Handling constrained many-objective optimization problems via determinantal point processes

Although various research studies have been performed to solve constrained multi-objective optimization and many-objective optimization problems, more attention should be paid to the widely existing constrained many-objective optimization problems (CMaOPs). Balancing convergence, diversity and feasibility is an essential issue for CMaOPs. To this end, traditional methods tend to adopt one-by-one selection or deletion strategies. However, these strategies rarely consider the quality of the entirety. Consequently, some poorly performed yet promising solutions might be discarded, finally degrading the performance. To overcome this drawback, this article first introduces the determinantal point processes (DPPs) in Machine Learning to handle CMaOPs. A new algorithm is proposed by applying the DPPs rather than traditional selection strategies for selecting population and archive. To effectively utilize DPPs, two novel Kernel Matrices are designed to represent convergence, diversity, and feasibility qualities of solutions in population and archive, respectively. Besides, a new ε-constrained technique is tailored for the update strategies of archive and corner solution set to handle CMaOPs, especially those with complex constraints. Experiments on 16 different CMaOPs of 77 instances with up to 15 objectives demonstrated the superiority of the proposed method to the state-of-the-art algorithms.