Optimizing Multi- and Many-Objective Problems on Varied Budgets: Hybridizing NSGA-III with Local Searches

Regina Carla Lima Corrêa de Sousa; Fillipe Goulart; Dênis Vargas; Felipe Campelo; Elizabeth Wanner

doi:10.5540/03.2025.011.01.0454

Optimizing Multi- and Many-Objective Problems on Varied Budgets: Hybridizing NSGA-III with Local Searches

Regina Carla Lima Corrêa de Sousa
, Fillipe Goulart
, Dênis Vargas
, Felipe Campelo
, Elizabeth Wanner

School of Engineering Mathematics and Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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Abstract

This study addresses the challenges faced by Multi- and Many-Objective EvolutionaryAlgorithms in converging to the optimal Pareto Front under limited budgets. It proposes integratingthese algorithms with deterministic single-objective local search techniques tailored for scalarizedmulti-objective optimization problems to accelerate convergence. Two integrations of NSGA-IIIwith local search techniques based on SQP and BFGS algorithms are proposed and evaluatedthrough numerical experiments on DTLZ1-4 problems across various budget scenarios. Performanceprofiles constructed using IGD+ and epsilon-indicator performance indicators demonstrate that thehybrid algorithms outperform NSGA-III. Statistical analysis confirms the superiority of the hybridapproaches, making them more efficient and reliable for the addressed problems.

Original language	English
Title of host publication	Proceeding Series of the Brazilian Society of Computational and Applied Mathematics
Publisher	SBMAC
Volume	11
Edition	1
DOIs	https://doi.org/10.5540/03.2025.011.01.0454
Publication status	Published - 20 Jan 2025
Event	CNMAC 2024: XLIII National Congress of Applied Computing and Computational Mathematics - Armação Resort Convention Center, Porto de Galinhas, Brazil, Porto de Galinhas, Brazil Duration: 16 Aug 2024 → 20 Sept 2024 https://www.cnmac.org.br/novo/index.php/CNMAC/ano/2024/

Publication series

Name	Proceeding Series of the Brazilian Society of Computational and Applied Mathematics
Publisher	SBMAC
Number	1
Volume	11
ISSN (Electronic)	2359-0793

Conference

Conference	CNMAC 2024
Abbreviated title	CNMAC 2024
Country/Territory	Brazil
City	Porto de Galinhas
Period	16/08/24 → 20/09/24
Internet address	https://www.cnmac.org.br/novo/index.php/CNMAC/ano/2024/

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10.5540/03.2025.011.01.0454

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Lima Corrêa de Sousa, R. C., Goulart, F., Vargas, D., Campelo, F., & Wanner, E. (2025). Optimizing Multi- and Many-Objective Problems on Varied Budgets: Hybridizing NSGA-III with Local Searches. In Proceeding Series of the Brazilian Society of Computational and Applied Mathematics (1 ed., Vol. 11). (Proceeding Series of the Brazilian Society of Computational and Applied Mathematics; Vol. 11, No. 1). SBMAC. https://doi.org/10.5540/03.2025.011.01.0454

Lima Corrêa de Sousa, Regina Carla ; Goulart, Fillipe ; Vargas, Dênis et al. / Optimizing Multi- and Many-Objective Problems on Varied Budgets : Hybridizing NSGA-III with Local Searches. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics. Vol. 11 1. ed. SBMAC, 2025. (Proceeding Series of the Brazilian Society of Computational and Applied Mathematics; 1).

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abstract = "This study addresses the challenges faced by Multi- and Many-Objective EvolutionaryAlgorithms in converging to the optimal Pareto Front under limited budgets. It proposes integratingthese algorithms with deterministic single-objective local search techniques tailored for scalarizedmulti-objective optimization problems to accelerate convergence. Two integrations of NSGA-IIIwith local search techniques based on SQP and BFGS algorithms are proposed and evaluatedthrough numerical experiments on DTLZ1-4 problems across various budget scenarios. Performanceprofiles constructed using IGD+ and epsilon-indicator performance indicators demonstrate that thehybrid algorithms outperform NSGA-III. Statistical analysis confirms the superiority of the hybridapproaches, making them more efficient and reliable for the addressed problems.",

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Lima Corrêa de Sousa, RC, Goulart, F, Vargas, D, Campelo, F & Wanner, E 2025, Optimizing Multi- and Many-Objective Problems on Varied Budgets: Hybridizing NSGA-III with Local Searches. in Proceeding Series of the Brazilian Society of Computational and Applied Mathematics. 1 edn, vol. 11, Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, no. 1, vol. 11, SBMAC, CNMAC 2024, Porto de Galinhas, Brazil, 16/08/24. https://doi.org/10.5540/03.2025.011.01.0454

Optimizing Multi- and Many-Objective Problems on Varied Budgets: Hybridizing NSGA-III with Local Searches. / Lima Corrêa de Sousa, Regina Carla; Goulart, Fillipe; Vargas, Dênis et al.
Proceeding Series of the Brazilian Society of Computational and Applied Mathematics. Vol. 11 1. ed. SBMAC, 2025. (Proceeding Series of the Brazilian Society of Computational and Applied Mathematics; Vol. 11, No. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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PY - 2025/1/20

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N2 - This study addresses the challenges faced by Multi- and Many-Objective EvolutionaryAlgorithms in converging to the optimal Pareto Front under limited budgets. It proposes integratingthese algorithms with deterministic single-objective local search techniques tailored for scalarizedmulti-objective optimization problems to accelerate convergence. Two integrations of NSGA-IIIwith local search techniques based on SQP and BFGS algorithms are proposed and evaluatedthrough numerical experiments on DTLZ1-4 problems across various budget scenarios. Performanceprofiles constructed using IGD+ and epsilon-indicator performance indicators demonstrate that thehybrid algorithms outperform NSGA-III. Statistical analysis confirms the superiority of the hybridapproaches, making them more efficient and reliable for the addressed problems.

AB - This study addresses the challenges faced by Multi- and Many-Objective EvolutionaryAlgorithms in converging to the optimal Pareto Front under limited budgets. It proposes integratingthese algorithms with deterministic single-objective local search techniques tailored for scalarizedmulti-objective optimization problems to accelerate convergence. Two integrations of NSGA-IIIwith local search techniques based on SQP and BFGS algorithms are proposed and evaluatedthrough numerical experiments on DTLZ1-4 problems across various budget scenarios. Performanceprofiles constructed using IGD+ and epsilon-indicator performance indicators demonstrate that thehybrid algorithms outperform NSGA-III. Statistical analysis confirms the superiority of the hybridapproaches, making them more efficient and reliable for the addressed problems.

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M3 - Conference Contribution (Conference Proceeding)

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T3 - Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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PB - SBMAC

Y2 - 16 August 2024 through 20 September 2024

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Lima Corrêa de Sousa RC, Goulart F, Vargas D, Campelo F, Wanner E. Optimizing Multi- and Many-Objective Problems on Varied Budgets: Hybridizing NSGA-III with Local Searches. In Proceeding Series of the Brazilian Society of Computational and Applied Mathematics. 1 ed. Vol. 11. SBMAC. 2025. (Proceeding Series of the Brazilian Society of Computational and Applied Mathematics; 1). doi: 10.5540/03.2025.011.01.0454

Optimizing Multi- and Many-Objective Problems on Varied Budgets: Hybridizing NSGA-III with Local Searches

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