Multiobjective Optimization Differential Evolution Enhanced with Principle Component Analysis for Constrained Optimization

Multiobjective optimization evolutionary algorithms have been successfully applied to solving constrained optimization problems. This paper proposes a new multiobjective optimization differential evolution algorithm for constrained optimization. Through a study of fitness landscapes using principle component analysis, we discover a statistic method of identifying the valley direction in a valley landscape. Based on this discovery, a new search operator called PCA-projection is constructed which projects an individual to a position along the valley direction. Then multiobjective optimization differential evolution using this projection operator is designed for constrained optimization. A comparative experiment has been implemented between the proposed algorithm and a state-of-the-art multiobjective differential evolution algorithm on a standard set of 24 benchmarks. Experimental results show that the new algorithm makes a significant improvement in terms of solution accuracy. The proposed algorithm is also competitive with ten evolutionary algorithms participated in an IEEE CEC 2006 competition and is ranked third in terms of the final rank.