithm

(3) Population inhibition behavior is introduced whichcan greatly accelerate the convergence speed

(4) Population expansion behavior can improve globaloptimization capability and avoid premature conver-gence

From the experiment we can find out that the behavior offishes is essential for better performance We will introduce


AFSALAFSA

0 10 20 30 40 50 60The number of iterations

0

05

1

15

2

25

3

35

Opt

imal

val

ue


Figure 15 Shaffer function

some new behaviors in future work and apply this idea toother optimization tasks

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (Grant no 61005052) the Funda-mental Research Funds for the Central Universities (Grantno 2010121068) the Natural Science Foundation of FujianProvince of China (Grant no 2011J01369) and the Scienceand Technology Project of Quanzhou (Grant no 2012Z91)

References

[1] X L Li S H Feng and J X Qian ldquoParameter tuningmethod ofrobust pID controller based on artificial fish school algorithmrdquoChinese Journal of Information and Control vol 33 no 1 pp112ndash115 2004

[2] X L Li F Lu G H Tian and J X Qian ldquoApplications ofartificial fish school algorithm in combinatorial optimizationproblemsrdquo Chinese Journal of Shandong University (EngineeringScience) vol 34 no 5 pp 65ndash67 2004

[3] X L Li and J X Qian ldquoStudies on artificial fish swarm opti-mization algorithm based on decomposition and coordinationtechniquesrdquo Chinese Journal of Circuits and Systems vol 8 no1 pp 1ndash6 2003

[4] W J Tian and Y Tian ldquoAn improved artificial fish swarm algo-rithm for resource levelingrdquo in Proceedings of the InternationalConference on Management and Service Science (MASS rsquo09) pp1ndash6 Wuhan China September 2009

[5] T X Zheng and J Q Li ldquoMulti-robot task allocation andscheduling based on fish swarm algorithmrdquo in Proceedings ofthe 8th World Congress on Intelligent Control and Automation(WCICA rsquo10) pp 6681ndash6685 Jinan China July 2010

[6] W J Tian and J C Liu ldquoAn improved artificial fish swarmalgorithm for multi robot task schedulingrdquo in Proceedings ofthe 5th International Conference onNatural Computation (ICNCrsquo09) pp 127ndash130 August 2009

[7] M F Zhang C Shao F C Li Y Gan and J M Sun ldquoEvolvingneural network classifiers and feature subset using artificial fishswarmrdquo in Proceedings of the IEEE International Conferenceon Mechatronics and Automation (ICMA rsquo06) pp 1598ndash1602Luoyang China June 2006

[8] W J Tian Y Geng J C Liu and L Ai ldquoOptimal parameteralgorithm for image segmentationrdquo in Proceedings of the 2ndInternational Conference on Future Information Technology andManagement Engineering (FITME rsquo09) pp 179ndash182 SanyaChina December 2009

[9] C-J Wang and S-X Xia ldquoApplication of probabilistic causal-effect model based artificial fish-swarm algorithm for faultdiagnosis in mine hoistrdquo Journal of Software vol 5 no 5 pp474ndash481 2010

[10] D Y Chen L Shao Z Zhang and X Y Yu ldquoAn image recon-struction algorithm based on artificial fish-swarm for electricalcapacitance tomography systemrdquo in Proceedings of the 6thInternational Forum on Strategic Technology (IFOST rsquo11) pp1190ndash1194 Harbin China August 2011

[11] Y M Cheng M Y Jiang and D F Yuan ldquoNovel clusteringalgorithms based on improved artificial fish swarm algorithmrdquoin Proceedings of the 6th International Conference on FuzzySystems and Knowledge Discovery (FSKD rsquo09) pp 141ndash145Tianjin China August 2009

[12] X L Chu Y Zhu J T Shi and J Q Song ldquoMethod of imagesegmentation based on fuzzyC-means clustering algorithm andartificial fish swarm algorithmrdquo in Proceedings of the IEEE Inter-national Conference on Intelligent Computing and IntegratedSystems (ICISS rsquo10) pp 254ndash257 Guilin China October 2010

[13] X Li ldquoA clustering algorithm based on artificial fish schoolrdquoin Proceedings of the 2nd International Conference on ComputerEngineering and Technology (ICCET rsquo10) vol 7 pp V7766ndashV7769 Chengdu China April 2010

