Biogeography-Based Optimization. Dan Simon Cleveland State University Fall 2008

Transcription

1 Biogeography-Baed Optimizatio Da Simo Clevelad State Uiverity Fall 2008

2 Outlie. Biogeography 2. Optimizatio 3. Other Populatio-Baed Optimizer 4. Bechmark Fuctio & Reult 5. Seor Selectio & Reult 6. Cocluio 2

3 Biogeography The tudy of the geographic ditributio of biological orgaim Mauritiu 600 3

4 Biogeography Specie migrate betwee ilad via flotam, wid, flyig, wimmig, 4

5 Biogeography Habitat Suitability Idex (HSI): Some ilad are more uitable for habitatio tha other Suitability Idex Variable (SIV): Habitability i related to feature uch a raifall, topography, diverity of vegetatio, temperature, etc. 5

6 Biogeography A habitat uitability improve: The pecie cout icreae Emigratio icreae (more pecie exit the habitat) Immigratio decreae (fewer pecie come ito the habitat) 6

7 Biogeography P = probability that habitat cotai S pecie S pecie at time t, ad o migratio occurred P ( t Δt) = P P ( t)( λ Δt ( t) λ Δt P ( t) μ μ Δt) Δt S pecie at time t, ad pecie immigrated S pecie at time t, ad pecie emmigrated 7

8 8 Biogeography Covert the differece equatio ito a differetial equatio = = = = max max ) (,, ) ( 0 ) ( S S P P S S P P P S P P P λ μ λ μ λ μ λ μ μ λ (S max ) coupled differetial equatio that ca be combied ito a igle matrix equatio.

9 9 Biogeography AP P = = ) ( 0 0 ) ( ) ( 0 0 ) ( A μ λ λ μ μ λ λ μ μ λ λ μ μ λ

10 Biogeography Suppoe E=I. The μ = Ek / k λ = E( k / ) k where k = pecie cout, = S max 0

11 Biogeography So the populatio reache equilibrium whe P i equal to the eigevector correpodig to the zero eigevalue of A AP P EA E A = = = ' / 0 0 / 2 / 2 / / 0 0 /

12 2 Biogeography [ ] = = = = = ),..., 2) ) / ceil(( ( 2)) ) /,...,ceil(( ( )! )!( (! ) ( 2 i v i i i v v v v v v P i i T i

13 Biogeography-Baed Optimizatio. Iitialize a et of olutio to a problem. 2. Compute fite (HSI) for each olutio. 3. Compute S, λ, ad μ for each olutio. 4. Modify habitat (migratio) baed o λ, μ. 5. Mutatatio baed o probability. 6. Typically we implemet elitim. 7. Go to tep 2 for the ext iteratio if eeded. 3

14 Bechmark Fuctio 4 tadard bechmark fuctio were ued to evaluate BBO relative to other optimizer. Ackley Fletcher-Powell Griewak Pealty Fuctio # Pealty Fuctio #2 Quartic Ratrigi Roebrock Schwefel.2 Schwefel2.2 Schwefel2.22 Schwefel2.26 Sphere Step 4

15 Bechmark Fuctio Fuctio ca be categorized a Separable or oeparable for example, (xy) v. xy Regular or irregular for example, i x v. ab(x) Uimodal or multimodal for example, x 2 v. co x 5

16 Bechmark Fuctio Pealty fuctio #: oeparable, regular, uimodal 6

17 Bechmark Fuctio Step fuctio: i= eparable, irregular, uimodal f ( x) = [floor( x i 0.5)] 2 7

18 Bechmark Fuctio Ratrigi: i= oeparable, regular, multimodal 2 f ( x) = 0 [ x i 0 co(2π x i )] 8

19 Roebrock: Bechmark Fuctio f ( x) = i= [00( x oeparable, regular, uimodal i xi ) ( xi ) ] 9

20 Bechmark Fuctio Schwefel 2.22: f ( x) = i= oeparable, irregular, uimodal x i x i= i 20

21 Bechmark Fuctio Schwefel 2.26: f ( x) = i= eparable, irregular, multimodal x i i x i 2

22 Optimizatio Algorithm At coloy optimizatio (ACO) Biogeography-baed optimizatio (BBO) Differetial evolutio (DE) Evolutioary trategy (ES) Geetic algorithm (GA) Populatio-baed icremetal learig (PBIL) Particle warm optimizatio (PSO) Stud geetic algorithm (SGA) 22

