فهرست نشریات علمی دسترسی آزاد ایران

Multi-objective optimization is central to addressing complex real-world problems involving competing objectives. The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) remains a widely used approach in this domain; however, it can face challenges in convergence, solution diversity, and robustness—particularly for multi-modal or discrete problems. This paper introduces a variant of NSGA-II that incorporates a fuzzy-based non-dominated sorting scheme using a $\Gamma$ function over trapezoidal fuzzy numbers, designed to provide more flexible and nuanced dominance assessments.The proposed method employs two tunable parameters to adjust fuzziness levels, allowing adaptive control over the trade-off between exploration and exploitation. Comprehensive experiments on the ZDT benchmark suite (ZDT1–ZDT6), conducted under realistic time constraints, are used to evaluate the approach. Results indicate that the fuzzy-enhanced NSGA-II frequently offers Pareto front approximations that are at least comparable to, and in many cases modestly improved over, those produced by the standard NSGA-II—particularly on test problems with discrete or multi-modal Pareto fronts.Both visual and statistical analyses across multiple runs support observations of efficient convergence and front coverage, while a sensitivity study highlights practical considerations for parameter selection. Overall, the fuzzy-based sorting strategy expands the methodological toolkit for multi-objective evolutionary optimization, offering a flexible and general framework suitable for diverse and challenging problem settings.