پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 31 |
| تعداد شمارهها | 834 |
| تعداد مقالات | 8,015 |
| تعداد مشاهده مقاله | 14,852,479 |
| تعداد دریافت فایل اصل مقاله | 9,586,503 |
A Fuzzy Non-Dominated Sorting Approach for Enhanced Multi-Objective Optimization: A Modified of NSGA-II | ||
| Iranian Journal of Fuzzy Systems | ||
| دوره 22، شماره 4، مهر و آبان 2025، صفحه 77-96 اصل مقاله (3.19 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2025.49820.8796 | ||
| نویسنده | ||
| Hamideh Nasabzadeh* | ||
| Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Multiobjective Optimization؛ Evolutionary Algorithms؛ NSGA-II Algorithm؛ Fuzzy Number؛ Pareto Front Approximation؛ Non-Dominated Sorting | ||
| مراجع | ||
|
[1] C. A. Coello Coello, Particle swarm optimization in a multiobjective scenario, in: S. Q. Zeng (Ed.), Guide to Design Principles of Interactive Multimedia, Springer, New York, (2007), 249-281. ISBN: 978-0-387-33254-3. [2] K. Deb, Multi-objective optimization using evolutionary algorithms, Wiley, Chichester, 2001. ISBN: 978-0-471 87339-6. [3] K. Deb, H. Jain, An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: Introducing NSGA-III, IEEE Transactions on Evolutionary Computation, 18(4) (2014), 576-601. https://doi.org/10.1109/TEVC.2013.2281535 [4] K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6(2) (2002), 182-197. https://doi.org/10.1109/4235.996017 [5] C. M. Fonseca, P. J. Fleming, Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization, Proc. 5th International Conference Genetic Algorithms, (1993), 416-423. [6] A. Ghaffari, M. Akbari, Z. Forouzanfar, A novel fuzzy adaptive algorithm for multi-objective optimization with enhanced convergence, Big Data and Computational Vision, 5(1) (2024), 15-28. https://doi.org/10.22105/ bdcv.2024.481945.1208 [7] D. E. Goldberg, Genetic algorithms in search, optimization, and machine learning, Addison-Wesley, Reading, MA, 1989. [8] H. Ishibuchi, Y. Hitano, N. Tsukamoto, Evolutionary many-objective optimization: A short review, Proc. IEEE Congress on Evolutionary Computation (CEC), (2008), 2419-2426. https://doi.org/10.1109/CEC.2008. 4631169 [9] H. Ishibuchi, T. Murata, A multiobjective genetic algorithm for the flowshop scheduling problem, IEEE Transactions on Systems, Man, and Cybernetics, Part C, 28(3) (1998), 397-407. https://doi.org/10.1109/5326.704576 [10] S. Karimi, S. R. Seyed Tabatabaei, H. R. Pourreza, Integrated energy management and optimization of a multi microgrid system considering economic and environmental criteria, Expert Systems with Applications, 183 (2021), 115231. https://doi.org/10.1016/j.eswa.2021.115231 [11] A. Kaufmann, Introduction to fuzzy logic: From preference to consensus, Academic Press, New York, 1985. ISBN: 978-0-442-26163-0. [12] M. K¨oppen, The artificial immune system: A novel paradigm to search in the discrete domain, in: A. Kistner (Ed.), Applied Soft Computing Technologies: The Challenge of Complexity, Springer, Berlin, (2005), 27-42. https: //doi.org/10.1007/978-3-540-31880-4-28 [13] S. Kukkonen, J. Lampinen, GDE3: The third evolution step of generalized differential evolution, Proc. IEEE Congress on Evolutionary Computation, (2007), 4433-4440. https://doi.org/10.1109/CEC.2007.4424990 [14] R. Kumar, S. Maheshwari, S. S. Chouhan, A. Kumar, Multiobjective optimization based on evolutionary algorithms: A review, IEEE Access, 11 (2023), 8678-8698. https://doi.org/10.1109/ACCESS.2023.3237147 [15] B. Naderi, F. Jolai, R. Tavakkoli-Moghaddam, Evolutionary algorithms for multi-objective optimization: A com prehensive survey, International Journal of Production Research, 60(17) (2022), 5081-5121. https://doi.org/ 10.1080/00207543.2022.2045451 [16] J. D. Schaffer, Multiple objective optimization with vector evaluated genetic algorithms, Proc. 1st International Conference Genetic Algorithms, (1985), 93-100. [17] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65) 90241-X [18] Q. Zhang, W. Liu, H. Li, The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances, Proc. IEEE Congress on Evolutionary Computation, (2009), 203-208. https://doi.org/10.1109/CEC. 2009.4982949 [19] X. Zhang, Y. Tian, Y. Jin, Approximate non-dominated sorting for evolutionary many-objective optimization, Information Sciences, 369 (2016), 14-33. https://doi.org/10.1016/j.ins.2016.06.007 [20] E. Zitzler, K. Deb, L. Thiele, Comparison of multiobjective evolutionary algorithms: Empirical results, Evolutionary Computation, 8(2) (2000), 173-195. https://doi.org/10.1162/106365600568202 [21] E. Zitzler, S. K¨unzli, Indicator-based selection in multiobjective search, in: Parallel Problem Solving from Na ture– PPSN VIII, Lecture Notes in Computer Science, 3242 (2004), 832-842. https://doi.org/10.1007/ 978-3-540-30217-9-84 [22] E. Zitzler, M. Laumanns, L. Thiele, SPEA2: Improving the strength Pareto evolutionary algorithm, Technical Report 103, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, 2001. [23] E. Zitzler, L. Laumanns, L. Thiele, C. M. Fonseca, V. Grunert da Fonseca, Multiobjective optimization using evolutionary algorithms: From theory to practice, IEEE Transactions on Evolutionary Computation, 8(4) (2004), 371-395. https://doi.org/10.1109/TEVC.2004.830712 | ||
|
آمار تعداد مشاهده مقاله: 379 تعداد دریافت فایل اصل مقاله: 265 |
||