A Geometric Structure-Based Particle Swarm Optimization Algorithm for Multiobjective Problems

This paper presents a novel evolutionary strategy for multiobjective optimization in which a population's evolution is guided by exploiting the geometric structure of its Pareto front. Specifically, the Pareto front of a particle population is regarded as a set of scattered points on which interpolation is performed using a geometric curve/surface model to construct a geometric parameter space. On this basis, the normal direction of this space can be obtained and the solutions located exactly in this direction are chosen as the guiding points. Then, the dominated solutions are processed by using a local optimization technique with the help of these guiding points. Particle populations can thus evolve toward optimal solutions with the guidance of such a geometric structure. The strategy is employed to develop a fast and robust algorithm based on correlation analysis for solving the optimization problems with more than three objectives. A number of computational experiments have been conducted to compare the algorithm to another three popular multiobjective algorithms. As demonstrated in the experiments, the proposed algorithm achieves remarkable performance in terms of the solutions obtained, robustness, and speed of convergence.