多目的Particle Swarm Optimizationに基づく制約条件付き大域的最適化手法

This paper proposes a constrained global optimization method based on Multi-Objective Particle Swarm Optimization (MOPSO). A constrained optimization problem is transformed into another bi-objective problem which minimizes both the original objective function and the total amount of constraint violations. Then, the global optimum of the former problem is obtained as the Pareto optimal solution of the latter one having no constraint violation. In order to find the particular Pareto optimal solution, the proposed method introduces to MOPSO the following operations such as (a) restricting the number of Pareto optimal solutions obtained at each iteration of MOPSO to urge particles to approach the feasible set of the original constrained problem, (b) choosing the most promising Pareto optimal solution as the global best solution so as to exclude solutions dominated by it, and (c) encouraging to add Pareto optimal solutions if the number of them is too small to recover the diversity of search. Numerical examples verify the effectiveness, efficiency and wide applicability of the proposed method. For some famous engineering design problems, in particular, it can find solutions which are comparative to or better than the previously known best ones.

[1]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[2]  Shiyuan Yang,et al.  Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm , 2007, Inf. Process. Lett..

[3]  R. Haftka,et al.  Constrained particle swarm optimization using a bi-objective formulation , 2009 .

[4]  Carlos A. Coello Coello,et al.  Use of a self-adaptive penalty approach for engineering optimization problems , 2000 .

[5]  Sven Leyffer,et al.  Nonlinear programming without a penalty function , 2002, Math. Program..

[6]  W. Zangwill.  Non-Linear Programming Via Penalty Functions , 1967 .

[7]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[8]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[9]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[10]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..

[11]  Eitaro Aiyoshi,et al.  A penalty approach to handle inequality constraints in particle swarm optimization , 2010, 2010 IEEE International Conference on Systems, Man and Cybernetics.

[12]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[13]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[14]  C.A. Coello Coello,et al.  MOPSO: a proposal for multiple objective particle swarm optimization , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[15]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[16]  Maurice Clerc,et al.  The particle swarm - explosion, stability, and convergence in a multidimensional complex space , 2002, IEEE Trans. Evol. Comput..

[17]  Carlos A. Coello Coello,et al.  THEORETICAL AND NUMERICAL CONSTRAINT-HANDLING TECHNIQUES USED WITH EVOLUTIONARY ALGORITHMS: A SURVEY OF THE STATE OF THE ART , 2002 .

[18]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[19]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[20]  Ling Wang,et al.  A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization , 2007, Appl. Math. Comput..

[21]  Kalyanmoy Deb,et al.  Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems , 1999, Evolutionary Computation.