A GENETIC ALGORITHM FOR THE MAXIMUM 2-PACKING SET PROBLEM

被引:2
|
作者
Antonio Trejo-Sanchez, Joel [1 ]
Fajardo-Delgado, Daniel [2 ]
Octavio Gutierrez-Garcia, J. [3 ]
机构
[1] Natl Council Sci & Technol, Ctr Res Math, Carretera Sierra Papacal,Chuburna Puerto Km 5, Merida 97302, Mexico
[2] Natl Technol Inst Mexico Ciudad Guzman, Dept Syst & Computat, Av Tecnol 100, Ciudad Guzman 49000, Jalisco, Mexico
[3] Mexico Autonomous Inst Technol ITAM, Dept Comp Sci, Rio Hondo 1, Ciudad De Mexico 01080, Mexico
关键词
maximum 2-packing set; genetic algorithms; graph algorithms; SELF-STABILIZING ALGORITHM; GRAPH;
D O I
10.34768/amcs-2020-0014
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Given an undirected connected graph G = (V, E), a subset of vertices S is a maximum 2-packing set if the number of edges in the shortest path between any pair of vertices in S is at least 3 and S has the maximum cardinality. In this paper, we present a genetic algorithm for the maximum 2-packing set problem on arbitrary graphs, which is an NP-hard problem. To the best of our knowledge, this work is a pioneering effort to tackle this problem for arbitrary graphs. For comparison, we extended and outperformed a well-known genetic algorithm originally designed for the maximum independent set problem. We also compared our genetic algorithm with a polynomial-time one for the maximum 2-packing set problem on cactus graphs. Empirical results show that our genetic algorithm is capable of finding 2-packing sets with a cardinality relatively close (or equal) to that of the maximum 2-packing sets. Moreover, the cardinality of the 2-packing sets found by our genetic algorithm increases linearly with the number of vertices and with a larger population and a larger number of generations. Furthermore, we provide a theoretical proof demonstrating that our genetic algorithm increases the fitness for each candidate solution when certain conditions are met.
引用
收藏
页码:173 / 184
页数:12
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