Integration of Niching Strategies into the C-DEEPSO Algorithm: An Approach for Multimodal Optimization
Resumo
The goal of this study is to improve the performance of the CDEEPSO algorithm in solving multimodal optimization problems by developing the FER-CDEEPSO variant. This approach aims to reduce premature convergence and improve the location of multiple global optima. Niching strategies based on the Fitness Euclidean-distance Ratio (FER) metric were inserted in the social and cognitive components of the movement equation, integrating concepts from FER-PSO and FER-DE with Crowding. At the end of optimization, the K-Means algorithm is used to identify and extract the optima. Experiments were conducted on classical multimodal benchmark functions of the literature. Results demonstrated that FER-CDEEPSO overcame the instabilities of its isolated variants and exhibited competitive spatial accuracy and computational efficiency compared to a highly relevant classic baseline (original FER-DE). By steering both guiding components through the FER metric instead of a global leader, the algorithm keeps several niches populated until the end of the run.
Palavras-chave:
Multimodal Optimization, Niching algorithms, FER-CDEEPSO
Referências
Ahrari, A., Deb, K., and Preuss, M. (2017). Multimodal optimization by covariance matrix self-adaptation evolution strategy with repelling subpopulations. Evolutionary Computation, 25(3):439–471.
Ahrari, A., Elsayed, S., Sarker, R., Essam, D., and Coello Coello, C. A. (2022). Static and dynamic multimodal optimization by improved covariance matrix self-adaptation evolution strategy with repelling subpopulations. IEEE Transactions on Evolutionary Computation, 26(3):527–541.
Brits, R., Engelbrecht, A. P., and van den Bergh, F. (2002a). A niching particle swarm optimizer. In Proceedings of the 4th Asia-Pacific Conference on Simulated Evolution and Learning (SEAL 2002), pages 692–696, Singapore.
Brits, R., Engelbrecht, A. P., and van den Bergh, F. (2002b). Solving systems of unconstrained equations using particle swarm optimization. In IEEE International Conference on Systems, Man and Cybernetics (SMC 2002), volume 3, page 6 pp., Hammamet, Tunisia.
Cho, D.-H., Jung, H.-K., and Lee, C.-G. (1999). Induction motor design for electric vehicle using a niching genetic algorithm. In IEEE International Electric Machines and Drives Conference. IEMDC’99. Proceedings (Cat. No.99EX272), pages 290–292.
De Jong, K. A. (1975). An Analysis Of The Behavior Of A Class Of Genetic Adaptive Systems. Ph.d. thesis, University of Michigan. ProQuest Dissertation No. 7609381.
Fieldsend, J. E. (2014). Running up those hills: Multi-modal search with the niching migratory multi-swarm optimiser. In 2014 IEEE Congress on Evolutionary Computation (CEC), pages 2593–2600. IEEE.
Gaspar-Cunha, A., Takahashi, R., and Antunes, C. H., editors (2012). Manual de Computação Evolutiva e Metaheurística. Imprensa da Universidade de Coimbra; Editora da Universidade Federal de Minas Gerais, Coimbra.
Goldberg, D. E. and Richardson, J. (1987). Genetic algorithms with sharing for multimodal function optimization. In Proceedings of the Second International Conference on Genetic Algorithms on Genetic Algorithms and their Application (ICGA’87), pages 41–49, Hillsdale, NJ, USA. L. Erlbaum Associates Inc.
Harik, G. R. (1995). Finding multimodal solutions using restricted tournament selection. In Proceedings of the 6th International Conference on Genetic Algorithms, page 24–31, San Francisco, CA, USA. Morgan Kaufmann Publishers Inc.
Jamil, M. and Yang, X.-S. (2013). A literature survey of benchmark functions for global optimisation problems. International Journal of Mathematical Modelling and Numerical Optimisation, 4(2):150–194.
Kennedy, J. and Eberhart, R. (1995). Particle swarm optimization. In Proceedings of ICNN’95 - International Conference on Neural Networks, volume 4, pages 1942–1948 vol.4.
Li, X. (2004). Adaptively choosing neighbourhood bests using species in a particle swarm optimizer for multimodal function optimization. In Genetic and Evolutionary Computation – GECCO 2004, pages 105–116, Berlin, Heidelberg. Springer Berlin Heidelberg.
Li, X. (2007). A multimodal particle swarm optimizer based on fitness euclidean-distance ratio. In Proceedings of the 9th Annual Conference on Genetic and Evolutionary Com putation, GECCO ’07, page 78–85, New York, NY, USA. Association for Computing Machinery.
