Abstract：In order to improve the search efficiency of particle swarm optimization and overcome the weakness of the decomposition method to deal with complex multi-objective problems, an improved self-adaptive multi-objective particle swarm optimization based on decomposition is proposed by considering the important influence of parent solutions selection and population updating on the convergence of algorithm and the distribution uniformity of solutions. To improve the convergence speed,a new fitness evaluation method is first designed to estimate solutions’ quality and the quality offspring solution won in the competition is added to the parent candidate solutions under the premise of ensuring diversity of evolutionary population by decomposition method. Next, to avoid the algorithm falling into local optimum, the personal optimal and global optimal positions are randomly selected from current particles’ neighbors or outside of neighbors when updating the particles. Last, to enhance the ability of algorithm to deal with complex problems, external archive is introduced as a candidate output population and crowding distance is used to maintain its diversity.The numerical experiments are carried out on twelve test functions and compared with five multi-objective optimization algorithms that can show the superiority of proposed algorithm.
庞锐, 高兴宝. 基于分解的改进自适应多目标粒子群优化算法[J]. 复杂系统与复杂性科学, 2018, 15(2): 77-87.
PANG Rui , GAO Xingbao. An Improved Self-Adaptive Multi-Objective Particle Swarm Optimization Based on Decomposition[J]. Complex Systems and Complexity Science, 2018, 15(2): 77-87.
[1]Kennedy J, Eberhart R C. Particle swarm optimization[C]. Proceedings of the 1995 International Conference on Neural Networks, Perth, Australia, 1995: 1942-1948. [2]Dorigo M, Birattari M, Stutzle T.Ant colony optimization[J]. IEEE Computational Intelligence Magazine,2006,1(4): 28-39. [3]Karaboga D. An idea based on honey bee swarm for numerical optimization[R]. Kayseri:Erciyes University,2005. [4]Storn R, Price K. Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces, TR-95-012[R]. Barkeley: Global International Computer Science Institute,1995. [5]Jiao L CH, Wang L. A novel genetic algorithm based on immunity[J]. IEEE Transactions on Systems, Man, and Cybernetics,2000,30(5): 552-561. [6]刘长平,叶春明.一种新颖的仿生群智能优化算法:萤火虫算法[J]. 计算机应用研究, 2011, 28(9):3295-3297. Liu Changping, Ye Chunming. Novel bio-inspired swarm intelligence optimization algorithm:firefly algorithm[J]. Application Research of Computers,2011,28(9): 3295-3297. [7]段海滨.蚁群算法的原理及其应用[M].北京:科学出版社, 2005. [8]Coello C A C, Lechuga M S. MOPSO: a proposal for multiple objective particle swarm optimization[C].Proceedings of IEEE Congress on Evolutionary Computation, Honolulu,2002: 1051-1056. [9]Coello C A C, Pulido G T, Lechuga M S. Handling multiple objective particle swarm optimization[J].IEEE Transaction on Evolutionary Computation,2004,8(3): 256-279. [10] Nebro A, Durillo J, Nieto J G, et al. SMPSO: a new PSO-based meta-heuristic form multi-objective optimization[C].Proceedings of IEEE Symposium on Computational Intelligence in Miulti-Criteria Decision-Making,2009: 66-73. [11] Li X D. A non-dominated sorting particle swarm optimizer for multiobjective optimization[C]. Proceedings of the Genetic and Evolutionary Computation Conference, Chicago,2003: 37-48. [12] Huang V L, Suganthan P N, Liang J J. Comprehensive learning particle swarm optimizer for solving multiobjective optimization problems[J]. International Journal of Intelligence Systems,2006,21(2): 209-226. [13] Peng W, Zhang Q. A decomposition-based multi-objective particle swarm optimization algorithm for continuous problems[C]. IEEE International Conference on Granular Computing, Hangzhou:IEEE, 2008:534-537. [14] Martinez S Z, Coello C C. A multi-objective particle swarm optimizer based on decomposition[C]. Proceedings of Annual Conference on Genetic and Evolutionary Computation,2011: 69-76. [15] Dai C, Wang Y P, Miao Y. A new multi-objective particle swarm optimization algorithm based on decomposition[J]. Information Science,2015,325(12): 541-557. [16] Moubayed N Al, Petrovski A, McCall J. D(2)MOPSO:MOPSO based on decomposition and dominance with archiving using crowding distance in objective and solution spaces[J]. Evolutionary Computation,2014,1(22): 47-77. [17] Zhao S Z, Suganthan P N. Two-lbests based multi-objective particle swarm optimizer[J]. Engineering Optimization,2011,1(43): 1-17. [18] Wang H F, Fu Y P, Huang M, et al. A hybrid evolutionary algorithm with adaptive multi-population strategy for multi-objective optimization problems[J]. Soft Computing,2017,20(2): 5975-5987. [19] 公茂果, 焦李成, 杨咚咚. 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 CH, Yang D D. Research on evolutionary multi-objective optimization algorithms[J]. Journal of Software,2009,20(2):271-289. [20] Deb K, Pratap A, Agarwal S, et al. A fast and elitist multi-objective genetic algorithm:NSGA-II[J]. IEEE Transaction on Evolutionary Computation,2002,6(2): 182-197. [21] Zhang Q F, Li H. MOEA/D: a multi-objective evolutionary algorithm based on decomposition[J].IEEE Transaction on Evolutionary Computation,2007,11(6): 712-731. [22] Lin Q ZH, Li J Q, Du Z H, et al. A novel multi-objective particle swarm optimization with multiple search strategies[J]. European of Operational Research,2015,247(3): 732-744. [23] Bosman P A N, Thierens D. The balance between proximity and diversity in multiobjective evolutionary algorithms[J]. IEEE Transaction on Evolutionary Computation,2003,7(2): 174-188. [24] Zitzler E, Deb K, Thiele L. Comparison of multi-objective evolutionary algorithms:Empirical results[J]. Evolutionary Computation,2008,8: 173-195. [25] Deb K,Thiele L, Laumanns M, et al. Scalable multi-objective optimization test problems[C].Proceedings of the 2002 Congress on Evolutionary Computation,Hawaii, USA,2002: 825-830. [26] Zhang CH J, Li X Y, Gao L, et al.An improved electromagnetism-like mechanism algorithm for constrained optimization[J]. Expert Systems with Applications,2013,40: 5621-5634.
