A REVIEW OF ARTIFICIAL FISH SWARM OPTIMIZATION METHODS AND APPLICATIONS

Transcription

1 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 A REVIEW OF ARTIFICIAL FISH SWARM OPTIMIZATION METHODS AND APPLICATIONS 1 Mehd Neshat, 2 Al Adel, 3 Ghodrat Sepdnam, 4 Mehd Sargolzae, 5 Adel Naaran Toos 1 Department of computer scence, Shrvan Branch, Islamc Azad Unversty, Shrvan, Iran Emals: neshat_mehd@eee.org 2 Department of computer Engneerng, Shrvan Branch, Islamc Azad Unversty, Shrvan, Iran Emal: Adel_a@yahoo.com 3 Department of computer scence and Hardware Engneerng, Shrvan Branch, Islamc Azad Unversty, Shrvan, Iran Emals: sepdnam@ferdows.um.ac.r 4 Department of computer scence, Shrvan Branch, Islamc Azad Unversty, Shrvan, Iran Emals: m.sargolzae@uva.nl 5 Department of computer scence and software Engneerng, Shrvan Branch, Islamc Azad Unversty, Shrvan, Iran Emals: adelna@csse.unmelb.com.au Submtted: Jan. 10, 2012 Accepted: Feb. 9, 2012 Publshed: mar. 1, 2012 Abstract- The Swarm Intellgence s a new and modern method employed n optmzaton problems. The Swarm Intellgence method s based on the en masse movement of lvng anmals lke brds, fshes, ants and other socal anmals. Mgraton, seekng for food and fghtng wth enemes are 107

2 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons socal behavors of anmals. Optmzaton prncple s seen n these anmals. The Artfcal Fsh Swarm Optmzaton (AFSA) method s one of the Swarm Intellgence approaches that works based on the populaton and stochastc search. Fshes show very ntellgently socal behavors. Ths algorthm s one of the best approaches of the Swarm Intellgence method wth consderable advantages lke hgh convergence speed, flexblty, error tolerance and hgh accuracy. ths paper revew the AFSA algorthm, ts evoluton stages from the start pont up to now, mprovements and applcatons n varous felds lke optmzaton, control, mage processng, data mnng, mprovng neural networks, networks, schedulng, and sgnal processng and so on. Also, varous methods combnng the AFSA wth other optmzaton methods lke PSO, Fuzzy Logc, Cellular Learnng Automata or ntellgent search methods lke Tabu search, Smulated Annealng, Chaos Search and etc. Index terms: Artfcal Fsh Swarm Optmzaton, Swarm Optmzaton, Natural Computng. I. INTRODUCTION Most speces of anmals show socal behavors. In some speces ths s the top member of the group whch leads all members of that group. For example, ths behavor s very apparent n lons, monkeys and deer. However, there are other knds of anmals whch lve n groups but have no leader. In ths type of anmals each member has a self organzer behavor whch enables t to move around ts envronment and response to ts natural needs wth no need to leader lke brds, fshes and sheep droves. Ths type of anmals has no knowledge about ther group and envronment. Instead, they can move n the envronment va exchangng data wth ther adacent members. Ths smple nteracton between partcles makes group behavor more sophstcated as f we are lookng for a partcle n a wde envronment. Ths revew consders Artfcal Fsh Swarm Optmzaton (AFSO), a relatvely recent addton to the feld of natural computng, that has elements nspred by the socal behavors of natural swarms, and connectons wth evolutonary computaton. AFSO has found wdespread applcaton n complex optmzaton domans, and s currently a maor research topc, offerng an alternatve to the more establshed evolutonary computaton technques that may be appled n many of the same domans. Ths paper s structured as follows. Secton 2 brefly revews the general formulaton of AFSO. Secton 3 revews the mproved of AFSO.Secton 4 revews the motvatons for, and research nto, hybrd algorthms, many of whch nvolve evolutonary technques. Secton 5 108

3 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 hghlghts some recent research nto the applcaton of AFSO to combnatoral problems. Secton 6 concludes. II. GENERAL FORMULATION In nature, the fsh can fnd the more nutrtous area by ndvdual search or followng after other fsh, the area wth much more fsh s generally most nutrtous. The basc dea of the AFSO s to mtate the fsh behavors such as prayng, swarmng, and followng wth local search of fsh ndvdual for reachng the global optmum [5]. The envronment where an AF lves s manly the soluton space and s the states of other AFs. Its next behavor depends on ts current state and ts local envronmental state (ncludng the qualty of the queston solutons at present and the states of nearby companons). An AF would nfluence the envronment va ts own actvtes and ts companons' actvtes. A new evolutonary computaton technque, Artfcal Fsh Swarm Optmzaton (AFSO) was frst proposed n 2002 [1]. AFSO possess smlar attractve features of genetc algorthm (GA) such as ndependence from gradent nformaton of the obectve functon, the ablty to solve complex nonlnear hgh dmensonal problems. Furthermore, they can acheve faster convergence speed and requre few parameters to be adusted. Whereas the AFSO does not possess the crossover and mutaton processes used n GA, so t could be performed more easly. AFSO s also an optmzer based on populaton. The system s ntalzed frstly n a set of randomly generated potental solutons, and then performs the search for the optmum one teratvely [6]. Artfcal Fsh (AF) s a fcttous entty of true fsh, whch s used to carry on the analyss and explanaton of problem, and can be realzed by usng anmal ecology concept. Wth the ad of the obect-orented analytcal method, we can regard the artfcal fsh as an entty encapsulated wth one s own data and a seres of behavors, whch can accept amazng nformaton of envronment by sense organs, and do stmulant reacton by the control of tal and fn. The envronment n whch the artfcal fsh lves s manly the soluton space and the states of other artfcal fsh. Its next behavor depends on ts current state and ts envronmental state (ncludng the qualty of the queston solutons at present and the states of other companons), and t nfluences the envronment va ts own actvtes and other companons actvtes [3]. 109

