List Colouring of Graphs Using a Genetic Algorithm
The List Colouring Problem (LCP) is an NP-Hard optimization problem in which the goal is to find a proper list colouring of a graph G = (V, E) such that the number of colours used is minimized. This paper deals with the development and implementation of a Genetic Algorithm for the list colouring of graphs. Initial solutions are generated using two heuristics in equal proportion. Experiments have been carried out on randomly generated planar graphs with a list of colours for each vertex. Results for 32 graphs with size varying from 10 to 750 show that the proposed Genetic Algorithm implementation tends towards lower values of the number of colours used.
KeywordsList colouring Genetic Algorithm
- 1.Baber, C.L.: An Introduction to List Colorings of Graphs, M.Sc. thesis, Faculty of the Virginia Polytechnic Institute and State University (2009)Google Scholar
- 2.Laurenta, B., Hao, J.K.: List graph colouring for multiple depot vehicle scheduling. Int. J. Math. Oper. Res. 1(1/2) (2009)Google Scholar
- 3.Achlioptas, D., Mollo, M.: The Analysis of a List-Coloring Algorithm on a Random Graph (1997)Google Scholar
- 4.Satratzemi, M., Tsours, C.: A heuristic algorithm for the list coloring of a random graph. In: The 7th Balkan Conference on Operational Research. Constanta, Romania (2005)Google Scholar
- 5.Deb, K.: Multiple-Objective Optimization Using Evolutionary Algorithms. Wiley, New York (2008)Google Scholar