Abstract:In order to improve the convergence precision and search performance of multi-objective optimization algorithms, a multi-population of multi-objective particle swarm optimization algorithm based on velocity communication is proposed. The algorithm introduces the speed communication mechanism, divides the population into multiple sub-populations to achieve speed information sharing, improves the particle single search mode, and enhances the global search ability of the algorithm. Chaos mapping is used to optimize the inertia weight, and the particle search ergodicity and globality are improved. In order to reduce the possibility that the algorithm falls into the local optimal Pareto frontier in the late stage of operation, different mutation operations are performed on each sub-population. The algorithm is compared with NSGA-Ⅱ, SPEA2, AbYSS, MOPSO, SMPSO and GWASF-GA state-of-the-art multi-objective optimization algorithms. Experimental results show that the solution set obtained by this algorithm has better convergence and distribution.
[1]Wei L X, Li X, Fan R, et al. A Hybrid Multi-objective Particle Swarm Optimization Algorithm Based on R2 Indicator [J]. [WTBX][STBX]IEEE Access[STBZ][WTBZ], 2018, 6: 14710-14721.
[2]刘彬, 顾昕峰, 孙超, 等. 基于梯形区间软约束的多目标优化预测控制算法研究 [J]. 计量学报, 2018, 39(4): 562-567.
Liu B, Gu X F, Sun C, et al. Research on Multi-objective Optimization Predictive Control Algorithm Based on Trapezoidal Interval Soft Constraint [J]. [WTBX][STBX]Acta Metrologica Sinica[STBZ][WTBZ], 2018, 39(4): 562-567.
[3]滕峰成, 郝宇, 林晓乐. 基于PSO算法的MFF模型的参数辨识与优化 [J]. 计量学报, 2017, 38(2): 209-214.
Teng F C, Hao Y, Lin X L. Parameter Identification and Optimization of MFF Model Based on PSO Algorithm [J]. [WTBX][STBX]Acta Metrologica Sinica[STBZ][WTBZ], 2017, 38(2): 209-214.
[4]
杨景明,马明明,车海军,等. 多目标自适应混沌粒子群优化算法[J]. 控制与决策, 2015, 30(12): 2168-2174.
Yang J M, Ma M M, Che H J, et al. Multi-objective adaptive chaotic particle swarm optimization algorithm [J]. [WTBX][STBX]Control & Decision[STBZ][WTBZ], 2015, 30(12): 2168-2174.
[5]谢承旺, 王志杰, 夏学文. 应用档案精英学习和反向学习的多目标进化算法 [J]. 计算机学报, 2017, 40(3): 757-772.
Xie C W, Wang Z J, Xia X W. Multi-objective evolutionary algorithm for applying archive elite learning and opposition learning [J]. [WTBX][STBX]Journal of Computer[STBZ][WTBZ], 2017, 40(3): 757-772.
[6]Zhang J H, Ding X M. A Multi-Swarm Self-Adaptive and Cooperative Particle Swarm Optimization [J]. [WTBX][STBX]Engineering Applications of Artificial Intelligence[STBZ][WTBZ], 2011, 24(6): 958-967.
[7]刘衍民, 赵庆祯, 隋常玲. 基于动态多种群的多目标粒子群算法 [J]. 计算机仿真, 2011, 28(5): 241-245.
Liu Y M, Zhao Q Z, Shui C L. Multi-objective particle swarm optimization algorithm based on dynamic multi-group [J]. [WTBX][STBX]Computer Simulation[STBZ][WTBZ], 2011, 28(5): 241-245.
[8]Mokarram V, Banan M R. A new PSO-based algorithm for multi-objective optimization with continuous and discrete design variables [J]. [WTBX][STBX]Structural & Multidisciplinary Optimization[STBZ][WTBZ], 2018, 57(2): 509-533.
[9]Srinivas N , Deb K . Multi-objective optimization using non-dominated sorting in genetic algorithms [J]. [WTBX][STBX]Evolutionary Computation[STBZ][WTBZ], 2014, 2(3): 221-248.
[10]公茂果, 焦李成, 杨咚咚, 等. 进化多目标优化算法研究 [J]. 软件学报, 2009, 20(2): 271-289.
Gong M G, Jiao L C, Yang D D, et al. Research on Evolutionary Multi-objective Optimization Algorithm [J]. [WTBX][STBX]Journal of Software[STBZ][WTBZ], 2009, 20(2): 271-289.
[11]Coello C A C, Pulido G T, Lechuga M S. Handling multiple objectives with particle swarm optimization [J]. [WTBX][STBX]IEEE Transactions on Evolutionary Computation[STBZ][WTBZ], 2004, 8(3): 256-279.
[12]Kennedy J, Eberhart R. Particle swarm optimization [C]//Proc of 1995 IEEE Int Conf Neural Networks. Perth, Australia, 1995: 1942-1948.
[13]付亚平, 王洪峰, 黄敏, 等. 基于自适应多种群策略的混合多目标优化算法 [J]. 系统工程学报, 2017, 32(6): 738-748.
Fu Y P, Wang H F, Huang M, et al. Hybrid multi-objective optimization algorithm based on adaptive multi-group strategy [J]. [WTBX][STBX]Journal of Systems Engineering[STBZ][WTBZ], 2017, 32(6): 738-748.
