Aplicación del algoritmo NSGA-II en la resolución multiobjetivo del problema de la suma de subconjuntos

Noriel Cosme Toribio; Abraham De Sedas; Daniel Sánchez Díaz

doi:10.48204/synergia.v4n2.8548

Submitted October 30, 2025

Published 2025-11-01

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Vol. 4 No. 2 (2025): Synergía

Application of the NSGA-II algorithm in the multi-objective resolution of the sum of subsets problem

Noriel Cosme Toribio ⁺⁻
Abraham De Sedas ⁺⁻
Daniel Sánchez Díaz ⁺⁻

DOI https://doi.org/10.48204/synergia.v4n2.8548

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DOI: 10.48204/synergia.v4n2.8548

Published: 2025-11-01

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Cosme Toribio , N., De Sedas , A., & Sánchez Díaz , D. (2025). Application of the NSGA-II algorithm in the multi-objective resolution of the sum of subsets problem. Synergía, 4(2), 264–276. https://doi.org/10.48204/synergia.v4n2.8548

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Abstract

The study presents the NSGA-II algorithm as an efficient and optimal tool for solving the Subset Sum Problem (SSP), which is a binary knapsack problem with diverse applications in areas such as investment management, production planning, and electronic circuit design. NSGA-II is a multi-objective genetic algorithm that uses selection, crossover, and mutation techniques, along with a non-dominated sorting approach, to evolve a population of solutions and obtain a set of non-dominated solutions known as the Pareto front. The study provides a detailed description of the algorithm's functioning, including the genetic operators and the non-dominated sorting approach. Furthermore, experimental results are presented to demonstrate the effectiveness and efficiency of the algorithm in solving the SSP. Overall, the study provides a solid foundation for understanding the fundamentals and applications of the NSGA-II algorithm in multi-objective optimization.

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References

Coello Coello, C. A. (2006). Evolutionary multi-objective optimization: a historical view of the field. IEEE Computational Intelligence Magazine, 1(1), 28–36.
https://doi.org/10.1109/MCI.2006.1597056
Davis, L. (1991). Handbook of Genetic Algorithms. Van Nostrand Reinhold.
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. A. M. T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation, 6(2), 182-197.
Garey, M.R. and Johnson, D.S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York.
Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Professional.
Marinakis, Y., & Marinaki, M. (2010). A hybrid genetic–particle swarm optimization algorithm for the vehicle routing problem. Expert Systems with Applications, 37(2), 1446–1455. https://doi.org/10.1016/j.eswa.2009.06.106
Reeves, C. R. (1993). Genetic Algorithms: Principles and Perspectives - A Guide to GA Theory. Springer.
Van Veldhuizen, D. A., & Lamont, G. B. (1998). Evolutionary computation and convergence to a pareto front. In Late breaking papers at the genetic programming 1998 conference (pp. 221-228).

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[1] Coello Coello, C. A. (2006). Evolutionary multi-objective optimization: a historical view of the field. IEEE Computational Intelligence Magazine, 1(1), 28–36.

[2] https://doi.org/10.1109/MCI.2006.1597056

[3] Davis, L. (1991). Handbook of Genetic Algorithms. Van Nostrand Reinhold.

[4] Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. A. M. T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation, 6(2), 182-197.

[5] Garey, M.R. and Johnson, D.S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York.

[6] Goldberg, D. E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Professional.

[7] Marinakis, Y., & Marinaki, M. (2010). A hybrid genetic–particle swarm optimization algorithm for the vehicle routing problem. Expert Systems with Applications, 37(2), 1446–1455. https://doi.org/10.1016/j.eswa.2009.06.106

[8] Reeves, C. R. (1993). Genetic Algorithms: Principles and Perspectives - A Guide to GA Theory. Springer.

[9] Van Veldhuizen, D. A., & Lamont, G. B. (1998). Evolutionary computation and convergence to a pareto front. In Late breaking papers at the genetic programming 1998 conference (pp. 221-228).

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