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A multi-objective particle swarm optimization (MOPSO) is known as a multiple point search-based meta-heuristic approach to find diverse Pareto solutions efficiently for design problem consisting of continuous design variables, but has difficulty to handle the constraint conditions. Overcoming the disadvantage, this study proposes a hybrid algorithm incorporating MOPSO and sensitivity analysis on constrained conditions. When design candidate with constraint violation appears during searching process, the design candidate is moved to the feasible domain using gradient information of the constraint conditions. Then, the design candidate is moved to the feasible boundary using the bi-section method. The forced transferee is applied to the design candidate in MOPSO algorithms. The proposed approach is different from the other hybrid approaches that the Pareto candidates are improved by local searching algorithms. Rather, the approach recovers the violated design candidate to the Pareto candidate by moving to the feasible boundary. This approach is useful for the design problem such as most structural design problems that the constraint sensitivity is easily obtained and that the Pareto sets will exist on the feasible boundary. Through several numerical examples, the diversity and convergency of the Pareto solutions as the performance of the proposed method are investigated.

Constraint Handling in Multiobjective Particle Swarm Optimization Incorporating Sensitivity Analysis on Constraint Condition