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Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem

Author

Listed:
  • Raja Marappan

    (Department of Computer Applications, School of Computing, SASTRA Deemed University, Tirumalaisamudram 613401, India)

  • Gopalakrishnan Sethumadhavan

    (Department of Computer Applications, School of Computing, SASTRA Deemed University, Tirumalaisamudram 613401, India)

Abstract

The graph coloring problem is an NP -hard combinatorial optimization problem and can be applied to various engineering applications. The chromatic number of a graph G is defined as the minimum number of colors required to color the vertex set V ( G ) so that no two adjacent vertices are of the same color, and different approximations and evolutionary methods can find it. The present paper focused on the asymptotic analysis of some well-known and recent evolutionary operators for finding the chromatic number. The asymptotic analysis of different crossover and mutation operators helps in choosing the better evolutionary operator to minimize the problem search space and computational complexity. The choice of the right genetic operators facilitates an evolutionary algorithm to achieve faster convergence with lesser population size N through an adequate distribution of promising genes. The selection of an evolutionary operator plays an essential role in reducing the bounds for minimum color obtained so far for some of the benchmark graphs. This research also focuses on the necessary and sufficient conditions for the global convergence of evolutionary algorithms. The stochastic convergence of recent evolutionary operators for solving graph coloring is newly analyzed.

Suggested Citation

  • Raja Marappan & Gopalakrishnan Sethumadhavan, 2020. "Complexity Analysis and Stochastic Convergence of Some Well-known Evolutionary Operators for Solving Graph Coloring Problem," Mathematics, MDPI, vol. 8(3), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:303-:d:324756
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    References listed on IDEAS

    as
    1. Lü, Zhipeng & Hao, Jin-Kao, 2010. "A memetic algorithm for graph coloring," European Journal of Operational Research, Elsevier, vol. 203(1), pages 241-250, May.
    2. Demange, Marc & Ekim, Tınaz & Ries, Bernard & Tanasescu, Cerasela, 2015. "On some applications of the selective graph coloring problem," European Journal of Operational Research, Elsevier, vol. 240(2), pages 307-314.
    3. Philippe Galinier & Jin-Kao Hao, 1999. "Hybrid Evolutionary Algorithms for Graph Coloring," Journal of Combinatorial Optimization, Springer, vol. 3(4), pages 379-397, December.
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