Li, X., Engelbrecht, A. P., and Epitropakis, M. G. (2013). Benchmark functions for CEC’2013 special session and competition on niching methods for multimodal function optimization. Technical report, Evolutionary Computation and Machine Learning Group, RMIT University, Melbourne, Australia.
Liang, J., Qu, B., Mao, X., Niu, B., and Wang, D. (2014). Differential evolution based on fitness euclidean-distance ratio for multimodal optimization. Neurocomputing, 137:252–260. Advanced Intelligent Computing Theories and Methodologies.
Marcelino, C. G., Almeida, P. E. M., Wanner, E. F., Carvalho, L. M., and Miranda, V. (2016). Fundamentals of the C-DEEPSO algorithm and its application to the reactive power optimization of wind farms. In 2016 IEEE Congress on Evolutionary Computation (CEC), pages 1547–1554. IEEE.
Miranda, V. and Alves, R. (2013). Differential evolutionary particle swarm optimization (deepso): A successful hybrid. In 2013 BRICS Congress on Computational Intelligence and 11th Brazilian Congress on Computational Intelligence (BRICS-CCI & CBIC), pages 368–374.
Parrott, D. and Li, X. (2006). Locating and tracking multiple dynamic optima by a particle swarm model using speciation. IEEE Transactions on Evolutionary Computation, 10(4):440–458.
Petrowski, A. (1996). A clearing procedure as a niching method for genetic algorithms. In Proceedings of IEEE International Conference on Evolutionary Computation, pages 798–803.
Preuss, M. (2012). Improved topological niching for real-valued global optimization. In Applications of Evolutionary Computation (EvoApplications 2012), volume 7248 of Lecture Notes in Computer Science, pages 386–395. Springer.
Qu, B. Y., Suganthan, P. N., and Das, S. (2013). A distance-based locally informed particle swarm model for multimodal optimization. IEEE Transactions on Evolutionary Computation, 17(3):387–402.
Qu, B. Y., Suganthan, P. N., and Liang, J. J. (2012). Differential evolution with neighborhood mutation for multimodal optimization. IEEE Transactions on Evolutionary Computation, 16(5):601–614.
Shribate, D. M. (2025). Optimization techniques in machine learning: A comprehensive review. International Journal of Innovative Science and Research Technology (IJISRT), 10(3).
Storn, R. and Price, K. (1997). Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4):341–359.
Veeramachaneni, K., Peram, T., Mohan, C., and Osadciw, L. A. (2003). Optimization using particle swarms with near neighbor interactions. In Genetic and Evolutionary Computation — GECCO 2003, pages 110–121, Berlin, Heidelberg. Springer Berlin Heidelberg.
Ahrari, A., Elsayed, S., Sarker, R., Essam, D., and Coello Coello, C. A. (2022). Static and dynamic multimodal optimization by improved covariance matrix self-adaptation evolution strategy with repelling subpopulations. IEEE Transactions on Evolutionary Computation, 26(3):527–541.
Brits, R., Engelbrecht, A. P., and van den Bergh, F. (2002a). A niching particle swarm optimizer. In Proceedings of the 4th Asia-Pacific Conference on Simulated Evolution and Learning (SEAL 2002), pages 692–696, Singapore.
Brits, R., Engelbrecht, A. P., and van den Bergh, F. (2002b). Solving systems of unconstrained equations using particle swarm optimization. In IEEE International Conference on Systems, Man and Cybernetics (SMC 2002), volume 3, page 6 pp., Hammamet, Tunisia.
Cho, D.-H., Jung, H.-K., and Lee, C.-G. (1999). Induction motor design for electric vehicle using a niching genetic algorithm. In IEEE International Electric Machines and Drives Conference. IEMDC’99. Proceedings (Cat. No.99EX272), pages 290–292.
De Jong, K. A. (1975). An Analysis Of The Behavior Of A Class Of Genetic Adaptive Systems. Ph.d. thesis, University of Michigan. ProQuest Dissertation No. 7609381.
Fieldsend, J. E. (2014). Running up those hills: Multi-modal search with the niching migratory multi-swarm optimiser. In 2014 IEEE Congress on Evolutionary Computation (CEC), pages 2593–2600. IEEE.
Gaspar-Cunha, A., Takahashi, R., and Antunes, C. H., editors (2012). Manual de Computação Evolutiva e Metaheurística. Imprensa da Universidade de Coimbra; Editora da Universidade Federal de Minas Gerais, Coimbra.
Goldberg, D. E. and Richardson, J. (1987). Genetic algorithms with sharing for multimodal function optimization. In Proceedings of the Second International Conference on Genetic Algorithms on Genetic Algorithms and their Application (ICGA’87), pages 41–49, Hillsdale, NJ, USA. L. Erlbaum Associates Inc.