4 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons The AF realzes external percepton by ts vson shown n Fgure.1. s the current state of a AF, Vsual s the vsual dstance, and v s the vsual poston at some moment. If the state at the vsual poston s better than the current state, t goes forward a step n ths drecton, and arrves the next state; otherwse, contnues an nspectng tour n the vson. The greater number of nspectng tour the AF does, the more knowledge about overall states of the vson the AF obtans. Certanly, t does not need to travel throughout complex or nfnte states, whch s helpful to fnd the global optmum by allowng certan local optmum wth some uncertanty. Fgure. 1. Vson concept of the Artfcal Fsh v v v Let = x, x,..., x ) and = ( x 1, x 2,..., x n ) then ths process can be expressed as follows: ( 1 2 n ( ), ( 0 n] v x = x + Vsual. rand, (1) next v = +. Step. rand(). (2) v v Where Rand ( ) produces random numbers between 0 and 1, Step s the step length, and x s the optmzng varable, n s the number of varables. The AF model ncludes two parts (varables and functons). The varables nclude: s the current poston of the AF, Step s the movng step length, Vsual represents the vsual dstance, try_number s the try number and δ s the crowd factor (0 < δ < 1). The functons nclude the behavors of the AF: AF_Prey, AF_Swarm, AF_Follow, AF_Move, AF_Leap and AF_Evaluate. a. The Basc functons of AFSA Fsh usually stay n the place wth a lot of food, so we smulate the behavors of fsh based on ths characterstc to fnd the global optmum, whch s the basc dea of the AFSO. The basc behavors of AF are defned (9, 10) as follows for maxmum: 110

5 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 AF_Prey: Ths s a basc bologcal behavor that tends to the food; generally the fsh perceves the concentraton of food n water to determne the movement by vson or sense and then chooses the tendency. Behavor descrpton: Let be the AF current state and select a state randomly n ts vsual dstance, Y s the food concentraton (obectve functon value), the greater Vsual s, the more easly the AF fnds the global extreme value and converges. = + Vsual rand( ) (3). If Y < Y n the maxmum problem, t goes forward a step n ths drecton; ( t+ 1) = ( t) + ( t) ( t). Step. rand(). (4) Otherwse, select a state randomly agan and udge whether t satsfes the forward condton. If t cannot satsfy after try_number tmes, t moves a step randomly. When the try_number s small n AF_Prey, the AF can swm randomly, whch makes t flee from the local extreme value feld. ( t + 1) ( t) = + Vsual rand( ) (5). AF_Swarm: The fsh wll assemble n groups naturally n the movng process, whch s a knd of lvng habts n order to guarantee the exstence of the colony and avod dangers. Behavor descrpton: Let be the AF current state, c be the center poston and n f be the number of ts companons n the current neghborhood (d <Vsual), n s total fsh number. If Yc > Y and n f n < δ, whch means that the companon center has more food (hgher ftness functon value) and s not very crowded, t goes forward a step to the companon center; ( t+ 1) = ( t) + c c ( t) ( t). Step. rand(). (6) Otherwse, executes the preyng behavor. The crowd factor lmts the scale of swarms, and more AF only cluster at the optmal area, whch ensures that AF move to optmum n a wde feld. AF_Follow: In the movng process of the fsh swarm, when a sngle fsh or several ones fnd food, the neghborhood partners wll tral and reach the food quckly. Behavor descrpton: Let be the AF current state, and t explores the companon n the neghborhood (d <Vsual), whch has the greatest Y. If Y > Y and n f n < δ, whch means that the companon 111

6 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons state has hgher food concentraton (hgher ftness functon value) and the surroundngs s not very crowded, t goes forward a step to the companon, ( t+ 1) = ( t) + ( t) ( t). Step. rand(). (7) Otherwse, executes the preyng behavor. AF_Move: Fsh swm randomly n water; n fact, they are seekng food or companons n larger ranges. Behavor descrpton: Chooses a state at random n the vson, then t moves towards ths state, n fact, t s a default behavor of AF_Prey. + 1) ( t) = + Vsual rand( ) (8) ( t. AF_Leap: Fsh stop somewhere n water, every AF s behavor result wll gradually be the same, the dfference of obectve values (food concentraton, FC) become smaller wthn some teratons, t mght fall nto local extremum change the parameters randomly to the stll states for leapng out current state. Behavor descrpton: If the obectve functon s almost the same or dfference of the obectve functons s smaller than a proporton durng the gven (m-n) teratons, Chooses some fsh randomly n the whole fsh swarm, and set parameters randomly to the selected AF. The β s a parameter or a functon that can make some fsh have other abnormal actons (values), eps s a smaller constant. f ( BestFC( m) BestFC( n)) < eps + 1) ( t) = + β. Vsual rand( ) (9) ( t some some. AF_Swarm makes few fsh confned n local extreme values move n the drecton of a few fsh tendng to global extreme value, whch results n AF fleeng from the local extreme values. AF_Follow accelerates AF movng to better states, and at the same tme, accelerates AF movng to the global extreme value feld from the local extreme values. III. IMPROVED AFSA ASFA s one of the best Swarm Intellgence algorthms. However, t has dsadvantages ncludng: Hgher tme complexty, lower convergence speed, lack of balance between global search and local search, and not use of the experences of group members for the next moves. It has many 112

7 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 advantages, such as good robustness, global search ablty, tolerance of parameter settng, and t s also proved to be nsenstve to ntal values. In recent years many researchers have attempted to mprove ths algorthm. In ths secton, a number of mprovements are revewed. a. The Improved Basc Behavors n AFSA1 [8] To enhance the performance of the AFSO1[8], the nformaton of global best AF s added to the behavors of the AF. The realzaton of the behavors n IAFSA s as follows for mnmum: a..prayng behavor ( AF_Prey): Let be the AF current state and select a state randomly wthn vsual dstance, Y = f () s the food consstence of an AF: = af _ vsual. rand() (10) + If Y < Y n the mnmum problem, t goes forward a step n the drecton of the vector sum of the t+ 1 and the = t + best _ af, best af t t _ s the best AF state n all AFs tll now. + Otherwse, select a state best _ af best _ af t t * af _ step * rand() (11) randomly agan and udge whether t satsfes the forward requrement. If the forward requrement cannot be satsfed after try _ number tmes, the AF would move a step randomly; ths can help the AF flee from the local extreme feld. t+ 1 t = + af _ vsual * rand() a.. Swarmng behavor ( AF_Swarm): Let be the AF current state, (12) c be the center poston of several AF and n f be the number of ts companons wthn the AF s vsual range. If Y < Y andy c < af _ delta * Y / n f, whch c means that the fellow center has lower ftness value and the surroundng envronment s not very crowded, and then the AF goes forward a step n the drecton of the vector sum of the c and the _. best af t+ 1 = t + c c t t + best _ af best _ af t t * af Otherwse, the preyng behavor s executed. a.. Followng behavor ( AF_Follow): _ step * rand() (13) 113

