Difficulty Controllable and Scalable Constrained Multi-objective Test Problems

In this paper, we propose a general toolkit to construct constrained multi-objective optimisation problems (CMOPs) with three different kinds of constraint functions. Based on this toolkit, we suggested eight constrained multi-objective optimisation problems named CMOP1-CMOP8. As the ratio of feasible regions in the whole search space determines the difficulty of a constrained multi-objective optimisation problem, we propose four test instances CMOP3-6, which have very low ratio of feasible regions. To study the difficulties of proposed test instances, we make some experiments with two popular CMOEAs - MOEA/D-CDP and NSGA-II-CDP, and analysed their performances.