[14] Y LuoWWei and S XWang ldquoOptimization of PID controllerparameters based on an improved artificial fish swarm algo-rithmrdquo in Proceedings of the 3rd International Workshop onAdvanced Computational Intelligence (IWACI rsquo10) pp 328ndash332Suzhou China August 2010

[15] D Yazdani H Nabizadeh EM Kosari and A N Toosi ldquoColorquantization using modified artificial fish swarm algorithmrdquo inAI 2011 Advances in Artificial Intelligence Proceedings of the24th Australasian Joint Conference Perth Australia December5ndash8 2011 vol 7106 of Lecture Notes in Computer Science pp382ndash391 Springer Berlin Germany 2011

[16] Z H Huang and Y D Chen ldquoA two-stage exon recognitionmodel based on synergetic neural networkrdquoComputational andMathematical Methods inMedicine vol 2014 Article ID 5031327 pages 2014

[17] D Bing and D Wen ldquoScheduling arrival aircrafts on multi-runway based on an improved artificial fish swarm algorithmrdquoin Proceedings of the International Conference on Computationaland Information Sciences (ICCIS rsquo10) pp 499ndash502 ChengduChina December 2010


[18] A L Qi HWMa and T Liu ldquoA weak signal detectionmethodbased on artificial fish swarm optimized matching pursuitrdquo inProceedings of the World Congress on Computer Science andInformation Engineering pp 185ndash189 2009

[19] J Zhang and L Shen ldquoAn improved fuzzy c-means clusteringalgorithm based on shadowed sets and PSOrdquo ComputationalIntelligence and Neuroscience vol 2014 Article ID 368628 10pages 2014

[20] X Song C R Wang J Wang and B Zhang ldquoA hierarchicalrouting protocol based on AFSO algorithm for WSNrdquo in Pro-ceedings of the International Conference onComputerDesign andApplications (ICCDA rsquo10) pp V2-635ndashV2-639 QinhuangdaoChina June 2010

[21] T Liu A L Qi Y B Hou and X T Chang ldquoFeature opti-mization based on artificial fish-swarm algorithm in intrusiondetectionsrdquo in Proceedings of the International Conference onNetworks Security Wireless Communications and Trusted Com-puting pp 542ndash545 2009

[22] W Guo G H Fang and X F Huang ldquoAn improved chaoticartificial fish swarm algorithm and its application in optimizingcascade hydropower stationsrdquo inProceedings of the InternationalConference on Business Management and Electronic Information(BMEI rsquo11) vol 3 pp 217ndash220 Guangzhou China May 2011

[23] X Z Gao YWu K Zenger and XHuang ldquoA knowledge-basedArtificial Fish-swarm Algorithmrdquo in Proceedings of the 13thIEEE International Conference on Computational Science andEngineering (CSE rsquo10) pp 327ndash332HongKong December 2010

[24] XMa ldquoApplication of adaptive hybrid sequences niche artificialfish swarm algorithm in vehicle routing problemrdquo in Proceed-ings of the 2nd International Conference on Future Computer andCommunication (ICFCC rsquo10) vol 1 pp V1-654ndashV1-658WuhanChina May 2010

[25] A M A Rocha T F M C Martins and E M G P FernandesldquoAn augmented Lagrangian fish swarm basedmethod for globaloptimizationrdquo Journal of Computational andAppliedMathemat-ics vol 235 no 16 pp 4611ndash4620 2011

[26] F J Och ldquoMinimum error rate training in statistical machinetranslationrdquo in Proceedings of the 41st Annual Meeting of theAssociation forComputational Linguistics (ACL rsquo03) pp 160ndash167Sapporo Japan July 2003

[27] C R Wang C L Zhou and J W Ma ldquoAn improved artificialfish swarm algorithm and its application in feed-forward neuralnetworksrdquo in Proceedings of the 4th International Conferenceon Machine Learning and Cybernetics pp 18ndash21 GuangzhouChina 2005

[28] E M G P Fernandes T F M C Martins and A M AC Rocha ldquoFish swarm intelligent algorithm for bound con-strained global optimizationrdquo in Proceedings of the InternationalConference on Computational and Mathematical Methods inScience and Engineering (CMMSE rsquo09) pp 1ndash3 June 2009