8 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons Let denote the AF current state, and the AF explores ts neghborhood area to fnd the AF whch has the smallery. If Y < Y and Y af _ delta* Y / n f <, whch means that the AF has lower ftness value and the surroundng envronment s not very crowded, the AF goes forward a step n the drecton of the vector sum of the t+ 1 = t + t t + best _ af best _ af a.v. Movng behavor ( AF_Move): t t * af _ step * rand() and the _. The AF chooses a state randomly wthn the vsual range, and then t moves towards ths state, t s a default behavor of an AF. t+ 1 t = + af _ vsual * rand() a.v. Other behavors Other behavors of IAFSO1 such as leapng behavor and evaluatng behavor are the same as AFSO. The leapng behavor [3] s proposed to ncrease the probablty to leap out local extremes. The evaluatng behavor s based on the evaluaton to the envronment of an AF, and can help the AF select a proper behavor to execute. The swallowng behavor [8] s executed f the ftness functon value s bgger (for mnmum optmzaton) than a gven threshold n updatng process of AFSO. Expermental results show that the IAFSO1 has advantages of faster convergence speed and hgher global search accuracy than the standard AFSO by addng lmted computng complexty, because of ts good performance, the IAFSO1 mght replace the AFSO n future optmzaton applcatons. b. cultured Artfcal Fsh-swarm Algorthm (CAFAC) [9] A novel cultured AFSA (Artfcal Fsh-swarm Algorthm) wth the crossover operator, namely CAFAC [9], s proposed to enhance ts optmzaton performance. The crossover operator utlzed s to promote the dversfcaton of the artfcal fsh and make them nhert ther parents characterstcs. The Culture Algorthms (CA) s also combned wth the AFA so that the blnd search can be combated wth. In the CAFAC, a crossover operator s utlzed to mprove the dversfcaton of the artfcal fsh and make the artfcal fsh nhert ther parents characterstcs. The CA s further combned wth the modfed AFA together to overcome the shortcomng of blnd search. A total of 10 hgh-dmenson and mult-peak functons are employed to examne the (15) best (14) af 114

9 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 performance of our CAFAC. Smulaton results show that t can ndeed outperform the orgnal AFA. c. Improved Artfcal Fsh-swarm optmzaton (IAFSO2) [10] In order to mprove the algorthm s stablty and the ablty to search the global optmum, they propose an mproved AFSO (IAFSO)[10]. When the artfcal fsh swarm s optmum value s not varant after defned generatons, they add leapng behavor and change the artfcal fsh parameter randomly. By the way, they can ncrease the probablty to obtan the global optmum. c.. The elmnaton of step restrcton In the AFSO, the step of artfcal fsh s a random number n (0, step) whle they execute searchng behavor, swarmng behavor and chasng behavor. The three AF s behavors are local actons whch ncrease the probabltes of ndvdual evoluton and premature. The actual step of IAFSO2 s a random number n the defned area to guarantee the better global search capacty. c.. The leapng behavor The searchng behavor, swarmng behavor and chasng behavor are all local behavors n some degree. If the obectve functons value s not changed after several teratons, t manfests that the functon mght fall nto local mnmum. If the program contnues teratng, every AF s result wll gradually be same and the probablty of leapng out local optmum wll be smaller. To ncrease the probablty to leap out local optmum and attan global optmum, they attempt to add leapng behavor to AF. The AF s leapng behavor s defned as follow. If the obectve value s dfference between K tmes and K+N tmes s smaller than eps n the teraton process, we select randomly an AF accordng to the proporton p(0<p<1) and change ts parameters randomly n the defned area. AFSO s a novel method to search global optmal value by AF s searchng behavor, swarmng behavor and chasng behavor. The step constrans n the three behavors affects the global search capacty of the AF. Therefore, they elmnate the step constran n IAFSO2. In addton, they add leapng behavor to AFSO n order to reduce the possblty of AF fallng nto local optmum. They desgn the data structure and procedure n order to apply AFSO and IAFSO2 to the tranng process of three layouts feed-forward neural networks and the comparson result demonstrates that the IAFSO2 has better global astrngency and stablty. Therefore, the mprovement of AFSO n the paper s effectve, and IAFSO2 s an effectve method to tran feed-forward neural networks. d. Improved Artfcal Fsh-swarm optmzaton (IAFSO3) [11] 115

10 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons The algorthm heren presented s a modfed verson of the artfcal fsh swarm algorthm for global optmzaton [11]. The new deas are focused on a set of movements, closely related to the random, the searchng and the leapng fsh behavors. An extenson to bound constraned problems s also presented. To assess the performance of the new fsh swarm ntellgent algorthm, a set of seven benchmark problems s used. A senstvty analyss concernng some of the user defned parameters s presented. They present a new verson of the artfcal fsh swarm algorthm, heren denoted by Fsh Swarm Intellgent (FSI) algorthm. Our modfcatons are focused on: 1. The extenson to bound constraned problems meanng that any fsh movement wll be mantaned nsde the bounds along the teratve process; 2. Modfed procedures to translate random, searchng and leapng fsh behavors; 3. The ntroducton of a selectve procedure; 4. Dfferent termnaton condtons. The four man algorthms are shown n the followng: 116

