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A Constraint-Tightening Feasible-Trajectory-Guided Two-Stage Evolutionary Algorithm

Year: 2026
Type: article
Abstract: Constrained multi-objective optimization problems (CMOPs) are widely encountered in practical engineering and scientific applications. To address these issues, this paper proposes a Constraint-Tightening Feasible-Trajectory-Guided Two-Stage Evolutionary Algorithm (CT-FTREA). By dividing the optimization process into a feasible-region-guided stage and a constrained Pareto front (CPF)-focused search stage, the algorithm effectively improves search efficiency and solution quality under complex constraints. In the first stage, CT-FTREA introduces an adaptive constraint boundary tightening strategy based on the number of function evaluations. By gradually reducing the ε-constraint boundaries, the population is guided from a relaxed search space toward the feasible region. This stage also employs objective-space reference points and a weighted fitness evaluation mechanism to select and evolve individuals, while an elite archive strategy preserves obtained feasible solutions, thereby enhancing the population’s ability to advance toward the feasible Pareto front. In the second stage, CT-FTREA exchanges the roles of the population and the archive, shifting the search focus to the fine-grained approximation of the CPF. An improved elite selection strategy combined with a differential evolution operator is used to generate offspring, adaptively balancing the exploration and exploitation capabilities of the population. The computational complexity of CT-FTREA is O(FEmax×N), where FEmax is the maximum number of function evaluations and N is the population size. Extensive experiments on 28 benchmark instances and four real-world engineering problems show that CT-FTREA outperforms seven state-of-the-art algorithms. Specifically, it achieves the best IGD result with a 54% improvement and the best HV result with a 50% improvement over competing methods on the test problems. The algorithm also demonstrates statistically significant advantages in terms of convergence, solution quality, and robustness (Wilcoxon rank-sum test at a 0.05 significance level). CT-FTREA algorithm offers an efficient and robust solution to CMOPs, with competitive performance on both benchmark and real-world problems.
Source: Mathematics
Language: English
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7133510865
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