[29] L Wang and L J Ma ldquoA hybrid artificial fish swarm algorithmfor Bin-packing problemrdquo in Proceedings of the InternationalConference on Electronic and Mechanical Engineering and Infor-mation Technology (EMEIT rsquo11) pp 27ndash29 Harbin ChinaAugust 2011

[30] K C Zhu andM Y Jiang ldquoQuantum artificial fish swarm algo-rithmrdquo in Proceedings of the 8th World Congress on IntelligentControl andAutomation (WCICA rsquo10) pp 1ndash5 Jinan China July2010

[31] W Xiu-Xi Z Hai-Wen and Z Yong-Quan ldquoHybrid artificialfish school algorithm for solving ill-conditioned linear systems

of equationsrdquo in Proceedings of the IEEE International Confer-ence on Intelligent Computing and Intelligent Systems (ICIS rsquo10)vol 1 pp 290ndash294 Xiamen China October 2010

[32] M Y Jiang and YM Cheng ldquoSimulated annealing artificial fishswarm algorithmrdquo in Proceedings of the 8th World Congress onIntelligent Control and Automation (WCICA rsquo10) pp 1590ndash1593Jinan China July 2010

[33] F J Och and H Ney ldquoThe alignment template approach tostatistical machine translationrdquo Computational Linguistics vol30 no 4 pp 417ndash449 2004

[34] G Dersquoath ldquoThe multinomial diversity model linking Shannondiversity to multiple predictorsrdquo Ecology vol 93 no 10 pp2286ndash2296 2012

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



are presented in Section 4 In Section 5 some experimentaltests results and conclusions are given Section 6 concludesthe paper

2 Related Work

In recent years researchers have made some attempts toimprove the performance of artificial fish swarm algorithmIn [22] chaos optimization is first employed to initialize theposition of individual artificial fish and applied to obtain theneighborhood of the global optimum solution Gao et alreported an improved artificial fish swarm algorithm withcrossover operator based on parentsrsquo characteristics [23] In[24] the concept of ecological niche is also being intro-duced to overcome the shortcoming of traditional artificialfish swarm algorithm to obtain optimal solution Rochaet al reported an augmented Lagrangian methodology witha stochastic population based algorithm which solves asequence of simple bound global optimization subproblemsusing a fish swarm intelligent algorithm [25]

Some researchers have tried to improve the performanceof AFSA by combining different algorithm with AFSA Animproved AFSO (IAFSO) [27] is proposed to train forwardneural network using a hybrid of artificial fish swarm algo-rithm and particle swarm optimization In [28] some newideas are proposed which focus on a set of movements offishes Wang and Ma reported a hybrid artificial fish swarmalgorithm which is combined with CF and artificial fishswarm algorithm to solve the Bin packing problem [29] In[30] quantum rotation gate is used to update the position ofartificial fish swarm which employs the quantum nongate tospeed up the convergenceThe experimental results show thatthe performance of AFSA is significantly improved A hybridalgorithmbased on particle swarmoptimization and artificialfish swarm algorithm [31] is reported which owns a goodglobally convergent performance with a faster convergentrate In [32] a simulated annealing artificial fish swarm algo-rithm is proposed which can obtain better optimizationprecision and convergence speed

Log-linear model is a mathematical model which iswidely used in part-of-speech tagging statistical machinetranslation and other fields Och and Ney introduced thelog-linear model for statistical machine translation (SMT) inwhich translation is considered as optimization problem Itsefficiency is comparable to the globalmethod [33] In [34] themultinomial diversity model (MDM) based on generalizedlinear models is proposed which can be used for modelselection and graphical and numerical interpretation

In this paper we proposed an improved algorithm basedon log-linear model which can transform the traditionalsingle probability model to adaptive model

3 Introduction to AFSA

Suppose 119883 is the state vector of artificial fish swarm Let119883 = (119909

1 1199092 119909

119899) where 119909

1 1199092 119909

119899is status of fishes

The action of artificial fish occurs only in the radius of a circlewith vision The artificial fish realizes external perception byits vision shown in Figure 1

Step

Xn1Xn2

X

X

Xnext

Figure 1 Vision concept of the artificial fish

Suppose 119883V is the visual position at some moment 119883V =

(119909V1 119909

V2 119909

V119899) 119883next is the new position Let Step be the

moving step length Visual represents the visual distance and120575 is the crowd factor (0 lt 120575 lt 1)Then themovement processis represented as