11 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 IV. HYBRID AFSA Despte of ts many advantages, the AFSA has some dsadvantages. Dfferent researchers have tred to mprove ths algorthm by usng dfferent algorthm and combnng them wth ths algorthm. In ths paper, some of these composte approaches are revewed. a. CF-AFSA A Hybrd Artfcal Fsh Swarm Algorthm, whch s combned wth CF and Artfcal Fsh Swarm Algorthm, s proposed n ths paper to solve the Bn packng problem. Experment results compared wth GA shows that the Hybrd Artfcal Fsh Swarm Algorthm has a good performance wth broad and prosperous applcaton [12]. The dmenson of search space s establshed as n, the scale of fsh N. Each artfcal fsh can be expressed as a vector of n dmenson = x, x,..., x ) ( 1,2,..., ) ; functon Y=f() ( 1 2 n = N shows the current concentraton of food of artfcal fsh; d = d(, )(, 1,2,..., ), = N means the dstance between the artfcal fsh and the artfcal fsh ; δ sgnfes congeston degree factor; TryNumber ndcates the largest tryng number of each movement of artfcal fsh; Vsual means the feld of vson of artfcal fsh. a. THE DESCRIPTION OF ALGORITHM Step 1: Intalzaton Step2: Calculate ftness value Step3: Each artfcal fsh ( = 1,2,..., N) Step3.1: Followng; udge whether the state after followng s better than the prevous state, and f so, turn to. Step4, otherwse turn to Step3.2; Step3.2: Clusterng; udge whether the state after clusterng s better than the prevous state, and f so, turn to. Step4, otherwse turn to Step3.3; 117

12 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons Step3.3: Foragng; Step4: Update the current best value; Step5: Update the dstance among fsh swarm,(, 1,2,..., ) d, = N Step6: If already acheve the maxmum evoluton algebra, ext; otherwse, turn to Step3. b. AFSA-PSO (HAP) A hybrd of artfcal fsh swarm algorthm (AFSA) and partcle swarm optmzaton (PSO) s used to tranng feed forward neural network. After the two algorthms are ntroduced respectvely, the hybrd algorthm based on the two s expressed. The hybrd not only has the artfcal fsh behavors of swarm and follow, but also takes advantage of the nformaton of the partcle. An experment wth a functon approxmaton s smulated, whch proves that the hybrd s more effectve than AFSA and PSO [13]. b.. Behavor of searchng food In general, the fsh stroll at random. When the fsh dscover a water area wth more food, they wll go quckly toward the area. Let us assume that s the AF state at present, and S. The behavor of follow can be expressed as the followng: + step f y > y prey( ) = (16) + step else b.. Behavor of swarm In the process of swmmng, the fsh wll swarm spontaneously n order to share the food of the swarm. Let us assume that s the AF state at present, and of swarm to AF can be expressed n Formula 4. = nf. The behavor c / x s c + step swarm( ) = c pery( ) yc f > δy nf else b.. Behavors of Agents When one fsh of the fsh swarm dscovers more food, the other fsh wll share wth t. Let us assume that s the AF state at present, and y = max{ f ( ) S}. The behavor of follow can be expressed n Formula 5. max (17) + step follow( ) = pery( max max ) f ymax > δy nf else (18) 118

13 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 Accordng to the character of the problem, the AF evaluates the envronment at present, and then selects an approprate behavor. For example, behavors of follow and swarm are both smulated, the better of mproved ts state wll be executes. Ths process ndcates the flexblty of AFSA. MFNN tranng by a new algorthm, HAP, s proposed. HAP s a hybrd of PSO and AFSA; t has the advantages of the two at the same tme. When the nformaton of the AFSA s enough, AFSA wll be executed, and otherwse, the PSO wll be executed. Wth the above performance, HAP s a good algorthm to tranng MFNN. To demonstrate the performance of HAP, desgns of functon approxmaton wth three layers ANN are smulated. c. AFSA- SFLA In order to overcome the defects of Shuffled Frog Leapng Algorthm (SFLA) such as slow searchng speed n the late evoluton and easly trappng nto local extremum, a Composte Shuffled Frog Leapng Algorthm (CSFLA) based on the basc dea of Artfcal Fsh-Swarm Algorthm (AFSA) s put forward n ths paper n whch the follow behavor of fsh swarm s used to accelerate the optmzaton speed and the swarm behavor to mprove the capacty of out of local extremum. The test results ndcate that CSFLA ncreases the convergence velocty outstandngly and enhances the global searchng performance effectvely [14]. d. AFSA CLA A new algorthm whch s obtaned by hybrdzng cellular learnng automata and artfcal fsh swarm algorthm (AFSA) s proposed for optmzaton n contnuous and statc envronments. In the proposed algorthm, each dmenson of search space s assgned to one cell of cellular learnng automata and n each cell a swarm of artfcal fshes are located whch have the optmzaton duty of that specfc dmenson. In fact, n the proposed algorthm for optmzng D-dmensonal space, there are D one-dmensonal swarms of artfcal fshes that each swarm s located n one cell and they contrbute wth each other to optmze the D-dmensonal search space. The learnng automata n each cell are responsble for makng dversty n artfcal fshes swarm of that dmenson and equvalence between global search and local search processes. The proposed algorthm wth standard AFSA, Cooperatve Partcle swarm optmzaton (PSO) and global verson of PSO n 10 and 30- dmensonal spaces are practced on sx standard ftness functons. Expermental results show that presented method has an acceptable performance [15]. e. CSA- AFSA Ths hybrd method, a QoS multcast routng algorthm based on clonal selecton and artfcal fsh swarm algorthms (CSA-AFSA). The hybrd algorthms reasonably use the superortes 119

