基于Pareto最优解集的多目标粒子群优化算法

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结合Pareto 支配思想、精英保留策略、锦标赛和排挤距离选择技术, 对传统的粒子更新策略进行改进, 给出了一种新的粒子淘汰准则, 提出了一种基于Par et o 最优解集的多目标粒子群优化算法。
O(N) N Pareto Pareto O(N2) OMN) O(N) O(MN) Pareto (pbest) 5 in iti aliz e pbest 1= pop I l pop I for each individua idd le_pop=Ipopk,j; popk-li/ p best, i= tourname nt_selection/mid dle_pop Genuine. 86GHz( IG) 30 C1=C2 0. tour -size= 2 17 3 g h il pool= round(pool/ 2) round( SCH 1 mid dle -gbest= tou rnament_select ion( midd le_gbest) 10 2x)=( f1(x)=/1+(A1-B1)2+ d dle gbest (A2-B2)2 3.3 Pareto A1=0. 5s in1-2cos1+ sin 2 1. 5c0s2 Step 1 POI I, t A2=1.5s in1-cos1+2sin 2 t=0 0.5c0s2 P B1=0. 5sinx1-2c0sx 1+ sin x 2 1. cost 2 reto B2= 1. 5sin 1- cosx 1+ 2sin 2 0.5c0sx2 1(x)=x1 Step 3 (2)(3) ZDT130|/0.1 x)=g(x)(1-Jx1/g(x)7 p g(x)=1+9∑x,∥n-1) Pareto 2(x)=g(x)/(1-(x1/(x)21 pbest ZDT230|0.1 best g(x)=1+9∑x;)(n-1) p 5 ); f2(x)=g(x)1-Jx1/g(x) ZDT3300.17 s in( 10Jx 1)7 g(x)=1+9∑x;)/(n-1 p(-4 1)sin(41) /2(x)=g(x)1-01(xyg(x)2 ZDT6100.1 g(x)=1+9(2x;)/(n-1)025 Pareto f1(x)=(1+g(x)cos(0.01 (1)n, Ternary 2(x)=(1+g(x)cos(0.5mx1) objective 12 /0, 11 sin(0. 5Jx2) (2)S function 3(x)=(1+g(x)sin(0.5T1) (MN 0 0.5) F +d2+∑1d-d F (4 C1994-2013ChinaAcademicJournalElectronicPublishingHouse.Allrightsreservedhttp://www.criki.net NSGAII(rea+ coded) NSGAll( binary-co- 2.0 de) 0 0.5 Pareto flx) (x) 图1问题SCH中100个粒子图2问题PO中100个粒子 迭代1000次时 Pareto曲线迭代550次时 Pareto曲线 Paret o 0.35厂 1.0 0.30 0.8 0 0.20 0.6 0.15 0.4 0.10 [1 Parsopoulos K e, V rahatisMN. Particle Sw am Opt imizat ion 0.05 M ethod in Multt Objective Problems[ Cl Proc of the ACM 0 0.5060.70.80.9 00.20.40.60.8 S ym p on A pplied Comput ing, 2002: 603-607 fle A(x) 2 Coel lo C a C. an U dated Survey of Evol ut ionary MultiOb 图3问题D1中100个粒子图4问题ZDT中200个粒子 jective Optimization T echniques: S tate of the Art and Future 迭代1000次时 Pareto曲线迭代1000次时 Pareo曲线 Tren ds[ C] l Proc of the 1999 Congress on Evolutionary 1.00 Compu tation. 1999:313 0.98 [3 Deb k, Pratap A, Agarw al S, Meyarivan T. A Fast and Elitist 0.6 MultiObject ive Genetic Algorithm: NSGA-IJI. IEEE 0.94 Trans on E volu ti on ary Comput ation, 2002, 6(2): 182197 0.9 4 Zitzler E, T hiele L. SPE A2: Im proving the Strength Pareto 0.90 Evolutionary Algorithm [R ]. Technique Report: 103, Sw is s Federal In st itute of Technology( ETH) Zurich: Computer 0 0.86 En gineering and Netw orks Laboratory (TIK, 2001 0.50.60.70.80.9 00.0050.010.0150.02 A(x) Al) [5 Coello C A. Evolutionary Algorithms for Sol ving Multi Ol 图5问题Z2中100个粒子图6问题Z3中100个粒子 jective Problem s[ M]. New Y or k: Kluw er Academ iC, 2002 迭代500次时 Pareto曲线迭代500次时 Parcto曲线 [61 Laumanns M. a Unified Model for Mul tiobjective e volt 1.0 tionary Algorithm s with Elitism[ C] h Proc of the 2000 CoIr Evolut ionary Comput at ion, 2000: 465 [7] Eberhart R C, Kenn edy J. A New Opt mizer U sing Part icle Swarm T heory[ c] Proc of the 6th Int'l Sy mp Micro Ma ch ine and h uman Science. 1995: 3943. 0 [8 Mostagh im S, Teich J. Strategies for Finding Good Local G uides in Multt o bjective Particle Sw arm Optimization[ C] ll P of 2003 e ee s Intel lis mp,2003:2633 0.20.40.60.810 f(x) 2007,34(7):187192 图7问题ZDT6中200个粒子迭代1000次时 Pareto曲线 3.5 3.0 2004,41(7):12861291 2.5 EMOPSO: A 1.5 : G T, Coello C a, qu Multiobjective Particle sy O ptimizer with Emph 1.0 Efficiency C] Proc of Evolutionary Multt objective O ptt mization.2007:272285, f(x)00.5f(x) flx) f(x) 图8三目标函数100个粒子图9三目标函数200个粒子 迭代600次时的 Pareto曲线选代600次时的 Pareto曲线 Pareto Paret 88 1994-2013ChinaAcademicJournalelEctronicPublishingHouseAllrightsreservedhttp://www.cnki.net

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