An improved version of DMOEA-ϵC for many-objective optimization problems: IDMOEA-ϵC

The decomposition strategy and the ϵ-constraint method are two important strategies in the field of multi-objective optimization. DMOEA-6C first attempts to incorporate the ϵ-constraint method into the decomposition strategy and solve a multi-objective optimization problem (MOP) via optimizing a series of scalar constrained subproblems collaboratively with the help of information from neighboring subproblems. However, given the inefficiency of applying DMOEA-6C to deal with many-objective optimization problems (MaOPs), a two-stage upper bound vectors generation procedure is proposed to generate widely spread upper bound vectors in a high-dimensional space. Besides, a boundary points maintenance mechanism is put forward to remedy the diversity loss of a population in DMOEA-ϵC. Based on the above, DMOEA-6C with the two-stage upper bound vectors generation procedure and the boundary points maintenance mechanism, named as IDMOEA-ϵC, is presented for MaOPs. IDMOEA-6C is compared with four state-of-the-art many-objective evolutionary algorithms, including HypE, NSGA-III, MOEADD, and Two-Arch2. Experimental studies demonstrate that IDMOEA-ϵC outperforms or performs competitively against these algorithms on the majority of sixteen DTLZ test instances with up to 10 objectives.