A two-archive algorithm with decomposition and fitness allocation for multi-modal multi-objective optimization

Abstract This paper proposes a two-archive algorithm with decomposition and fitness allocation for multi-modal multi-objective optimization problems which have more than one Pareto-optimal solution set corresponding to the same objective vector. The general framework of the proposed method uses two archives, the convergence archive (CA) and the diversity archive (DA), which focus on the convergence and diversity of population, respectively. Both archives are based on a decomposition-based framework. In CA, the population update strategy adopts a fitness scheme, which is designed according to the change state of population during evolution, combining the convergence of the objective space with the diversity of the decision space. In DA, we use the crowding distance strategy to ensure the diversity of the decision space. Moreover, different neighborhood criteria are used to ensure the convergence and diversity of population for two archives. The algorithm is shown to not only locate and maintain a larger number of Pareto-optimal sets, but also to obtain good diversity and convergence in both the decision and objective spaces. In addition, the proposed algorithm is empirically compared with five state-of-the-art evolutionary algorithms on two series of test functions. Comparison results show that the proposed algorithm has better performance than the competing algorithms.