A POTENTIAL WEAKNESS OF THE GENETIC ALGORITHM IN MULTIMODAL OPTIMIZATIONS

Authors

DOI:

https://doi.org/10.26034/lu.akwi.2026.8841

Keywords:

Optimization, genetic algorithm, generation, crossover, mutation, selection, multimodal fitness function, random search

Abstract

The genetic algorithms are robust and stable evolutionary computation techniques that typically
provide a solution. This fact is undisputedly an important positive feature, particularly in the situation when no feasible solution is available. Yet this robustness and the fact that living nature utilizes analogous mechanisms for its development and propagation sometimes lead to unrealistic expectations in their capabilities. In particular, when they are used as function optimizers they sometimes tend to demonstrate also their weak points. In this article, we demonstrate the limits of the genetic algorithm in a multimodal model task. The task consists in the identification of a de Bruijn sequence of a given length between general binary sequences. Generally, the multimodality of the fitness function can lead to the stagnation of the genetic algorithm well below the desirable fitness function values which hinders the genetic algorithm from finding the optimized solution of the task under consideration.

Author Biographies

Roman Knobloch, Technical University of Liberec, Department of Mathematics

Roman Knobloch was born in Turnov, Czechoslovakia. After high school, he studied mathematics and physics at the Faculty of Mathematics and Physics, Charles University in Prague. He is occupied as an assistant professor at the Department of Mathematics of the Technical University in Liberec, the
Czech Republic. His principal areas of interest are: mathematical modeling, up-to-date optimization techniques, continuum mechanics, and bit fields generation.

Jaroslav Mlynek, Technical University of Liberec, Department of Mathematics

Jaroslav Mlynek was born in Trnava, Czechoslovakia and he studied numerical mathematics at Charles University in Prague at the Faculty of Mathematics and Physics. His professional activities are focused on the study of convergence of evolutionary algorithms, especially differential algorithms. He also deals with the optimization of fiber winding on polymer composite frames and the optimization of heating
of thin-walled metal molds in the production of artificial leather. He currently holds the position of an associate professor at the Technical University of Liberec.

References

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D. E. Goldberg. Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, 2000.

L. Levine. Algebraic combinatorics. Lecture Notes, 21 18.312, Cornell University, Ithaca, NY, US, 2011.

Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs. Springer, Springer-Verlag Berlin Heidelberg New York, 1999.

G. Mitsuo and Ch. Runwei. Genetic Algorithms and Engineering Optimization. Joh Wiley Sons, Inc., 605 Third Avenue, New York, 2000.

W. Rudin. Principles of Mathematical Analysis. McGraw-Hill Education, London, 1976.

J. Sawada, A. Williams, and D. Wong. A surprisingly simple de Bruijn sequence construction. Discrete Mathematics, 339:127–131, 2016.

D. Simon. Evolutionary Optimization Algorithms, Biologically-Inspired and Population-Based Approaches to Computer Intelligence. Willey, Published by John Wiley Sons, Inc., Hoboken, New Jersey, 2013.

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Published

2026-09-02

Issue

No. 22 (2026)

Section

Trends

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Copyright (c) 2026 Roman Knobloch, Jaroslav Mlynek

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This work is licensed under a Creative Commons Attribution 4.0 International License.