Preference-Inspired Co-Evolutionary Algorithms With Local PCA Oriented Goal Vectors for Many-Objective Optimization

It remains a challenge to identify a satisfactory set of tradeoff solutions for many-objective optimization problems that have more than three objectives. Coevolving the solutions with preference is becoming increasingly popular due to the enhanced local search capability, which makes it suitable for solving many-objective optimization problems. The framework of preference-inspired co-evolutionary algorithms (PICEAs) is suitable for obtaining promising performance for such problems, and the PICEA with goal vectors (PICEA-g) has achieved good performance in many applications. In this paper, an improved PICEA-g is proposed to further resolve this long-standing problem. The local principal component analysis operator is used as a controller to further expand the ability of the PICEA-g algorithm and enhance the convergence of PICEA-g. The proposed algorithm was evaluated using several widely used benchmark test suites that had 3-15 objectives and made a systematic comparison with five state-of-the-art multi-objective evolutionary algorithms. The resulting substantial amount of experimental results revealed that the algorithm we proposed could have good performance on most of the test suites assessed in our research, and it performs very well compared with other many-objective optimization algorithms. In addition, a sensitivity test was carried out to explore the impact of a key parameter in the algorithm we proposed in this study.