An Efficient Memetic Algorithm for the Minimum Load Coloring Problem

• Main Authors: Zhiqiang Zhang, Zhongwen Li, Xiaobing Qiao, Weijun Wang
• Format: Article
• Language: English
• Published: MDPI AG 2019-05-01
• Series: Mathematics
• Subjects: minimum load coloring; memetic algorithm; evolutionary; local search
• Online Access: https://www.mdpi.com/2227-7390/7/5/475

Given a graph <i>G</i> with <i>n</i> vertices and <i>l</i> edges, the load distribution of a coloring <i>q</i>: <i>V &#8594;</i> {red, blue} is defined as <i>d_q</i> = (<i>r_q</i>, <i>b_q</i>), in which <i>r_q</i> is the number of edges with at least one end-vertex colored red and <i>b_q</i> is the number of edges with at least one end-vertex colored blue. The minimum load coloring problem (MLCP) is to find a coloring <i>q</i> such that the maximum load, <i>l_q</i> = 1/<i>l</i> &#215; max{<i>r_q</i>, <i>b_q</i>}, is minimized. This problem has been proved to be NP-complete. This paper proposes a memetic algorithm for MLCP based on an improved K-OPT local search and an evolutionary operation. Furthermore, a data splitting operation is executed to expand the data amount of global search, and a disturbance operation is employed to improve the search ability of the algorithm. Experiments are carried out on the benchmark DIMACS to compare the searching results from memetic algorithm and the proposed algorithms. The experimental results show that a greater number of best results for the graphs can be found by the memetic algorithm, which can improve the best known results of MLCP.