A Memetic Algorithm with Two Distinct Solution Representations for the Partition Graph Coloring Problem
In this paper we propose a memetic algorithm (MA) for the partition graph coloring problem. Given a clustered graph G = (V,E), the goal is to find a subset V * ⊂ V that contains exactly one node for each cluster and a coloring for V * so that in the graph induced by V *, two adjacent nodes have different colors and the total number of used colors is minimal. In our MA we use two distinct solution representations, one for the genetic operators and one for the local search procedure, which are tailored for the corresponding situations, respectively. The algorithm is evaluated on a common benchmark instances set and the computational results show that compared to a state-of-the-art branch and cut algorithm, our MA achieves solid results in very short run-times.
KeywordsCrossover Operator Genetic Operator Memetic Algorithm Network Design Problem Coloring Problem
Unable to display preview. Download preview PDF.
- 4.Demange, M., Monnot, J., Pop, P., Ries, B.: On the complexity of the selective graph coloring problem in some special classes of graphs. Theoretical Computer Science (in press, 2013)Google Scholar
- 5.Frota, Y., Maculan, N., Noronha T.F., Ribeiro, C.C.: Instances for the partition coloring problem, www.ic.uff.br/~celso/grupo/pcp.htm
- 10.Li, G., Simha, R.: The partition coloring problem and its application to wavelength routing and assignment. In: 1st Workshop on Optical Networks (2000)Google Scholar
- 13.Moscato, P.: Memetic algorithms: A short introduction. In: Corne, D., et al. (eds.) New Ideas in Optimization, pp. 219–234. McGraw Hill (1999)Google Scholar
- 16.Pop, P.C.: Generalized network design problems. Modeling and Optimization. De Gruyter Series in Discrete Mathematics and Applications, Germany (2012)Google Scholar
- 17.Pop, P.C., Hu, B., Raidl, G.R.: A memetic algorithm for the partition graph coloring problem. In: Extended Abstracts of the 14th International Conference on Computer Aided Systems Theory, Gran Canaria, Spain, pp. 167–169 (2013)Google Scholar