1、2 2004 M3CHINA MEASUREMENT TECHNOLOGYS k/ No.2Mar, 2004GrefenstetteI EMATLAB LC叶 欢 经亚枝( 2t bt?v1, 2210016)K 1:MATLAB/I LCTSP5GrefenstetteI E,i| L. EM,_ pB15TSP5。_ LT r。1oM:GrefenstetteI E; j (TSP);5;L. E;(GA)MATLABms |:O157.4 DS M :A cI|:1672-4984(2004)02-0058-03To implement grefenstette coding by M
2、ATLABAbstract:This paper paresents a way to implement the Grefenstette coding forTSP by Matlab and integrates it intothe basic geneticalgorithm to simulate theGA solution for a15-pointTSP.The outcome of the test has validated theproposed programming.Key wrods:Crefenstette coding;TSP ;GA MATLABTe:=(1
3、975-), 3,C 2t bt?v k9 / #N V,Z_C e“d。1 j 5(TSP) 1 BF5,i O BNP 45, V ? “ g “n 9, B 4 p K,y7s r p E 1 il。 H, L=5 L、 5 !、 L,Ve) Vy TSP5,y7TSP5 pZE91N。“ -,L. E(GA) p5 rZEB。5GA“I ZE,R g V U8I 1 I EB, /:L !B g VW=(A B C D E F G H I J), E g。 gsB110W|, !A =1,B=2, ,J=10,5B W1=(A D B HF IJ G E C) 8G1 =(1 4 2
4、8 6 9 10 7 5 3)。A ,TSP5 K1 I ZE, Ms LC 4,y?Ms P 8 3Bt 5 Hqil L。 6BI Z T “H”FZ T 2 , O V gi gj H,gj$ i 。 ,I 1248397156V U“BH L,1-2-4-3-8-5-9-6-7,I Z T“9i“Ms 4 LC5。B , GrefenstettetI E3#I EMATLAB LC,K L. EB15TSP5_ p。2 5 2.1 TSP问题的描述TSP5 Ve :XN gWM ,CBwgARN g,iO g ?BQ,KAR? g。 gQ,sBHR gK j L。m ,L !BmG =
5、(V ,E), V “,E H“, !D =(dij), ijW F ,TSP5 pBHYV O YVBQ K 。 !9 gV =v1 ,v2 , ,vnB T=(t1 ,t2 ,t3 ,ti tn), tiV(i =1,2, ,n), O:tn +1=t1,5TSP5 :minL =ni=1dti ,ti +12.2 GrefenstetteI E BTSP5 g VW,LgB T :T =(t1 ,t2,t3, ,tn)? B g,V g VW|58 g H,5i(i=1,2,3, ,n) gti g VW-t1 ,t2,t3, ,ti-1|gi(1gi n -i +1) VV U 8 g
6、, N“) W g。| gi B B V:G =(g1,g2 ,g3 , ,gn) VV UBH L, L. EB8y。 ,L !Bc E g V:W =(A B C D E F G H I J)C / H L:Tx =(AD B H F I J G E C)Ty =(B C A D E J H I F G)5Grefenstette4I ZE, H L VI :Gx =(1 3 1 5 3 4 4 3 2 1)Gy =(2 2 1 1 1 5 3 3 1 1)I ZE) iy8“BH L=il L,yN V P?0 T。3 GrefenstetteI E LC3.1 HqL ,5L !B15
7、 gTSP5。 g USsYMATLAB 3,i i115 Fxy, O US (d。8 “ !100, !200, q |0.8,Ms q |0.05。 LT “Sf。 af F(T)=n length(T), T,length(T)V U LT,nV U g “。I pTSP5L. E H, #GrefenstetteI Ef , 8 SfTSPinitialize(), f TSPdecode()Msf TSPmut(),CsY /。3.2 8 Sf TSPinitialize()YI T L. E 8 S ,9GrefenstetteI E LCc 8Sf TSPinitilize0
8、=, /:function pop=TSPinitialze(POPSIZE,NCITIES)for i=1POPSIZEfor j=1NCITIESpop(i ,j)=round(rand(NCITIES-j)+1;endendNf ,POPSIZENCITIES, sY 8 pTSP5cg (9 8)。f Rpop BPOPSIZE X NCITIES , il 3 S 8 8, BBH 8。 S 3,GrefenstetteI E H 8 y |gi1 gi NCITIES-i +1“B Hq, pop(i,j)=round(rand(NCITIES-j)+1 V Hq 。3.3 f T
9、SPdecode() 8 Tf TSPdecode(), /:function chromx, chromy =TSPdecode (POPSIZE,NCITIES,pop,x ,y)for i=1POPSIZEtempx=x;tempy=y ;for j=1NCITIESchromx(i,j)=tempx(pop(i,j);chromy(i,j)=tempy(pop(i,j);for k=(pop(i,j):(NCITIES-j)tempx(k)=tempx(k+1);tempy(k)=tempy(k+1);endendendf , - il- Sf ,pop - 8,7xy5 3.1 3U
10、S F。f Rchromxchromy (POPSIZE X NCITIES , il g US , BBH 8。TSP |I ,yN H 8 V LCM 。 n5, S US Fxy,yN5 tempxtempy 。 V g VW -t1,t2 ,t3, ,ti-1,i(i=1,2,3, ,NCITIES)。 H 8 ygi(pop(ij)tempx(y)sMUS,Mchromx(i ,j)chromy(i,j)。GrefenstetteI E1 p B gV g V| ,1 pf TSPdecode()“ LC: B g( )US,L|tempx(y)M . F ,/By 。3.4 Msf
11、 TSPmut()GrefenstetteI EKHq1gi n-i +1 8Ms T“9BK。Msf TSPmut() /:FunctionSelCh=TSPmut(POPSIZE,NCITIES,Pm ,SelCh)for i=1POPSIZEif randPmmpoint=round(rand(NCITIES-1)+1;SelCh(i,mpoint)=round(rand(NCITIES -mpoint)+1;end59endMsf Ms T, Pm Ms q,7SelCh il$Ms T 8。Ms$K1NCITIES-mpointW。4 _ MATLAB LCGrdfenstetteI
12、Er,Gv3.14HqB15TSP5 _。 Sf 、 fMsf sY P Bc4TSPinitialize(),TSPdecode()TSPmut()。4 0、 0 0sY? E、K i。 m m1。m1 m /:procedure GA for TSPbeginPOPSIZE=100; %Number of individualsMAXGEN =200;%Maximum numberof generationsNCITIES=15; %Number of citiesPc=0.8; %Crossover probabilityPm =0.05; %Mutation probabilityge
13、n=0; %Generation counterinitialize P(t);evaluate P(t);while genMAXGEN dobegingen=gen+1;select P(gen)from P(gen-1);reproduce pairs in P(gen);evaluate P(gen);endoutput resultend./m9 - H L( 3BH S L L) Uim。m29 - Lm,m39 Lm。m2 S L Uimm3 L Uim5 GrefenstetteI E TSP5L. EIEB, ) VZLL. E。4 BMATLAB LCNI E E,i| E_ pB15TSP5。_ kT Er。 ID1 , .L. E #.:S,19992 S .L. E#.: ,19963 Grefenstette J,et al.Genetic Algorithms for the Traveling SalesmanProblem In:Proc, of 1st Int.Conf.on Genetic Algorithms and TheirApplications,Lawrence Erlbaun Association,1985,166 16860