Harik, G. R. (1995). Finding multimodal solutions using restricted tournament selection. In Proceedings of the 6th International Conference on Genetic Algorithms, page 24–31, San Francisco, CA, USA. Morgan Kaufmann Publishers Inc.
Jamil, M. and Yang, X.-S. (2013). A literature survey of benchmark functions for global optimisation problems. International Journal of Mathematical Modelling and Numerical Optimisation, 4(2):150–194.
Kennedy, J. and Eberhart, R. (1995). Particle swarm optimization. In Proceedings of ICNN’95 - International Conference on Neural Networks, volume 4, pages 1942–1948 vol.4.
Li, X. (2004). Adaptively choosing neighbourhood bests using species in a particle swarm optimizer for multimodal function optimization. In Genetic and Evolutionary Computation – GECCO 2004, pages 105–116, Berlin, Heidelberg. Springer Berlin Heidelberg.
Li, X. (2007). A multimodal particle swarm optimizer based on fitness euclidean-distance ratio. In Proceedings of the 9th Annual Conference on Genetic and Evolutionary Com putation, GECCO ’07, page 78–85, New York, NY, USA. Association for Computing Machinery.
Li, X., Engelbrecht, A. P., and Epitropakis, M. G. (2013). Benchmark functions for CEC’2013 special session and competition on niching methods for multimodal function optimization. Technical report, Evolutionary Computation and Machine Learning Group, RMIT University, Melbourne, Australia.
Liang, J., Qu, B., Mao, X., Niu, B., and Wang, D. (2014). Differential evolution based on fitness euclidean-distance ratio for multimodal optimization. Neurocomputing, 137:252–260. Advanced Intelligent Computing Theories and Methodologies.
Marcelino, C. G., Almeida, P. E. M., Wanner, E. F., Carvalho, L. M., and Miranda, V. (2016). Fundamentals of the C-DEEPSO algorithm and its application to the reactive power optimization of wind farms. In 2016 IEEE Congress on Evolutionary Computation (CEC), pages 1547–1554. IEEE.
Miranda, V. and Alves, R. (2013). Differential evolutionary particle swarm optimization (deepso): A successful hybrid. In 2013 BRICS Congress on Computational Intelligence and 11th Brazilian Congress on Computational Intelligence (BRICS-CCI & CBIC), pages 368–374.
Parrott, D. and Li, X. (2006). Locating and tracking multiple dynamic optima by a particle swarm model using speciation. IEEE Transactions on Evolutionary Computation, 10(4):440–458.
Petrowski, A. (1996). A clearing procedure as a niching method for genetic algorithms. In Proceedings of IEEE International Conference on Evolutionary Computation, pages 798–803.
Preuss, M. (2012). Improved topological niching for real-valued global optimization. In Applications of Evolutionary Computation (EvoApplications 2012), volume 7248 of Lecture Notes in Computer Science, pages 386–395. Springer.
Qu, B. Y., Suganthan, P. N., and Das, S. (2013). A distance-based locally informed particle swarm model for multimodal optimization. IEEE Transactions on Evolutionary Computation, 17(3):387–402.
Qu, B. Y., Suganthan, P. N., and Liang, J. J. (2012). Differential evolution with neighborhood mutation for multimodal optimization. IEEE Transactions on Evolutionary Computation, 16(5):601–614.
Shribate, D. M. (2025). Optimization techniques in machine learning: A comprehensive review. International Journal of Innovative Science and Research Technology (IJISRT), 10(3).
Storn, R. and Price, K. (1997). Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4):341–359.
Veeramachaneni, K., Peram, T., Mohan, C., and Osadciw, L. A. (2003). Optimization using particle swarms with near neighbor interactions. In Genetic and Evolutionary Computation — GECCO 2003, pages 110–121, Berlin, Heidelberg. Springer Berlin Heidelberg.
Publicado
19/10/2026
Como Citar
PONTE, Daniel Arruda; SILVA, Dhener Rosemiro; MARCELINO, Carolina Gil; DELGADO, Carla Amor Divino Moreira.
Integration of Niching Strategies into the C-DEEPSO Algorithm: An Approach for Multimodal Optimization. In: ENCONTRO NACIONAL DE INTELIGÊNCIA ARTIFICIAL E COMPUTACIONAL (ENIAC), 23. , 2026, Cuiabá/MT.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2026
.
p. 873-884.
ISSN 2763-9061.
DOI: https://doi.org/10.5753/eniac.2026.30605.
