Multi-Objective Hybrid Algorithm Integrating Gradient Search and Evolutionary Mechanisms

Abstract

The current multi-objective evolutionary algorithm (MOEA) has attracted much attention because of its good global exploration ability, but its local search ability near the optimal value is relatively weak, and for optimization prob lems with large-scale decision variables, the number of populations and iterations required by MOEA are very large, so the optimization efficiency is low. Gradient-based optimization algorithms can overcome these problems well, but they are difficult to be applied to multi-objective problems (MOPs). Therefore, this paper introduced random weight function on the basis of weighted average gradient, developed multi-objective gradient operator, and combined it with non-dominated genetic algorithm based on reference points (NSGA- III) proposed by Deb in 2013 to develop multi-objective optimization algorithm (MOGBA) and multi-objective Hybrid Evolutionary algorithm (HMOEA). The latter greatly enhances the local search capability while retaining the good global exploration capability of NSGA-III. Numerical experiments show that HMOEA has excellent capture capability for various Pareto formations, and the efficiency is improved by times compared with typical multi-objective algorithms. And further HMOEA is applied to the multi-objective aerodynamic optimization problem of the RAE2822 airfoil, and the ideal Pareto front is obtained, indicating that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.