14 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons of both algorthms and try to overcome ther nherent drawback. An mproved ntalzaton method s used to make sure each ndvdual n ntal populaton s a reasonable multcast tree wthout loops. The smulaton carred out wth dfferent network scale. The results have demonstrated the hybrd algorthm has hgh speed of convergence and searchng capablty to solve QoS multcast routng effectvely [16]. f. CAFSA Accordng to the characterstcs of Artfcal Fsh-swarm Algorthm and Chaos Optmzaton Algorthm, A knd of artfcal Fsh-Swarm Algorthm wth Chaos s constructed by addng chaos to nfluence the update of the veloctes of artfcal fsh, so that precocous phenomenon s suppressed, the convergence rate and the accuracy s mproved. By testng two functons and NP hard problems of the Planar Locaton Problem, the expermental results show that the algorthm s an effcent global optmzaton algorthm for solvng global optmzaton problem [22]. In vew of the defects of AFSA wth slow convergence n the later perod, low optmzng precson, and on some ssues fall nto local optmum easly. As well as the characterstcs of chaos wth ergodcty and senstvty to the ntal value, add chaos to AFSA, gude the current optmzed ndvdual fsh wth Chaos teraton to further optmzaton. The man steps of Artfcal Fsh-Swarm Algorthm wth Chaos are as follows: Step1: Parameter settng, ntalze the state of fsh (populaton sze s N). In the feasble regon generate N artfcal fsh ndvdual randomly, vsual s the greatest percepton dstance of artfcal fsh, Step s the largest step, δ s crowed factor, n s the largest number of each artfcal fsh try to search food, c, d are chaotc mutaton parameters. Step2: Intalzaton of bulletn board. Calculate the functon value of each ntal fsh and compare the value, assgn the best artfcal fsh to ts bulletn board. Step3: Selectng behavor. Each artfcal fsh smulate the swarmng and followng behavor respectvely, and select the best behavor to perform by comparng the functon values, the default s searchng food behavor. Step4: Chaotc mutaton. Perform mutaton to the current status of each fsh depend on next=+ct-d, f the status out of the feasble regon, then generate next n feasble regon randomly. Calculate f (next), f f (next) s superor to f (), then, = next Otherwse, do not update; set t= 4t (1-t). 120

15 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 Step5: Update bulletn board. Accordng to the latest status of each fsh, update bulletn board by comparng ts ftness value, optmal state s best. Step6: Perform chaotc mutaton to the current optmal state of fsh that on the Bulletn board. Perform chaotc mutaton to the optmal state depend on next = + cu d, f the status out of the feasble regon, do not update. Calculated functon values f(cbest), f f(cbest) superor to f(best), then, best= f (cbest) otherwse, do not update; set u=4u(1-u). Step7: Check the termnaton condton. If meet, then ump out of teratve and output the optmal value; otherwse, turn to step3. Testng t wth sx-hump camel back functon and Applyng t to PLP demonstrates that the results that ths hybrd algorthm has got better than AA has got. Ths algorthm can solve the constraned and unconstraned problem effectvely. g. CSAFSA The dea of CSAFSA brngs the CS mechansm nto the operaton flow of AFSA. On one hand t can enhance the global search capabltes and get out of the local optmum easly. Whle on the other hand, t wll not reduce the convergence speed and search accuracy at the same tme. When all of the AF has completed one movement, evaluate the global best fsh, and then use the chaos optmzaton algorthm to search around the poston of best fsh wthn a certan radus. If better, then replace the global best fsh wth ths soluton [17]. The executon of CSAFSA s as follows: Step 1: Generate the ntal fsh swarm randomly n the search space; Step 2: Intalze the value of bulletn board, calculate the current functon value y of each AF, and assgn the value of best fsh to bulletn board; Step 3: Smulate fsh followng behavor and fsh swarmng behavor respectvely, and then select the behavor Results n better functon value y, and the default behavor s fsh preyng; Step 4: Check the functon value y wth the value of bulletn board. If better, then replace t; Step 5: Perform chaos search near the current best AF. If better soluton has been found, then replace the global best fsh wth ths soluton; Step 6: Judge whether the preset maxmum teraton number has acheved or a satsfactory optmum soluton has obtaned. If not satsfed, go to step 3. Otherwse go to step 7; Step 7: Output the optmum soluton. h. ICAFSA 121

16 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons As a newly-proposed stochastc global optmzaton algorthm, artfcal fsh swarm algorthm (AFSA) s featured by ts good global convergence and hgh convergence speed. However, t may suffer from the problem of beng trapped n local optmum and t has relatvely low search accuracy. Havng analyzed the defcences of AFSA and makng use of the ergodcty and nternal randomness of chaos optmzaton algorthm (COA), ths research further puts forward an mproved chaotc artfcal fsh swarm algorthm (ICAFSA). In ths mproved algorthm, chaos optmzaton s frst employed to ntalze the poston of ndvdual artfcal fsh and then AFSA s appled to obtan the neghborhood of the global optmum soluton. When there s no change or lttle change of the functon values on bulletn board n successve teratons, chaotc mutaton s then executed to help the artfcal fsh swarm get rd of the local optmum. The fndngs of case study show the feasblty and effectveness of the ICAFSA n the optmzaton operatons of cascade hydropower statons [19]. Improved chaotc artfcal fsh swarm algorthm (ICAFSA) has coupled the characterstcs of chaos search nto the searchng process of AFSA, n order to make up for the defcency of beng easly trapped nto the local optmum of AFSA n the latter phase. The process of chaos mutaton s as follows [20]: k k k k (1)Let the k th generaton of AF be Z = Z, Z,..., Z ) then map the varables to chaotc ( 1 2 varable nterval (0,1) respectvely to form chaotc varable sequence k* k* k* k* Z = ( Z, Z,..., Z ) the mappng equaton s as follows: 1 2 n n k* Z, Z k* k Z a = b a (19) Among whch, a and respectvely. b are the mnmum and maxmum of the th varable of (2)The chaotc varable Y = Y, Y,..., Y ) produced by Logstc Mappng Method s added to ( 1 2 n k* the varable Z by certan probablty, and then map the chaotc mutaton ndvduals to nterval (0, 1) as follows: W = Z +α. Y (20) k* k* Among whch, k* Z and k* W are the chaotc values of the th varable of the value of the th varable of Y, and α s the annealng operaton: k n 1 α = 1 (21) n k* Z and Z k k* W, Y s 122

