Local search for weighted sum coloring problem

Abstract

The weighted sum coloring problem (WSCP) is a weighted vertex coloring problem in which a weight is associated with each color. Its aim is to find a coloring of the vertices of a graph with the minimum sum of the costs of the used colors. The WSCP has important applications in the batch scheduling of distributed systems. In this paper, we obtain an integer linear programming (ILP) model for the WSCP, and design an efficient local search algorithm named LS-WSC to solve WSCP. To this end, we propose two ideas to make LS-WSC effective. Firstly, we design an adaptive strategy to change the number of color classes in current solution, which allows LS-WSC to search more feasible solution regions. Secondly, we design a greedy function and a tabu strategy, which make LS-WSC search in right direction. We also design a genetic algorithm GA-WSC to solve WSCP, which is used to experimentally evaluate the result of local search algorithms. The preliminary experimental results show that LS-WSC outperforms the famous CPLEX on almost all instances, and is competitive with the approximate algorithm GREEDY on most benchmark instances with vertex number less than 200. However, the performance of LS-WSC is worse than GREEDY algorithm′s on most benchmark instances with vertex number greater than 200. Overall, the performance of LS-WSC is only marginally better than GA-WSC′s. In order to improve the performance of LS-WSC, we use the configuration checking strategy to update the searching process of LS-WSC, and the new algorithm for solving WSCP is named as CCLS-WSC. The further experimental results show that CCLS-WSC algorithm outperforms the famous CPLEX, the approximate algorithm GREEDY, the genetic algorithm GA-WSC and LS-WSC on all benchmark instances.