Covariance matrix adaptive strategy for a multi-objective evolutionary algorithm based on reference point

In this article, an effective method, called an adaptive covariance strategy based on reference points (RPCMA-ES) is proposed for multi-objective optimization. In the proposed algorithm, search space is divided into independent sub-regions by calculating the angle between the objective vector and the reference vector. The reference vectors can be used not only to decompose the original multi-objective optimization problem into a number of single-objective subproblems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front (PF). In this respect, any single objective optimizers can be easily used in this algorithm framework. Inspired by the multi-objective estimation of distribution algorithms, covariance matrix adaptation evolution strategy (CMA-ES) is involved in RPCMA-ES. A state-of-the-art optimizer for single-objective continuous functions is the CMA-ES, which has proven to be able to strike a good balance between the exploration and the exploitation of search space. Furthermore, in order to avoid falling into local optimality and make the new mean closer to the optimal solution, chaos operator is added based on CMA-ES. By comparing it with four state-of-the-art multi-objective optimization algorithms, the simulation results show that the proposed algorithm is competitive and effective in terms of convergence and distribution.