Aspects of Implementing a Genetic Algorithm in Mixed Optimization Problems in A Variable-Size Design Space

Nikita Demidov

Abstract


This paper considers a mixed optimization problem in a variable-size design space. The objective of the study is to explore an approach to solving a mixed optimization problem in a variable-size design space that enables the base genetic algorithm to switch between design spaces of different sizes, using the example of tuning the parameters of an SVM classifier. To adapt the base genetic algorithm to the problem under consideration, an additional gene is introduced into the chromosome. This gene encodes a dimensional variable that enables switching between design spaces of different sizes during the optimization process, determining which gene groups are active and which are hidden (passive). A herewith, the genetic algorithm supports the encoding of parameters of different types in the chromosome genes using the Gray code. The encoded parameters can be either common to different design spaces or unique (individual), i.e., associated only with one specific design space. The experimental results obtained using the example of tuning the parameters of an SVM classifier confirm the feasibility of adapting the base genetic algorithm. This genetic algorithm allows switching between design spaces of different sizes in the process of mixed optimization, ensuring the simultaneous search for values of the optimized parameters in spaces of different sizes and obtaining high values of classification quality metrics, in particular, obtaining a high value of the - metric.


Full Text:

PDF (Russian)

References


A. P. Karpenko, Sovremennyye algoritmy poiskovoy optimi-zatsii: algoritmy, vdokhnovlennyye prirody: uchebnoye posobiye [Modern Search Engine Optimization Algorithms: Al-gorithms Inspired by Nature: A Tutorial]. Moscow, 2017, 448 p. (In Russ.).

A. L. Perezhogin, I. S. Bykov, “Obzor konstruktsiy i svoystv kodov Greya,” [Overview of Gray Code Constructions and Properties] Matematicheskiye voprosy kibernetiki. Vyp. 20, Moscow: FIZMATLIT, 2022, pp. 41–60. Available: https://10.20948/mvk-2022-41.

L. Sahoo, A. Banerjee, A. Bhunia, S. Chattopadhyay, “An effi-cient GA-PSO approach for solving mixed-integer nonlinear programming problem in reliability optimization,” Swarm and Evolutionary Computation, vol. 19, 2014, pp. 43–51.

Y. Gao, Y. Sun, J. Wu, “Difference-genetic co-evolutionary algorithm for nonlinear mixed integer programming problems,” Journal of Nonlinear Science and Its Applications, vol. 9, no. 3, 2016, pp. 1261–1284.

J. Pelamatti, L. Brevault, M. Balesdent, E.G. Talbi, Y. Guerin, “How to Deal with Mixed-Variable Optimization Problems: An Overview of Algorithms and Formulations,” in Advances in Structural and Multidisciplinary Optimization // A. Schumacher, T. Vietor, S. Fiebig, K. U. Bletzinger, K. Maute (eds). Springer, Cham, WCSMO 2017. https://doi.org/10.1007/978-3-319-67988-4_5.

J. Gamot, M. Balesdent, A. Tremolet, R., N.Melab, E.-G. Talbi, “Hidden-variables genetic algorithm for variable Wuilbercq-size design space optimal layout problems with application to aero-space vehicles,” Engineering Applications of Artificial Intelli-gence, vol. 121, 2023, pp. 105941. https://doi.org/10.1016/j.engappai.2023.105941.

K. Deb, R.B. Agrawal, “Simulated binary crossover for continu-ous search space,” Complex systems, vol. 9 (2), 1995, pp. 115–148.

E.-G. Talbi, Metaheuristics: from design to implementation. John Wiley & Sons, 2009, 624 p.

П.А. Шерстнев, Е.С. Семенкин, “SelfCSHAGA: Самоконфигу-рируемый генетический алгоритм оптимизации с адаптацией на основе истории успеха,” Вестник МГТУ им. Н.Э. Баумана. Сер. Приборостроение, 2025, № 2 (151), С. 122–139.

V. Stanovov, S. Akhmedova, E. Semenkin, “Genetic Algorithm with Success History based Parameter Adaptation,” Proceedings of the 11th International Joint Conference on Computational In-telligence (IJCCI 2019). SciTePress, 2019. pp. 180–187. https://doi.org/10.5220/0008071201800187.

O. Chapelle, V. Vapnik, O. Bousquet, S. Mukherjee, “Choosing multiple parameters for support vector machines,” Machine Learning, vol. 46, 2002, pp. 131–159. https://doi.org/10.1023/a:1012450327387.

J.-Y. Liu, B.-B. Jia, “Combining One-vs-One Decomposition and Instance-Based Learning for Multi-Class Classification,” IEEE Access, vol. 8, 2020, pp. 197499–197507. https://doi.org/10.1109/ACCESS.2020.3034448.

Kernel functions [Electronic resource]. – Access mode: https://scikit-learn.org/stable/modules/

svm.html#svm-kernels, free (date of access: 10.01.2026).

load_iris [Electronic resource]. – Access mode: https://scikit-learn.org/stable/modules/generated/ sklearn.datasets.load_iris.html, free (date of access: 10.01.2026).

load_wine [Electronic resource]. – Access mode: https://scikit-learn.org/stable/modules/generated/ sklearn.datasets.load_wine.html, free (date of access: 10.01.2026).

load_breast_cancer [Electronic resource]. – Access mode: https://scikit-learn.org/stable/modules/ generat-ed/sklearn.datasets.load_breast_cancer.html, free (date of ac-cess: 10.01.2026).

Support vector machines [Electronic resource]. – Access mode: https://scikit-learn.org/stable/ modules/svm.html#, free (date ac-cessed: 10.01.2026).

Thefittest [Electronic resource]. – Access mode: https://github.com/sherstpasha/thefittest, free (date accessed: 10.01.2026).

P. Sherstnev, “Thefittest: evolutionary machine learning in Py-thon,” Hybrid Methods of Modeling and Optimization in Com-plex Systems (HMMOCS-II 2023): Proceedings of the II Interna-tional Workshop. Krasnoyarsk: ITM Web of Conferences, vol. 59, 2024, Article 02020, 11 p.

Y. Matanga, P. Owolawi, C. Du, E. van Wyk, “Niching Global Optimisation: Systematic Literature Review,” Algorithms, vol. 17(10), 2024, p. 448. https://doi.org/10.3390/a17100448.

N. A. Demidov, “Podkhody k odnoklassovoy klassifikatsii regulyarnykh vyrazheniy,” [Approaches to one-class classifica-tion of regular expressions] IT-Standart , № 2, 2025, pp. 32–48.

E. G. Andrianova, N. A. Demidov, “Issledovaniye stsenariyev predvaritel'noy obrabotki dannykh i initsializatsii vlozheniy pri realizatsii algoritma PaCMAP,” [Study of data preprocessing scenarios and initialization of embeddings in the implementation of the PaCMAP algorithm] IT-Standart, № 4 (45), 2025, pp. 102–123.


Refbacks

  • There are currently no refbacks.


Abava  Кибербезопасность Monetec 2026 СНЭ

ISSN: 2307-8162