An Efficient Memetic Algorithm for the Minimum Load Coloring Problem

Abstract

Given a graph G with n vertices and l edges, the load distribution of a coloring q: V → {red, blue} is defined as dq = (rq, bq), in which rq is the number of edges with at least one end-vertex colored red and bq is the number of edges with at least one end-vertex colored blue. The minimum load coloring problem (MLCP) is to find a coloring q such that the maximum load, lq = 1/l × max{rq, bq}, 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.

Improved Differential Evolution Algorithm to Solve the Advertising Method Selection Problem

“…Many different types of heuristics and metaheuristics have been developed, including the genetic algorithm (GA) (Holland [16], Kampelis, Sifakis, Kolokotsa, Gobakis, Kalaitzakis, Isidori and Cristalli [17]; Lara-Ramirez, Garcia-Capulin, Estudillo-Ayala, Avina-Cervantes, Sanchez-Yanez, and Rostro-Gonzalez [18]), the memetic algorithm (Zhang, Li, Qiao, and Wang [19]; Cheng and Lai [20]), ant colony optimization (Ebadinezhad, Dereboylu, and Ever [21]; Jiang, Xu, and Chen [22], iterated local search (Gao, Zhu, Liu, Meng, and Zhang [23]; Hu, Liu, Wu, Li, Zhou, and Wang [24]), adaptive large neighborhood search (Liu,Du,Zhang,Li,and Shi [25]; Praseeratasang, Pitakaso, Sethanan, and Kaewman [26]; Theeraviriya, Pitakaso, Sillapasa, and Kaewman [27]), particle swam optimization (PSO) (Kennedy, Eberhart, and Shi [28], Xu and Ren [29]), and DE (Zhang,Feng,and Lin [30]; Dechampai, Tanwanichkul, Sethanan, and Pitakaso, [31]).…”