A Constrained Multi/Many-Objective Particle Swarm Optimization Algorithm With a Two-Level Balance Scheme

Constrained multi-objective optimization problems are common in practical engineering and are more difficult to handle than unconstrained problems. In general, it is necessary to find a balance between the convergence and diversity of solutions as well as the feasibility. For the constrained multi/many-objective optimization problem, a particle swarm optimization algorithm based on a two-level balance strategy is proposed. In contrast to existing views, the first level of the proposed algorithmic framework emphasizes convergence, while diversity and feasibility are considered together as the second-level scheme. An ensemble fitness ranking was used to improve the convergence of the proposed algorithm. To balance diversity and solution feasibility, the solutions are selected by combining the angles between the solutions using the constraint dominance principle. A penalty-based boundary-crossing approach is used as a utility function to calculate the fitness of the populations, which is compared with six state-of-the-art constrained multi/many-objective evolutionary optimization algorithms on multiple constrained test suites, and the experimental results show that the proposed algorithm is highly competitive in most test problems. Furthermore, to illustrate the effect of different utility functions on the performance of the algorithm, the Chebyshev decomposition method is employed and compared with the former, and the results show that different utility functions need to be chosen to cope with problems of different characteristics.