23 23 Average performace of 00 imulatio ( = 50) E4 2.E PSO E4 2.5E GA Step Sphere Schwefel Schwefel Schwefel Schwefel Roebrock Ratrigi E Quartic E5 4.2E E5 Pealty E7.3E6 9.7E4.2E4 2.2E7 Pealty Griewak Fletcher Ackley SGA PBIL ES DE BBO ACO

24 Aircraft Egie Seor Selectio Health etimatio Better maiteace Better cotrol performace 24

25 Aircraft Egie Seor Selectio What eor hould we ue? Meaure preure, temperature, peed A total of eor; ome ca be duplicated Etimate efficiecie ad airflow capacitie Optimize a combiatio of etimatio accuracy ad fiacial cot Ue a Kalma filter for health etimatio 25

26 Aircraft Egie Seor Selectio Suppoe we wat to pick N object out of K clae while chooig from each cla o more tha M time. Example: We have red ball, blue ball, ad gree ball (K=3). We wat to pick 4 ball (N=4) with each color choe o more tha twice (M=2). 6 Poibilitie: {B, B, G, G}, {R, B, G, G}, {R, B, B, G}, {R, R, G, G}, {R, R, B, G}, {R, R, B, B} 26

27 Aircraft Egie Seor Selectio Pick N object out of K clae while chooig from each cla o more tha M time. q(x)= ( x x 2 x M ) K = q x q 2 x 2 x MK Multiomial theorem: The umber of uique combiatio i equal to q N (order idepedet) 27

28 Aircraft Egie Seor Selectio Pick 20 object out of clae while chooig from each cla o more tha 4 time. q(x) = ( x x 2 x 3 x 4 ) = 3,755,070 x 20 2 hour of CPU time for a exhautive earch. So we eed a quick uboptimal earch trategy. 28

29 Aircraft Egie Seor Selectio ACO BBO DE ES GA PBIL PSO SGA Mea Bet Average ad bet performace over 00 Mote Carlo imulatio. Computatioal avig = 99.99% (2 hour 8 ecod). 29

30 Cocluio A ew biologically-motivated optimizer Paper ad Matlab code i at 30

31 Future Work Applicatio Covergece Dyamic/oiy fite fuctio Extictio i ot the ame a emigratio Take ilad proximity ito accout Model pecie populatio (demographic) Specie age affect extictio ad emigratio 3

32 Future Work Migratio curve are probably covex, ad vary betwee ilad Cotiuou BBO Coectio betwee BBO ad other Ea Migratio varie with pecie mobility Predator/prey relatiohip Populatio ize Cotraied BBO Multiobjective BBO 32

33 Future Work Number of ilad Combiatio with other EA Tabu earch, particle warm optimizatio, ue of global iformatio, etc. Local memory of pat performace for each ilad Fuzzy fite fuctio 33

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35 Other optimizatio method At coloy optimizatio: Baed o the pheromoe depoitio of at 35

36 Other optimizatio method Differetial evolutio: Baed o imple differece-baed modificatio of olutio 36 differece ew olutio exitig olutio exitig olutio

37 Other optimizatio method Evolutioary Strategy: Baed o multiple paret cotributig to offprig The mot fit offprig become the ext geeratio of paret 37

38 Other optimizatio method Geetic algorithm: Baed o atural electio i biological evolutio croover poit electio paret childre 38

39 Other optimizatio method Particle warm optimizatio: Baed o the warmig behavior of bird, fih, etc. Each particle (olutio) lear from it eighbor ad adjut itelf accordigly 39