119883V = 119883119894 + Visual times rand () 119894 isin (0 119899]

119883next = 119883 +119883V minus 1198831003817100381710038171003817119883V minus 119883

1003817100381710038171003817


where rand() produces random numbers between 0 and 1The basic behaviors of artificial fish are defined as follows

31 Prey Behavior Prey behavior is a basic biological behav-ior to find food Suppose 119883

119894is the current state of artificial

fish and 119883119895is a random state in its visual distance and 119884 is

the food concentration

119883119895= 119883119894+ Visual times rand () (2)

If 119884119894lt 119884119895 it goes forward a step in this direction

119883119905+1

119894= 119883119905

119894+

119883119895minus 119883119905

119894

10038171003817100381710038171003817119883119895minus 119883119905

119894

10038171003817100381710038171003817


32 Swarm Behavior Suppose 119883119888is the center position and

the number of artificial fish is 119899119891 If 119899119891119899 lt 120575 and 119884

119888gt 119884119894 it

goes forward a step to the companion center otherwise per-form prey behavior

119883119905+1

119894= 119883119905

119894+119883119888minus 119883119905

119894

1003817100381710038171003817119883119888 minus 119883119905

119894

1003817100381710038171003817


33 Follow Behavior Suppose119883max is the optimal state fromvisual neighbors and the number of partners of119883max is 119899119891 If


119899119891119899 lt 120575 and119884



119883119905+1

119894= 119883119905

119894+119883max minus 119883

119905

119894

1003817100381710038171003817119883max minus 119883119905

119894

1003817100381710038171003817



119883119905+1

119894= 119883119905



If (119884119898max minus 119884119899

max lt 119890119901119904)

119883119905+1

119894= 119883119905












1 1199092 119909

119899) where 119909

1 1199092 119909



119875119903(119905) =

sum119898exp [120573

119898ℎ119898(119905)]

sum119905sum119898exp [120573

119898ℎ119898(119905)] (8)





1(119905)


ℎ1(119905) =

sum119873

119894=1

10038161003816100381610038161003816119891 (119909119894) minus 119891119905

avg10038161003816100381610038161003816

119873 lowastmax1le119895le119873

(10038161003816100381610038161003816119891 (119909119895) minus 119891119905avg

10038161003816100381610038161003816)

(9)


119894 Consider ℎ

1(119905) isin


1(119905) ≪ 1means



ℎ2(119905) =

sum119873

119894=1radicsum119863

119889(119909119894119889minus 119909119889)2

119873 timesmax1le119895le119873

(radicsum119863

119889(119909119895119889minus 119909119889)2

)

(10)






119894119895= 119883119894minus 119883119895 and 119894 and



ℎ3(119905) =

sum119873

119895=1119889119894119895

119873 timesmax1le119894119895le119873

(119889119894119895)

119894 = 1 2 119873 (11)


43 New Behaviors


1 1199082 119908

119899] here119908

119894(119894 = 1 2 119899)


120596119894= 06 lowast 119890





0 02 04 06 08 1

04

05

06

07

08

09

1

x

120572 = 2

120572 = 6

120572 = 10



+ 03


119894



119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)

119883119895minus 119883119905

119894

10038171003817100381710038171003817119883119895minus 119883119905

119894

10038171003817100381710038171003817



119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)119883119888minus 119883119905

119894

1003817100381710038171003817119883119888 minus 119883119905

119894

1003817100381710038171003817



119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)119883max minus 119883

119905

119894

1003817100381710038171003817119883max minus 119883119905

119894

1003817100381710038171003817


(15)

If (119875119903(119905) gt 119877








Raw fishes



Yes

NoPr(t) gt R2









3= 02 in the







5 Experiment







119903(119905) gt 119877



119903(119905) gt 119877


(c) If 119875119903(119905) lt 119877







119899

sum

119905=1

1199092

119905 0


119899

sum

119905=1

(1199092

119905minus 10 cos (2120587119909

119905) + 10) 0


1

4000

119899

sum

119905=1

(119909119905minus 100)