17 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 (3)At last, chaotc mutaton varable a mutatve operaton. W k = a + ( b a ). W (22) k* k W s the chaotc value of the th varables of k* W s mapped to the feasble regon, and thus complete k k k k k W, W = W, W,..., W ). ( 1 2 n. AFSA- AL Ths research presents an augmented Lagrangan methodology wth a stochastc populaton based algorthm for solvng nonlnear constraned global optmzaton problems. The method approxmately solves a sequence of smple bound global optmzaton sub problems usng a fsh swarm ntellgent algorthm. A stochastc convergence analyss of the fsh swarm teratve process s ncluded. Numercal results wth a benchmark set of problems are shown, ncludng a comparson wth other stochastc-type algorthms [18]. The algorthm AFSA based on the augmented Lagrangan (AFSA AL) s presented below. Algorthm 1. AFS al Algorthm The heren proposed technque for solvng (3) uses a populaton-based algorthm that reles on swarm ntellgence to converge towards the mnmum value of the augmented Lagrangan functon. Ths s the subect of the next secton. Snce the AFS algorthm provdes a k k populaton of solutons, x s the best soluton. We emphasze the mportance of usng x as one of the ponts of the populaton for the sub problem (3), at teraton k + 1. The remanng ponts of the populaton are randomly generated n the set Ω. 123

18 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons. AHSN-AFSA The adaptve hybrd sequences nche artfcal fsh swarm algorthm (AHSN-AFSA) s ntroduced, and study on how to apply the algorthm to solve the vehcle routng problem. The concept of ecologcal nche s also beng ntroduced n order to overcome the shortcomng of tradtonal artfcal fsh swarm algorthm to obtan optmal soluton. Smulaton results show that the new algorthm has solved fast, stable performance and so on [21]. k. TAFSA In terms of some problems exstng n the process of large case base retreval, combnng tabu search method and the advantages of artfcal fsh school algorthm, multlevel search strategy based on tabu artfcal fsh swarm algorthm. Tabu artfcal fsh swarm algorthm apples tabu table wth a memory functon to artfcal fsh swarm algorthm and uses dfferent computng model n the smlarty calculaton accordng to propertes of dfferent types, effectvely to avod premature and blnd search and other ssues. Smulaton results show that the algorthm outperforms other algorthms, t not only mproves the retreval accuracy and retreval effcency of the case based reasonng system, but also s characterzed by requrng not much wth the ntal values and parameters, dversty search and overcomng the local maxmum, better coordnate the overall and local search capabltes and provdes an effectve retreval method to retreve the case of large case base [23]. l. AFSA-FCM Ths method apples the artfcal fsh swarm algorthm (AFSA) to fuzzy clusterng. An mproved AFSA wth adaptve Vsual and adaptve step s proposed. AFSA enhances the performance of the fuzzy C-Means (FCM) algorthm. A computatonal experment shows that AFSA mproved FCM outperforms both the conventonal FCM algorthm and the Genetc Algorthm (GA) mproved FCM [24]. l.1. ASFA fuzzy clusterng approach A new fuzzy clusterng algorthm based on FCM and AFSA s proposed here. The algorthm has the followng steps: Step 1(Determne parameter encodng) V = ( v1, v2,..., v p,..., vc ) (Represents the centrod of the clusters. It s consdered to be one AF. v p s the centrod of the th p cluster ( 1 p c ), where c s the number of clusters. V s a c*n dmenson- vector. 124

19 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 Step 2(Intalzaton) Defne the clusters number c, the populaton of AF N, fuzzness exponent m, termnaton crteron, vsual dstance of AF, step of AF, crowd factor and Trynumber. Determne maxmum teraton tme K for AFSA, set teraton counter k=1; ntalze the frst AF K K K K K populaton: AF = V, V,..., V,... V } where { 1 2 Represents the poston of the AF. Step 3(Global search) q N th q AF at the K V q. th K teraton. q N a) Accordng to K k k V q, calculate membershp matrx q = [ u c n. U, ] * 1, N s the populaton of b) Go to step 4 when the result satsfes the termnaton crteron, otherwse, ncrement k (k: =k+1) and go back to step 3(a). Step 4 (Local search) a) Fnd the best ndvdual AF: b) CalculateU c) UpdateV k+1 K +1 k V best d) Stop teraton f the result satsfes termnaton crteron, or, ncrement k and return to step 4(b). Ths algorthm s used to search for cluster centrod so that the obectve functon f s mnmzed. After each teraton, AFs swm to better locatons. Ths enables convergence to the global optmum. m. HAFSA Based on partcle swarm optmzaton (PSO) and artfcal fsh swarm algorthm (AFSA), a hybrd artfcal fsh swarm optmzaton algorthm s proposed. The novel method makes full use of the quckly local convergent performance of PSO and the global convergent performance of AFSA, and then s used for solvng ll-condtoned lnear systems of equatons. Fnally, the numercal experment results show that the hybrd artfcal fsh swarm optmzaton algorthm owns a good globally convergent performance wth a faster convergent rate. It s a new way for solvng ll-condtoned lnear systems of equatons [25]. n. NQAFSA 125

20 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons Artfcal Fsh Swarm Algorthm (AFSA) s a new swarm ntellgence optmzaton algorthm whch s desgned to fnd the sngle optmal soluton for a gven problem. But n some practcal applcatons, the global optmal soluton and some near optmal solutons are both needed. So a novel Nche Quantum Artfcal Fsh Swarm Algorthm (NQAFSA) s proposed n ths method to solve these problems. The quantum mechansm s ntroduced nto the AFSA to ncrease the dversty of speces. Artfcal Fsh (AF) are dvded nto several sub-swarms to form the nche and the restrcted competton selecton (RCS) strategy s used to mantan the nche. The performance of NQAFSA s valdated by the expermental results [26]. n.1. Nche Artfcal Fsh Swarm Algorthm based on Quantum theory Nchng technques can fnd multple solutons n multmodal domans, n contrast to AFSA that has been desgned to locate only sngle optmal soluton. A novel Nche Artfcal Fsh Swarm Algorthm based on Quantum theory called NQAFSA s proposed n ths method. Quantum mechansm s ntroduced nto AFSA so as to enhance populaton dversty and Nchng technology s ntroduced nto AFSA n order to fnd multple optmal solutons. The probablty ampltudes of quantum bts are employed to encode the poston of the AF. The quantum rotaton gate s used to update the poston of the AF n order to enable the AF to move and the quantum non-gate s employed to realze the mutaton of the AF for the purpose of speedng up the convergence. The nche strategy s realzed by the sub-swarm. The ntal artfcal fsh swarm s splt nto smaller swarms as sub-swarm whch s used to locate multple solutons n multmodal functon optmzaton problems. All the sub-swarm explores the search space n parallel way. The RCS strategy s employed to mantan the sub-swarm. The procedure of NQAFSA s shown as follows. Step1. Intalzaton, ncludng the number of sub-swarms N, the number of AF n each subswarm AF_total, AF_step,AF_vsual, try_number, mutaton probablty pm and so on. Step2. A total of N sub-swarms are created and they are all randomly dstrbuted n the search space. The postons of AFs are encoded by the probablty ampltudes of quantum bts. Step3. Perform the soluton space transformaton for every AF n each sub-swarm and calculate ftness value of the AF, then the best AF n each sub-swarm wll be ncluded n the bulletn board of that sub-swarm. Step4. AF execute AF_Pray, AF_Swarm, AF_Follow,AF_Move and evaluate the results of the four behavors. Then determne target poston and change the poston of the AF by quantum rotaton gate. 126

