DMaOEA-εC: Decomposition-based many-objective evolutionary algorithm with the ε-constraint framework

Real-world problems which involve the optimization of multiple conflicting objectives are named as multi-objective optimization problems (MOPs). This paper mainly deals with the widespread and especially challenging many-objective optimization problem (MaOP) which is a category of the MOP with more than three objectives. Given the inefficiency of DMOEA-εC which is a state-of-the-art decomposition-based multi-objective evolutionary algorithm with the ε-constraint framework when dealing with MaOPs, a number of strategies are proposed and embedded in DMOEA-εC. To be specific, in order to overcome the ineffectiveness induced by exponential number of upper bound vectors, a two-stage upper bound vectors generation procedure is put forward to generate widely spread upper bound vectors in a high-dimensional space. Besides, a boundary points maintenance mechanism and a distance-based global replacement strategy are presented to remedy the diversity loss of a population. What's more, given the feasibility rule adopted in DMOEA-εC is simple but less effective, a two-side update rule which maintains both feasible and infeasible solutions for each subproblem is proposed to speed the convergence of a population. DMOEA-εC with the above-mentioned strategies, denoted as DMaOEA-εC, is designed for both multi- and many-objective optimization problems in this paper. DMaOEA-εC is compared with five classical and state-of-the-art multi-objective evolutionary algorithms on 29 test instances to exhibit its performance on MOPs. Furthermore, DMaOEA-εC is compared with five state-of-the-art many-objective evolutionary algorithms on 52 test problems to demonstrate its performance when dealing with MaOPs. Experimental studies show that DMaOEA-εC outperforms or performs competitively against several competitors on the majority of MOPs and MaOPs with up to ten objectives.