2minus

119899

prod

119905=1

cos(119909119905minus 100

radic119905) + 1 0



119905=1119909119905

2119899minus 119890sum119899

119905=1cos (2120587119909

119905)119899 0


(sinradic1199091

2 + 1199092

2)2

minus 05

(1 + 0001 (1199091

2 + 1199092

2))2

0

Raw fishes


Yes

No

Yes



Yi gt Ymax


Pr(t) lt R3













Yes Yes Yes

Start

Yes

No



End

No

Log-linear model






Adaptivemove

behavior


minus10minus5

05

10

minus10

minus5

0

510

minus150

minus100

minus50

0





minus10minus5

05



0


minus10minus5

05

10

minus10minus5

05

10minus25

minus2

minus15

minus1

minus05

0


minus10minus5

05

10

minus10minus5

05

10minus20

minus15

minus10

minus5

0

5




minus1

minus08

minus06

minus04

minus02

0

minus10minus5

05

10

minus10minus5

05

10

5











0 10 20 30 40 50 600

2

4

6

8

10

12

14


Opt

imal

val

ue


AFSALAFSA


AFSALAFSA

0 10 20 30 40 50 6025

30

35

40

45

50

55

60

65

70

75


Opt

imal

val

ue













0 10 20 30 40 50 60244

246

248

25

252

254

256


Opt

imal

val

ue


AFSALAFSA


6 Conclusions




0 10 20 30 40 50 600

1

2

3

4

5

6


Opt

imal

val


AFSALAFSA








AFSALAFSA


0

05

1

15

2

25

3

35

Opt

imal

val

ue






Acknowledgments


References












































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




119899119891119899 lt 120575 and119884



119883119905+1

119894= 119883119905

119894+119883max minus 119883

119905

119894

1003817100381710038171003817119883max minus 119883119905

119894

1003817100381710038171003817



119883119905+1

119894= 119883119905



If (119884119898max minus 119884119899

max lt 119890119901119904)

119883119905+1

119894= 119883119905












1 1199092 119909

119899) where 119909

1 1199092 119909



119875119903(119905) =

sum119898exp [120573

119898ℎ119898(119905)]

sum119905sum119898exp [120573

119898ℎ119898(119905)] (8)





1(119905)


ℎ1(119905) =

sum119873

119894=1

10038161003816100381610038161003816119891 (119909119894) minus 119891119905

avg10038161003816100381610038161003816

119873 lowastmax1le119895le119873

(10038161003816100381610038161003816119891 (119909119895) minus 119891119905avg

10038161003816100381610038161003816)

(9)


119894 Consider ℎ

1(119905) isin


1(119905) ≪ 1means



ℎ2(119905) =

sum119873

119894=1radicsum119863

119889(119909119894119889minus 119909119889)2

119873 timesmax1le119895le119873

(radicsum119863

119889(119909119895119889minus 119909119889)2

)

(10)






119894119895= 119883119894minus 119883119895 and 119894 and



ℎ3(119905) =

sum119873

119895=1119889119894119895

119873 timesmax1le119894119895le119873

(119889119894119895)

119894 = 1 2 119873 (11)


43 New Behaviors


1 1199082 119908

119899] here119908

119894(119894 = 1 2 119899)


120596119894= 06 lowast 119890





0 02 04 06 08 1

04

05

06

07

08

09

1

x

120572 = 2

120572 = 6

120572 = 10



+ 03


119894



119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)

119883119895minus 119883119905

119894

10038171003817100381710038171003817119883119895minus 119883119905

119894

10038171003817100381710038171003817



119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)119883119888minus 119883119905

119894

1003817100381710038171003817119883119888 minus 119883119905

119894

1003817100381710038171003817



119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)119883max minus 119883

119905

119894

1003817100381710038171003817119883max minus 119883119905

119894

1003817100381710038171003817


(15)

If (119875119903(119905) gt 119877








Raw fishes



Yes

NoPr(t) gt R2









3= 02 in the







5 Experiment







119903(119905) gt 119877



119903(119905) gt 119877


(c) If 119875119903(119905) lt 119877







119899

sum

119905=1

1199092

119905 0


119899

sum

119905=1

(1199092

119905minus 10 cos (2120587119909

119905) + 10) 0


1

4000

119899

sum

119905=1

(119909119905minus 100)

