A Two-Phase Framework of Locating the Reference Point for Decomposition-Based Constrained Multi-Objective Evolutionary Algorithms

Reference point is a key component in decomposition-based constrained multi-objective evolutionary algorithms (CMOEAs). A proper way of updating it requires considering constraint-handling techniques due to the existing constraints. However, it remains unexplored in this field. To remedy this issue, this paper firstly designs a set of benchmark problems with difficulties that a CMOEA must update the reference point effectively. Then a two-phase framework of locating the reference point is proposed to enhance performance of the current decomposition-based CMOEAs by evolving two populations—the main and external population. At the first phase, the external population evolves along with the main population to identify the approximate locations of the constrained and unconstrained Pareto front (PF). At the second phase, a location estimation mechanism is designed to estimate the best fit reference point between the two PFs for the main population by evolving the external population. Besides, a replacement strategy is used to drive the main population to the promising regions. Experimental studies are conducted on 26 benchmark problems, and the results highlight the effectiveness of the proposed framework.