[14]李兵, 蒋慰孙. 混沌优化方法及其应用 [J]. 控制理论与应用, 1997, (4): 613-615.
Li B, Jiang W S. Chaos optimization method and its application [J]. [WTBX][STBX]Control theory and application[STBZ][WTBZ], 1997, (4): 613-615.
[15]Xia X, Liu J, Hu Z. An improved particle swarm optimizer based on tabu detecting and local learning strategy in a shrunk search space [J]. [WTBX][STBX]Applied Soft Computing Journal[STBZ][WTBZ], 2014, 23(23): 76-90.
[16]周新宇, 吴志健, 王晖, 等. 一种精英反向学习的粒子群优化算法 [J]. 电子学报, 2013, 41(8): 1647-1652.
Zhou X Y, Wu Z J, Wang H, et al. A Particle Swarm Optimization Algorithm for Elite Reverse Learning [J]. [WTBX][STBX]Electronic Journal[STBZ][WTBZ], 2013, 41(8): 1647-1652.
[17]徐辰华, 李成县, 喻昕, 等. 基于Cat混沌与高斯变异的改进灰狼优化算法 [J]. 计算机工程与应用, 2017, 53(4): 1-9.
Xu C H, Li C X, Yu X, et al. Improved Grey Wolf Optimization Algorithm Based on Cat Chaos and Gaussian Variation [J]. [WTBX][STBX]Computer Engineering and Applications[STBZ][WTBZ], 2017, 53(4): 1-9.
[18]康岚兰, 董文永, 田降森. 一种自适应柯西变异的反向学习粒子群优化算法 [J]. 计算机科学, 2015, 42 (10): 226-231.
Kang L L, Dong W Y, Tian J S. A Reverse Learning Particle Swarm Optimization Algorithm Based on Adaptive Cauchy Variation [J]. [WTBX][STBX]Computer science[STBZ][WTBZ], 2015, 42(10): 226-231.
[19]赵新超, 刘国莅, 刘虎球, 等. 基于非均匀变异和多阶段扰动的粒子群优化算法 [J]. 计算机学报, 2014, 37(9): 2058-2070.
Zhao X C, Liu G L, Liu H Q, et al. Particle swarm optimization algorithm based on non-uniform variation and multi-stage disturbance [J]. [WTBX][STBX]Journal of Computer[STBZ][WTBZ], 2014, 37(9): 2058-2070.
[20]Deb K, Pratap A, Agarwal S, et al. A fast and elitist multi-objective genetic algorithm: NSGA-Ⅱ [J]. [WTBX][STBX]IEEE Transactions on Evolutionary Computation[STBZ][WTBZ], 2002, 6(2): 182-197.
[21]Kim M, Hiroyasu T, Miki M, et al. SPEA2+: Improving the Performance of the Strength Pareto Evolutionary Algorithm 2 [C]// Parallel Problem Solving from Nature-PPSN Ⅷ. 2004:742-751.
[22]Nebro A Luna F, Alba E, et al. AbYSS: adapting scatter search to multi-objective optimization [J]. [WTBX][STBX]IEEE Transactions on Evolutionary Computation[STBZ][WTBZ], 2008, 12(4): 439-457.
[23]Nebro A J, Durillo J J, Garcia-Nieto J, et al. SMPSO: A new PSO-based metaheuristic for multi-objective optimization [C]// IEEE. 2009 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making. Nashville, TN, USA, 2009: 66-73.
[24]Saborido R, Ruiz A B, Luque M. Global WASF-GA: An Evolutionary Algorithm in Multi-objective Optimization to Approximate the Whole Pareto Optimal Front [J]. [WTBX][STBX]Evolutionary Computation[STBZ][WTBZ], 2017, 25(2): 309-349.
[25]Zitzler E, Deb K, Thiele L. Comparison of Multi-objective Evolutionary Algorithms: Empirical Results [J]. [WTBX][STBX]Evolutionary Computation[STBZ][WTBZ], 2000, 8(2): 173-195.
[26]Schaffer J D. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms [C]// International Conference on Genetic Algorithms. L. Erlbaum Associates Inc. 1985: 93-100.
[27]Kursawe F. A variant of evolution strategies for vector optimization [C]// International Conference on Parallel Problem Solving from Nature. Springer Berlin Heidelberg, 1990: 193-197.
[28]Griffel D. Multi-objective optimization using evolutionary algorithms by Deb [J]. [WTBX][STBX]Mathematical Gazette[STBZ][WTBZ], 2001, 83(497): 310-360.
[29]Hu W, Yen G G. Adaptive Multi-objective Particle Swarm Optimization Based on Parallel Cell Coordinate System [J]. [WTBX][STBX]IEEE Transactions on Evolutionary Computation[STBZ][WTBZ], 2015, 19(1): 1-18.
[30]Veldhuizen D A V, Lamont G B. On measuring multi-objective evolutionary algorithm performance [C]// IEEE. Congress on Evolutionary Computation. La Jolla, CA, USA, 2000.
[31]Schoot J R. Fault tolerant design using single and multi-criteria genetic algorithm optimization [D]. Massachusetts: Cambridge Institute of Technology, 1995.