2minus

119899

prod

119905=1

cos(119909119905minus 100

radic119905) + 1 0



119905=1119909119905

2119899minus 119890sum119899

119905=1cos (2120587119909

119905)119899 0


(sinradic1199091

2 + 1199092

2)2

minus 05

(1 + 0001 (1199091

2 + 1199092

2))2

0

Raw fishes


Yes

No

Yes



Yi gt Ymax


Pr(t) lt R3













Yes Yes Yes

Start

Yes

No



End

No

Log-linear model






Adaptivemove

behavior


minus10minus5

05

10

minus10

minus5

0

510

minus150

minus100

minus50

0





minus10minus5

05



0


minus10minus5

05

10

minus10minus5

05

10minus25

minus2

minus15

minus1

minus05

0


minus10minus5

05

10

minus10minus5

05

10minus20

minus15

minus10

minus5

0

5




minus1

minus08

minus06

minus04

minus02

0

minus10minus5

05

10

minus10minus5

05

10

5











0 10 20 30 40 50 600

2

4

6

8

10

12

14


Opt

imal

val

ue


AFSALAFSA


AFSALAFSA

0 10 20 30 40 50 6025

30

35

40

45

50

55

60

65

70

75


Opt

imal

val

ue













0 10 20 30 40 50 60244

246

248

25

252

254

256


Opt

imal

val

ue


AFSALAFSA


6 Conclusions




0 10 20 30 40 50 600

1

2

3

4

5

6


Opt

imal

val


AFSALAFSA








AFSALAFSA


0

05

1

15

2

25

3

35

Opt

imal

val

ue






Acknowledgments


References












































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0 02 04 06 08 1

04

05

06

07

08

09

1

x

120572 = 2

120572 = 6

120572 = 10



+ 03


119894



119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)

119883119895minus 119883119905

119894

10038171003817100381710038171003817119883119895minus 119883119905

119894

10038171003817100381710038171003817



119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)119883119888minus 119883119905

119894

1003817100381710038171003817119883119888 minus 119883119905

119894

1003817100381710038171003817



119883119905+1

119894= 119908119894119883119905

119894+ (1 minus 119908

119894)119883max minus 119883

119905

119894

1003817100381710038171003817119883max minus 119883119905

119894

1003817100381710038171003817


(15)

If (119875119903(119905) gt 119877








Raw fishes



Yes

NoPr(t) gt R2









3= 02 in the







5 Experiment







119903(119905) gt 119877



119903(119905) gt 119877


(c) If 119875119903(119905) lt 119877







119899

sum

119905=1

1199092

119905 0


119899

sum

119905=1

(1199092

119905minus 10 cos (2120587119909

119905) + 10) 0


1

4000

119899

sum

119905=1

(119909119905minus 100)

2minus

119899

prod

119905=1

cos(119909119905minus 100

radic119905) + 1 0



119905=1119909119905

2119899minus 119890sum119899

119905=1cos (2120587119909

119905)119899 0


(sinradic1199091

2 + 1199092

2)2

minus 05

(1 + 0001 (1199091

2 + 1199092

2))2

0

Raw fishes


Yes

No

Yes



Yi gt Ymax


Pr(t) lt R3













Yes Yes Yes

Start

Yes

No



End

No

Log-linear model






Adaptivemove

behavior


minus10minus5

05

10

minus10

minus5

0

510

minus150

minus100

minus50

0





minus10minus5

05



0


minus10minus5

05

10

minus10minus5

05

10minus25

minus2

minus15

minus1

minus05

0


minus10minus5

05

10

minus10minus5

05

10minus20

minus15

minus10

minus5

0

5




minus1

minus08

minus06

minus04

minus02

0

minus10minus5

05

10

minus10minus5

05

10

5











0 10 20 30 40 50 600

2

4

6

8

10

12

14


Opt

imal

val

ue


AFSALAFSA


AFSALAFSA

0 10 20 30 40 50 6025

30

35

40

45

50

55

60

65

70

75


Opt

imal

val

ue













0 10 20 30 40 50 60244

246

248

25

252

254

256


Opt

imal

val

ue


AFSALAFSA


6 Conclusions




0 10 20 30 40 50 600

1

2

3

4

5

6


Opt

imal

val


AFSALAFSA








AFSALAFSA


0

05

1

15

2

25

3

35

Opt

imal

val

ue






Acknowledgments


References












































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119903(119905) gt 119877



119903(119905) gt 119877


(c) If 119875119903(119905) lt 119877







119899

sum

119905=1

1199092

119905 0


119899

sum

119905=1

(1199092

119905minus 10 cos (2120587119909

119905) + 10) 0


1

4000

119899

sum

119905=1

(119909119905minus 100)

