Document Type : Research Paper
Author
Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran
Abstract
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.
Keywords
- Multiobjective Optimization
- Evolutionary Algorithms
- NSGA-II Algorithm
- Fuzzy Number
- Pareto Front Approximation
- Non-Dominated Sorting
Main Subjects
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