Large-scale cooperative co-evolution with bi-objective selection based imbalanced multi-modal optimization

Cooperative co-evolutionary algorithm (CC) which runs in a divide-and-conquer manner is effective to solve large-scale global optimization (LSGO) problems. Multi-modal optimization (MMO) intends to locate multiple optimal solutions. Using MMO methods in CC algorithm would be beneficial, because MMO optimizer can provide more information about the landscapes. In this paper, a bi-objective selection is proposed to introduce imbalance among the subpopulations of a MMO optimizer. Only the highly representative subpopulations will be active and evolved in the MMO procedure. With this imbalanced MMO technique, the CC's subcomponents could obtain sufficient coevolutionary information (multiple optima) from each other. In addition, more computational resources could be saved and used in CC procedure. Experiments and statistical comparisons are conducted on LSGO benchmark functions to verify the effectiveness of the proposed method. The results indicate that the proposed algorithm significantly outperforms seven state-of-the-art large-scale CC algorithms.