• constrained optimization;
  • particle swarm optimization (PSO);
  • multi-objective optimization;
  • multi-objective particle swarm optimization (MOPSO)


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 such operations 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 their number 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 comparable to or better than the previously known best ones. © 2011 Wiley Periodicals, Inc. Electron Comm Jpn, 95(1): 43–54, 2012; Published online in Wiley Online Library ( DOI 10.1002/ecj.10385