Performance Evaluation of a Hybrid NSGA-III for Multi and Many-Objective Optimization in Real-World Problems
Resumo
Several real-world problems can be modeled as optimization problems in which multiple conflicting objectives must be optimized simultaneously. Evolutionary algorithms (EA) are able to identify a set of non-dominated solutions (Pareto front) and are commonly used to solve these problems. Hybrid EAs that combine various optimization techniques can leverage the strengths of each method involved, enhancing their overall effectiveness. This study evaluates the performance of the well-known NSGA-III hybridized with Differential Evolution, Sine Cosine, and Arithmetic algorithms on optimization problems based on real-world applications with three, four and five objective functions, extracted from the CEC 2021 competition. Performance comparisons between the hybrid and original versions of NSGA-III were conducted using the IGD+ and HyperVolume indicators. Statistical analysis via the Wilcoxon test revealed significant improvements in NSGA-III performance when the hybrid version is considered.
Palavras-chave:
Multi-Objective Optimization Problems, Evolutionary Algorithms, Reference Points, Real-World Problems
Referências
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H. Ishibuchi, H. Masuda, Y. Tanigaki, and Y. Nojima, “Modified distance calculation in generational distance and inverted generational distance,” in Evolutionary Multi-Criterion Optimization, A. Gaspar-Cunha, C. Henggeler Antunes, and C. C. Coello, Eds. Cham: Springer International Publishing, 2015, pp. 110–125.
E. Zitzler and L. Thiele, “Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach,” IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257–271, 1999.
I. Das and J. E. Dennis, “Normal-boundary intersection: A new method for generating the pareto surface in nonlinear multicriteria optimization problems,” SIAM J. on Optimization, vol. 8, no. 3, pp. 631–657, Mar. 1998. [Online]. DOI: 10.1137/S1052623496307510
H. Chen, R. Cheng, J. Wen, H. Li, and J. Weng, “Solving large-scale many-objective optimization problems by covariance matrix adaptation evolution strategy with scalable small subpopulations,” Information Sciences, vol. 509, pp. 457–469, 2020.
K. Deb and H. Jain, “An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part i: solving problems with box constraints,” IEEE Transactions on Evolutionary Computation, vol. 18, no. 4, pp. 577–601, 2013.
H. Li and Q. Zhang, “Multiobjective optimization problems with complicated pareto sets, moea/d and nsga-ii,” IEEE Transactions on Evolutionary Computation, vol. 13, no. 2, pp. 284–302, 2008.
Q. Zhang and H. Li, “Moea/d: A multiobjective evolutionary algorithm based on decomposition,” IEEE Transactions on Evolutionary Computation, vol. 11, no. 6, pp. 712–731, 2007.
R. Storn and K. V. Price, “Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, vol. 11, pp. 341–359, 1997. [Online]. Available: [link]
D. E. Vargas, A. C. Lemonge, H. J. Barbosa, and H. S. Bernardino, “Differential evolution with the adaptive penalty method for constrained multiobjective optimization,” in 2013 IEEE Congress on Evolutionary Computation. IEEE, 2013, pp. 1342–1349.
D. Vargas, A. Lemonge, H. Barbosa, and H. Bernardino, “An algorithm based on differential evolution for structural multiobjective optimization problems with constraints (in Portuguese),” Rev Int Métodos Num Cálc Dise˜no Ing, vol. 32, no. 2, pp. 91–99, 2016.
J. P. G. Carvalho, D. E. Vargas, B. P. Jacob, B. S. Lima, P. H. Hallak, and A. C. Lemonge, “Multi-objective structural optimization for the automatic member grouping of truss structures using evolutionary algorithms,” Computers Structures, vol. 292, p. 107230, 2024. [Online]. Available: [link]
S. Mirjalili, “SCA: a sine cosine algorithm for solving optimization problems,” Knowledge-Based Systems, vol. 96, pp. 120–133, 2016.
L. Abualigah, A. Diabat, S. Mirjalili, M. Abd Elaziz, and A. H. Gandomi, “The arithmetic optimization algorithm,” Computer Methods in Applied Mechanics and Engineering, vol. 376, p. 113609, 2021.
A. Kumar, G. Wu, M. Z. Ali, Q. Luo, R. Mallipeddi, P. N. Suganthan, and S. Das, “A benchmark-suite of real-world constrained multi-objective optimization problems and some baseline results,” Swarm and Evolutionary Computation, vol. 67, p. 100961, 2021. [Online]. Available: [link]
H. Ishibuchi, H. Masuda, Y. Tanigaki, and Y. Nojima, “Modified distance calculation in generational distance and inverted generational distance,” in Evolutionary Multi-Criterion Optimization, A. Gaspar-Cunha, C. Henggeler Antunes, and C. C. Coello, Eds. Cham: Springer International Publishing, 2015, pp. 110–125.
E. Zitzler and L. Thiele, “Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach,” IEEE Transactions on Evolutionary Computation, vol. 3, no. 4, pp. 257–271, 1999.
I. Das and J. E. Dennis, “Normal-boundary intersection: A new method for generating the pareto surface in nonlinear multicriteria optimization problems,” SIAM J. on Optimization, vol. 8, no. 3, pp. 631–657, Mar. 1998. [Online]. DOI: 10.1137/S1052623496307510
Publicado
06/11/2024
Como Citar
NASCIMENTO, Paulo Lopes do; VARGAS, Dênis E. C.; WANNER, Elizabeth F..
Performance Evaluation of a Hybrid NSGA-III for Multi and Many-Objective Optimization in Real-World Problems. In: WORKSHOP DE SISTEMAS DE INFORMAÇÃO (WSIS), 15. , 2024, Rio Paranaíba/MG.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2024
.
p. 80-85.
DOI: https://doi.org/10.5753/wsis.2024.33677.
