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Constrained optimization problems (COPs) are common in many fields. To solve such problems effectively, in this paper, we propose a new constrained optimization evolutionary algorithm (COEA) named CACDE that combines an adaptive trial vector generation strategy-based differential evolution (DE) algorithm with a cluster-replacement-based feasibility rule. In CACDE, some potential mutation strategies, scale factors and crossover rates are stored in candidate pools, and each element in the pools is assigned a selection probability. During the trial vector generation stage, the mutation strategy, scale factor and crossover rate for each target vector are competitively determined based on these selection probabilities. Meanwhile, the selection probabilities are dynamically updated based on statistical information learned from previous searches in generating improved solutions. Moreover, to alleviate the greediness of the feasibility rule, the main population is divided into several clusters, and one vector in each cluster is conditionally replaced with an archived infeasible vector with a low objective value. The superior performance of CACDE is validated via comparisons with some state-of-the-art COEAs over 2 sets of artificial problems and 5 widely used mechanical design problems. The results show that CACDE is an effective approach for solving COPs, basically due to the use of adaptive DE and cluster-replacement-based feasibility rule. [ABSTRACT FROM AUTHOR]