21 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 Step5. Perform the mutaton operaton. Generate a random number every AF, f rand < p m, then execute mutaton operaton upon that AF. rand between 0 and 1 for Step6. Perform the soluton space transformaton for every AF and calculate ftness value of the AF agan, then update the bulletn board n each sub-swarm. Step7. The RCS strategy s executed to mantan the nche. Step8. If the stoppng crteron s satsfed, then stop and output the result; else go to Step4. o. Hyperbolc Penalty n the Mutated Artfcal Fsh Swarm Algorthm In ths method the mplementaton of a populaton-based paradgm n the hyperbolc penalty functon method to solve constraned global optmzaton problems s proposed. A mutated artfcal fsh swarm algorthm s used to solve the bound constraned sub problems. A smple tunng of the penalty parameters and three schemata for the mplementaton of an ntensfcaton local search procedure are ntroduced to promote convergence and mprove the global soluton. They may conclude that the proposed algorthm wth an HJ ntensfcaton strategy outsde the outer cycle provdes promsng results when solvng engneerng desgn problems. Future developments wll focus on assgnng dfferent penalty parameters to each pont of the populaton so that the level of nfeasble penalzaton depends on the magntude of constrant volaton [27]. p. Parallel Fsh Swarm Algorthm Wth the development of Graphcs Processng Unt (GPU) and the Compute Unfed Devce Archtecture (CUDA) platform, researchers shft ther attentons to general-purpose computng applcatons wth GPU. In ths method, they present a novel parallel approach to run artfcal fsh swarm algorthm (AFSA) on GPU. Experments are conducted by runnng AFSA both on GPU and CPU respectvely to optmze four benchmark test functons. Wth the same optmzaton performance, the runnng speed of the AFSA based on GPU (GPU- AFSA) can be as 30 tme fast as that of the AFSA based on CPU (CPU-AFSA).As far as we know; ths s the frst mplementaton of AFSA on GPU [28]. q. QAFSA In order to mprove the global search ablty and the convergence speed of the Artfcal Fsh Swarm Algorthm (AFSA), a novel Quantum Artfcal Fsh Swarm Algorthm (QAFSA) whch s based on the concepts and prncples of quantum computng, such as the quantum bt 127

22 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons and quantum gate s proposed n ths method. The poston of the Artfcal Fsh (AF) s encoded by the angle n [0, 2π ] based on the qubt s polar coordnate representaton n the 2- dmenson Hlbert space. The quantum rotaton gate s used to update the poston of the AF n order to enable the AF to move and the quantum non-gate s employed to realze the mutaton of the AF for the purpose of speedng up the convergence. Rapd convergence and good global search capacty characterze the performance of QAFSA. The expermental results prove that the performance of QAFSA s sgnfcantly mproved compared wth that of standard AFSA [29]. r. SA-AFSA Ths method presents a novel stochastc approach called the smulated annealng-artfcal fsh swarm algorthm (SA-AFSA) for solvng some multmodal problems. The proposed algorthm ncorporates the smulated annealng (SA) nto artfcal fsh swarm algorthm (AFSA) to mprove the performance of the AFSA. The hybrd algorthm has the followng features: the hybrd algorthm mantans 1) the strong local searchng ablty of the SA and 2) the swarm ntellgence of AFSA. The expermental results ndcate that n all the test cases, the SA- AFSA can obtan much better optmzaton precson and the convergence speed compared wth AFSA [30]. V. APPLICATION AFSA The AFSA s a new and modern algorthm for optmzaton purposes. In short term t has succeeded to get ts place among other optmzaton methods. Many researchers have appled ths algorthm n dfferent applcatons. In ths secton, ts dfferent applcatons are descrbed. a. Control a.. AFSA-FLC Ths method provdes an overvew on the Artfcal Fsh Swarm Algorthm (AFSA) for the automated desgn and optmzaton of fuzzy logc controller. A new optmzaton method for fuzzy logc controller desgn s proposed. The membershp functons of nput and output varables are defned by sx parameters, whch are adusted to maxmze the performance of the controller by usng AFSA. Ths method can mprove the capablty of search and convergence of algorthm. Smulaton experment on water level controller s dscussed by usng above method. The smulaton results show that fuzzy logc controller based on AFSA avods premature effectvely and prove ts feasblty [31]. 128

