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Over the past decade, surrogate-assisted evolutionary algorithms have demonstrated their effectiveness across various computationally expensive real-world domains. Nevertheless, the focus of surrogate-assisted multi-objective evolutionary algorithms has primarily centered on non-constrained optimization problems. There has been relatively limited exploration into addressing expensive constrained multi-objective optimization problems, which inherently require a delicate equilibrium between convergence, diversity, and feasibility. To bridge this gap, this paper concentrates on constrained multi-objective optimization problems where both objectives and constraints involve substantial computational costs. In response, a novel data-driven constrained multi-objective evolutionary algorithm is introduced, leveraging feasible region localization and performance-improvement exploration. For feasible region localization, a constraints-domain-search strategy is presented to locate the feasible region quickly. To enhance performance-improvement exploration, a progressive enhancement of convergence and diversity is achieved through the incorporation of constraint penalties. With the help of exploration and exploitation, the proposed algorithm can balance convergence, diversity, and feasibility while working within a limited number of function evaluations. By comparing the proposed algorithm with state-of-the-art algorithms on 66 mathematical problems and a resource-intensive black-box problem, its outstanding performance for solving multi-objective constrained black-box problems is validated. • A notably effective multi-objective constrained black-box optimization algorithm is proposed. • A constraints-domain-search strategy is designed to rapidly decrease the CV while avoiding a local minimum in the CV space. • A performance-improvement exploration strategy is presented through the integration of constraint penalties. • Comprehensive conclusions that can serve as valuable insights for future algorithm development are included. [ABSTRACT FROM AUTHOR]