Optimizing Multi- and Many-Objective Problems on Varied Budgets
hybridizing NSGA-III with Local Searches
DOI:
https://doi.org/10.5540/03.2025.011.01.0454Palavras-chave:
Many-Objective Problems, NSGA-III, Local SearchResumo
This study addresses the challenges faced by Multi- and Many-Objective Evolutionary Algorithms in converging to the optimal Pareto Front under limited budgets. It proposes integrating these algorithms with deterministic single-objective local search techniques tailored for scalarized multi-objective optimization problems to accelerate convergence. Two integrations of NSGA-III with local search techniques based on SQP and BFGS algorithms are proposed and evaluated through numerical experiments on DTLZ1-4 problems across various budget scenarios. Performance profiles constructed using IGD+ and epsilon-indicator performance indicators demonstrate that the hybrid algorithms outperform NSGA-III. Statistical analysis confirms the superiority of the hybrid approaches, making them more efficient and reliable for the addressed problems.
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Referências
S. B. Aceves, S. I. Valdez, and A. H. Aguirre. “A Broyden-based algorithm for multi-objective local-search optimization”. In: Information Sciences 594 (2022), pp. 264–285. issn: 0020-0255.
H. J. C. Barbosa, H. S. Bernardino, and A. M. S. Barreto. “Using Performance Profiles to Analyze the Results of the 2006 CEC Constrained Optimization Competition”. In: 2010 IEEE World Congress on Computational Intelligence - WCCI. 2010, pp. 1–8.
P. T. Boggs and T. J. W. Tolle. “Sequential quadratic programming”. In: Acta numerica 4 (1995), pp. 1–51.
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”. In: IEEE Transactions on Evolutionary Computation 18.4 (2014), pp. 577–601.
E. D. Dolan and J. More. “Benchmarking optimization software with performance profiles”. In: Mathematical Programming 91 (2002), pp. 201–213.
R. Gower, F. Hanzely, P. Richtárik, and S. U. Stich. “Accelerated stochastic matrix inversion: general theory and speeding up BFGS rules for faster second-order optimization”. In: Advances in Neural Information Processing Systems 31 (2018), pp. 1–11.
J. L. Guerrero, L. Martí, J. García, A. Berlanga, and J. M. Molina. “Introducing a Robust and Efficient Stopping Criterion for MOEAs”. In: 2010 IEEE Conference on Evolutionary Computation (CEC), part of 2010 IEEE World Congress on Computational Intelligence (WCCI 2010). Barcelona, Spain: IEEE Press, 2010.
H. Ishibuchi, H. Masuda, Y. Tanigaki, and Y. Nojima. “Modified Distance Calculation in Generational Distance and Inverted Generational Distance”. In: In: Gaspar-Cunha A., Henggeler Antunes C., Coello C. (eds) Evolutionary Multi-Criterion Optimization. EMO 2015. Lecture Notes in Computer Science, vol 9019. Springer, Cham., 2015, pp. 110–125.
F. Li, L. Gao, and W. Shen. “Surrogate-Assisted Multi-Objective Evolutionary Optimization With Pareto Front Model-Based Local Search Method”. In: IEEE Transactions on Cybernetics 54.1 (2024), pp. 173–186.
K. Miettinen. Nonlinear Multiobjective Optimization. International Series in Operations Research & Management Science. Springer US, 1999. isbn: 9780792382782.
R. Morrison and D. J. KennethA. “Measurement of Population Diversity”. English. In: Artificial Evolution. Ed. by Pierre Collet, Cyril Fonlupt, Jin-Kao Hao, Evelyne Lutton, and Marc Schoenauer. Vol. 2310. Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2002, pp. 31–41. isbn: 978-3-540-43544-0.
K. Sindhya, A. Sinha, K. Deb, and K. Miettinen. “Local search based evolutionary multi-objective optimization algorithm for constrained and unconstrained problems”. In: 2009 IEEE Congress on Evolutionary Computation. 2009, pp. 2919–2926. doi: 10.1109/CEC.2009.4983310.
Y. Tian, R. Cheng, X. Zhang, and Y. Jin. “PlatEMO: A MATLAB platform for evolutionary multi-objective optimization [educational forum]”. In: IEEE Computational Intelligence Magazine 12.4 (2017), pp. 73–87.
L. Uribe, A. Lara, K. Deb, and O. Schütze. “A new gradient free local search mechanism for constrained multi-objective optimization problems”. In: Swarm and Evolutionary Computation 67 (2021), p. 100938. issn: 2210-6502.
A. P. Wierzbicki. “A mathematical basis for satisficing decision making”. In: Mathematical Modelling 3.5 (Jan. 1982), pp. 391–405. issn: 02700255. doi: 10.1016/0270-0255(82)90038-0.
E. Zitzler, L. Thiele, M. Laumanns, C. M. Fonseca, and V. G. da Fonseca. “Performance assessment of multiobjective optimizers: an analysis and review”. In: IEEE Transactions on Evolutionary Computation 7.2 (2003), pp. 117–132. doi: 10.1109/TEVC.2003.810758.