23 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 a.. Self adaptve control algorthm of the artfcal fsh formaton Wth the deep study of swarm ntellgence, bologsts found that fsh swarm changes n formaton gradually n tme durng ther movement. Ths formaton change leads to a better and more effectve access to evade predator and opportunty to capture food, so that the group's overall performance s mproved. The archtecture of artfcal fsh formaton s establshed based on the behavoral model of artfcal fsh swarm. The mechansm of formaton change s analyzed. A self-adaptve control algorthm of formaton s proposed n ths method. The parameters optmzed PSO algorthm s used to smulate the process of keepng ts balance durng the formaton change. Thus, the problem on relatve bad adaptablty and large systematc traffc n exstng algorthms of formaton s resolved [32]. a.. AFSA for Mult Robot Task Schedulng The man am of ths study s managng robot tasks to mnmze the devaton between the resource requrements and stated desrable levels. Some mproved adaptve methods about step length are proposed n the Artfcal Fsh Swarm Algorthm (AFSA). In ths study resource levelng methods are used to solve task schedulng problems n autonomous mult robot group. Robots are consdered as resources. The expermental results show that proposed methods have better performances such as good and fast global convergence, strong robustness, nsenstve to ntal values, smplcty of mplementaton [33]. a.v. AFSA n UCAV Path Plannng The path plannng method based on artfcal fsh school algorthm (AFSA) was proposed to solve unmanned combat aeral vehcle (UCA V) path plannng problem under the 2-D radar threats envronment. Accordng to the path plannng requrements, the threat detecton and artfcal fsh codng method were desgned n detal. Besdes, the method of percevng threats was appled for advancng the feasblty of the path. A comparson of the results was made by WPSO, CFPSO and AFSA, whch showed that the method we proposed n ths paper was effectve. AFSA was much more sutable for solvng ths knd of problem [34]. a.v. AFSA for Fault Dagnoss n Mne Host It has been presented an ntellgent methodology for dagnosng ncpent faults n mne host. As Probablstc Causal-effect Model-Based dagnoss s an actve branch of Artfcal Intellgent, the feasblty of usng probablstc causal-effect model s studed and t s appled 129

24 Mehd Neshat, Al Adel, Ghodrat Sepdnam, Mehd Sargolzae, Adel Naaran Toos, A Revew of Artfcal Fsh Swarm Optmzaton Methods and Applcatons n artfcal fsh-swarm algorthm (AFSA) to classfy the faults of mne host. In probablstc causal-effect model, we employed probablty functon to nonlnearly map the data nto a feature space, and wth t, fault dagnoss s smplfed nto optmzaton problem from the orgnal complex feature set. And an mproved dstance evaluaton technque s proposed to dentfy dfferent abnormal cases. The proposed approach s appled to fault dagnoss of frcton host wth many steel ropes, and testng results show that the proposed approach can relably recognze dfferent fault categores. Moreover, the effectveness of the method of mappng httng sets problem to 0/1 nteger programmng problem s also demonstrated by the testng results. It can get 95% to 100% mnmal dagnoss wth cardnal number of fault symptom sets greater than 20 [35]. a.v. CAFAC Effcent dentfcaton and control algorthms are needed, when actve vbraton suppresson technques are developed for ndustral machnes. A new actuator for reducng rotor vbratons n electrcal machnes s nvestgated. Model-based control s needed n desgnng the algorthm for voltage nput, and therefore proper models for the actuator must be avalable. In addton to the tradtonal predcton error method a new knowledge-based Artfcal Fsh- Swarm optmzaton algorthm (AFA) wth crossover, CAFAC, s proposed to dentfy the parameters n the new model. Then, n order to obtan a fast convergence of the algorthm n the case of a 30kW two-pole squrrel cage nducton motor, they combne the CAFAC and Partcle Swarm Optmzaton (PSO) to dentfy parameters of the machne to construct a lnear tme-nvarant (LTI) state-space model. Besdes that, the predcton error method (PEM) s also employed to dentfy the nducton motor to produce a black box model wth correspondence to nput-output measurements [36]. a.v. MOAFSA Artfcal Fsh Swarm Algorthm (AFSA) s a knd of swarm ntellgence algorthm, whch has the features of fast convergence, good global search capablty, and strong robustness and so on. An approach usng AFSA to solve the multobectve optmzaton problem s proposed. In ths algorthm, the concept of Pareto domnance s used to evaluate the pros and cons of Artfcal Fsh (AF). Artfcal fsh swarm search the soluton space n parallel and External Record Set s used to save the found Pareto optmal solutons. The smulaton results of 4 benchmark test functons llustrate the effectveness of the proposed algorthm [37]. 130

25 INTERNATIONAL JOURNAL ON SMART SENSING AND INTELLIGENT SYSTEMS, VOL. 5, NO. 1, MARCH 2012 a.v. PID Controller Parameters Based on an Improved AFSA The artfcal fsh swarm algorthm s a new knd of optmzng method based on the model of autonomous anmals. After analyzng the dsadvantages of AFSA, an mproved artfcal fsh swarm algorthm s presented. Accordng to the ergodcty and stochastcty of chaos, the basc AFSA s combned wth chaos n order to ntalze the fsh school. The mprovement of the swarmng behavor ncreased the precson of the algorthm. In the behavor of preyng, the strategy of dynamcally adustng the parameter of step s presented n order to mprove the convergence rate of the algorthm. Ths mproved AFSA s appled n the optmzaton of the of PID controller parameters. The smulaton results show that ths mproved AFSA algorthm s effectve and better than the basc AFSA algorthm [38]. a.x. Optmum steelmakng charge plan usng AFSA An optmum furnace charge plan model for steelmakng contnuous castng plannng and schedulng s presented an artfcal fsh swarm optmzaton (AFSO) algorthm s used to solve the optmum charge plan problem. The computaton wth practcal data shows that the model and the solvng method are vey effectve [39]. a.x. AFSA for the Target Area on Smulaton Robots In ths research, they used an mproved algorthm of artfcal fsh, and dd the optmzaton n settng the border n the smulaton platform, especally n the feld of choosng ways of the robots; they used the Mult-threshold to reduce the uncontrollable actons when robots are n the game. And ths method gves them an acceptable way to solve the ssue [40]. b. Image processng b.. AFSA-Kmeans Data clusterng has been used n dfferent felds such as machne learnng, data mnng, wreless sensory networks and pattern recognton. One of the most well-known clusterng methods s K-means whch has been used effectvely n many of clusterng problems. But ths algorthm has problems such as convergence n local mnmum and senstvty to ntal ponts. A hybrd clusterng method, based on artfcal fsh swarm optmzaton (AFSO) and K-means so called KAFSO s proposed. In ths proposed algorthm, hgh ablty of AFSO n global searchng as well as hgh ablty of K-means n local searchng has been used cooperatvely. The proposed method has been tested on eght collectons of standard data and ts effcency has been compared wth standard methods PSO, Kmeans, K-PSO and AFSO. 131