In recent years, a large number of approaches to constrained multi-objective optimization problems (CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly fine-tuned strategy or technique might overfit some problem types, resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties. First, the constrained Pareto front (CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance (i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search, which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.
