Solving constrained multi-objective optimization problems (CMOPs) involves simultaneously achieving convergence to the Pareto front, preserving solution diversity, and satisfying complex constraints. To address these challenges, this paper proposes a Multi-Criteria Game-driven Constrained Multi-Objective Evolutionary Algorithm (MGCMOEA), which leverages the complementary roles of a main population and an auxiliary population to jointly explore both feasible and infeasible regions. The algorithm introduces a refined feasibility classification mechanism that differentiates weakly feasible solutions from infeasible ones, thereby accelerating convergence while preserving potentially valuable solutions. To enhance cooperation between populations, MGCMOEA incorporates a multi-criteria game-theoretic selection model that integrates dynamic game theory with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). This model improves the guidance provided by the auxiliary population during evolution. Furthermore, to overcome inefficiencies associated with static population sizes, a dynamic resource allocation strategy is adopted, enabling adaptive distribution of computational resources throughout the evolutionary process. Experimental results on 47 benchmark functions and 12 real-world CMOPs demonstrate that MGCMOEA consistently outperforms 8 state-of-the-art algorithms in terms of convergence, diversity, and feasibility.

The solution to constrained multi-objective optimization problems (CMOPs) requires optimizing the objective functions while satisfying the constraint conditions. To effectively address CMOPs, algorithms must balance objectives and constraints. However, the limited adaptability of specific constraint-handling techniques (CHTs) has hindered the widespread applicability of constrained multi-objective evolutionary algorithms (CMOEAs). To overcome this limitation, this article proposes a population state-based CMOEA. First, a model is developed to identify population states based on the positions of the primary and auxiliary populations. Tailored environmental selection models are then designed for the auxiliary population according to different states, enabling them to guide the evolution of the main population more effectively. By dynamizing the CHTs, the proposed algorithm can adapt to a broader and more complex range of CMOPs. Additionally, state-specific optimal individual selection methods are introduced, allowing the auxiliary population to escape local optima and accelerate exploration. A simple yet effective resource allocation model is incorporated to address the potential computational resource waste associated with dual populations, enhancing the resource utilization. Comprehensive tests, including comparisons with seven state-of-the-art algorithms, were conducted on 47 benchmark functions and 12 real-world problems. The experimental results demonstrate that the proposed CMOEA outperforms existing CMOEAs in its convergence and diversity.

The resolution of constrained multiobjective optimization problems involves simultaneously optimizing multiple objectives while adhering to specific constraints. Effective constrained multiobjective optimization solvers must strike a balance between objective optimization and constraint satisfaction. This study introduces a novel approach that compresses the mapping between the objective and constraint spaces to obscure their explicit information. This compression is achieved by normalizing both spaces and projecting them onto an $n$-dimensional spherical volume. The key advantage of this compression mapping is that it reduces fine-grained information redundancy while retaining the dominant convergence trend toward the ideal region, thereby providing a compact surrogate view for selection under constraints. Although this transformation inevitably causes some information loss, it retains the key property of convergence toward the origin. Based on the mapped space, a selection mechanism combining fast non-dominated sorting and crowding distance is employed to guide the population across infeasible regions and maintain diversity. To further enhance computational efficiency, a dynamic archiving strategy is introduced. This mechanism regulates the number and quality of archived individuals, storing only valuable solutions and comparing offspring with existing archives to prevent redundant evaluations. These components are integrated into a new constrained multiobjective evolutionary algorithm. The algorithm is comprehensively validated on 42 benchmark functions and 12 real-world problems. Experimental results demonstrate that the proposed method achieves superior performance compared to state-of-the-art constrained multiobjective evolutionary algorithms in terms of convergence and computational efficiency.

The effective resolution of constrained multi-objective optimization problems (CMOPs) requires a delicate balance between maximizing objectives and satisfying constraints. Previous studies have demonstrated that multi-swarm optimization models exhibit robust performance in CMOPs; however, their high computational resource demands can hinder convergence efficiency. This article proposes an environment selection model based on Bayes’ theorem, leveraging the advantages of dual populations. The model constructs prior knowledge using objective function values and constraint violation values, and then, it integrates this information to enhance selection processes. By dynamically adjusting the selection of the auxiliary population based on prior knowledge, the algorithm significantly improves its adaptability to various CMOPs. Additionally, a population size adjustment strategy is introduced to mitigate the computational burden of dual populations. By utilizing past prior knowledge to estimate the probability of function value changes, offspring allocation is dynamically adjusted, optimizing resource utilization. This adaptive adjustment prevents unnecessary computational waste during evolution, thereby enhancing both convergence and diversity. To validate the effectiveness of the proposed algorithm, comparative experiments were performed against seven constrained multi-objective optimization algorithms (CMOEAs) across three benchmark test sets and 12 real-world problems. The results show that the proposed algorithm outperforms the others in both convergence and diversity.