Many-objective optimization algorithm based on the similarity principle and multi-mechanism collaborative search

In the realm of many-objective optimization, environmental selection based on Pareto-dominance relations often yields a few dominance-resistant individuals (DRIs), which are hard to be naturally eliminated during the algorithm's iteration process. To accelerate algorithm convergence, ensure algorithm stability, and effectively search for boundary solutions, an elimination of similar individuals evolutionary algorithm (ESEA) based on multi-mechanism collaborative search is proposed in this paper to suppress significant DRIs that have a considerable impact on the algorithm's performance. In 2D or 3D objective spaces, by eliminating individuals with similar distances, the ESEA is able to ensure population diversity and attain a good distribution of solutions. In many-objective spaces, through introducing the ISDE+ indicator and eliminating angle-similar individuals, the ESEA can alleviate premature convergence and promote exploration in different regions of the search space, thereby increasing the possibility of discovering diverse and potentially superior solutions. This is conducive to maintaining boundary solutions well and enhancing the algorithm's ability to approximate the Pareto front. The proposed algorithm is compared with five state-of-the-art optimizers on 21 test problems. The experimental results demonstrate the promising performance of the proposed algorithm while effectively searching for the ideal Pareto front. It is obvious that eliminating similar individuals and conducting multiple mechanism collaborative searches can enhance the selection pressure toward the ideal Pareto front. Furthermore, the proposed ESEA can not only find a set of well-distributed points on the entire Pareto-optimal front but also effectively maintain boundary solutions extremely well.