2minus

119899

prod

119905=1

cos(119909119905minus 100

radic119905) + 1 0



119905=1119909119905

2119899minus 119890sum119899

119905=1cos (2120587119909

119905)119899 0


(sinradic1199091

2 + 1199092

2)2

minus 05

(1 + 0001 (1199091

2 + 1199092

2))2

0

Raw fishes


Yes

No

Yes



Yi gt Ymax


Pr(t) lt R3













Yes Yes Yes

Start

Yes

No



End

No

Log-linear model






Adaptivemove

behavior


minus10minus5

05

10

minus10

minus5

0

510

minus150

minus100

minus50

0





minus10minus5

05



0


minus10minus5

05

10

minus10minus5

05

10minus25

minus2

minus15

minus1

minus05

0


minus10minus5

05

10

minus10minus5

05

10minus20

minus15

minus10

minus5

0

5




minus1

minus08

minus06

minus04

minus02

0

minus10minus5

05

10

minus10minus5

05

10

5











0 10 20 30 40 50 600

2

4

6

8

10

12

14


Opt

imal

val

ue


AFSALAFSA


AFSALAFSA

0 10 20 30 40 50 6025

30

35

40

45

50

55

60

65

70

75


Opt

imal

val

ue













0 10 20 30 40 50 60244

246

248

25

252

254

256


Opt

imal

val

ue


AFSALAFSA


6 Conclusions




0 10 20 30 40 50 600

1

2

3

4

5

6


Opt

imal

val


AFSALAFSA








AFSALAFSA


0

05

1

15

2

25

3

35

Opt

imal

val

ue






Acknowledgments


References












































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Yes Yes Yes

Start

Yes

No



End

No

Log-linear model






Adaptivemove

behavior


minus10minus5

05

10

minus10

minus5

0

510

minus150

minus100

minus50

0





minus10minus5

05



0


minus10minus5

05

10

minus10minus5

05

10minus25

minus2

minus15

minus1

minus05

0


minus10minus5

05

10

minus10minus5

05

10minus20

minus15

minus10

minus5

0

5




minus1

minus08

minus06

minus04

minus02

0

minus10minus5

05

10

minus10minus5

05

10

5











0 10 20 30 40 50 600

2

4

6

8

10

12

14


Opt

imal

val

ue


AFSALAFSA


AFSALAFSA

0 10 20 30 40 50 6025

30

35

40

45

50

55

60

65

70

75


Opt

imal

val

ue













0 10 20 30 40 50 60244

246

248

25

252

254

256


Opt

imal

val

ue


AFSALAFSA


6 Conclusions




0 10 20 30 40 50 600

1

2

3

4

5

6


Opt

imal

val


AFSALAFSA








AFSALAFSA


0

05

1

15

2

25

3

35

Opt

imal

val

ue






Acknowledgments


References












































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




minus1

minus08

minus06

minus04

minus02

0

minus10minus5

05

10

minus10minus5

05

10

5











0 10 20 30 40 50 600

2

4

6

8

10

12

14


Opt

imal

val

ue


AFSALAFSA


AFSALAFSA

0 10 20 30 40 50 6025

30

35

40

45

50

55

60

65

70

75


Opt

imal

val

ue













0 10 20 30 40 50 60244

246

248

25

252

254

256


Opt

imal

val

ue


AFSALAFSA


6 Conclusions




0 10 20 30 40 50 600

1

2

3

4

5

6


Opt

imal

val


AFSALAFSA








AFSALAFSA


0

05

1

15

2

25

3

35

Opt

imal

val

ue






Acknowledgments


References












































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










0 10 20 30 40 50 60244

246

248

25

252

254

256


Opt

imal

val

ue


AFSALAFSA


6 Conclusions




0 10 20 30 40 50 600

1

2

3

4

5

6


Opt

imal

val


AFSALAFSA








AFSALAFSA


0

05

1

15

2

25

3

35

Opt

imal

val

ue






Acknowledgments


References












































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




AFSALAFSA


0

05

1

15

2

25

3

35

Opt

imal

val

ue






Acknowledgments


References












































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



research article log-linear model based behavior selection...

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