A Genetic Algorithm for the Maximal Clique Problem
The maximal clique problem (MaxClique) is known to be difficult (in terms of complexity) both in its exact and in the approximate form. Therefore, probabilistic algorithms for this problem are worthwhile to study. In this paper, we present an evolutionary (genetic) approach to solving the maximal clique problem (we are not directly concerned here with complexity). As opposed to previous work, our solution is inspired by a theoretical result  which improves the genetic algorithm. Experimental results for graphs with various properties are given; the convergence towards a good solution (in almost all of the runs, the global optimum) turns out to be quick.
KeywordsGenetic Algorithm Approximation Algorithm Fitness Function Maximal Clique Probabilistic Algorithm
Unable to display preview. Download preview PDF.
- Croitoru, C., Radu,C.: “Quadratic programs on graphs”, The Scientific Annals of the “Al.I.Cuza” University, section la, Mathematics and Computer Science, Iasi, Romania, vol. xxxiv, 1988.Google Scholar
- Michalewicz, Z.: “Genetic Algorithms+Data Structures = Evolutionary Programs”, Springer Verlag, 1992.Google Scholar
- Murthy, A S., Parthasarathy, G., Sastry, V.U.K.: “Clique Finding — A Genetic Approach”, Proc. of the First IEEE ICEC Conference, Orlando, USA, 1994, pp. 18–21.Google Scholar
- Back, T., Khuri, S.: “An Evolutionary Heuristic for the Maximal Independent Set Problem”, Proc. of the first IEEE ICEC Conference, Orlando, USA, 1994, pp. 531–535.Google Scholar
- Garey, MR., Johnson, D.S.: Computers and Intractability Freeman, San Francisco, 1979.Google Scholar
- Hougardy, S., Promel, H.J., Steger, A.: “Probabilistically checkable proofs and their consequences for approximation algorithms”, research report, Forschungsinstitut fur Diskrete Mathematik, Univ. of Bonn, 1993.Google Scholar
- Arora, S., Safa, S.: “ Approximating MaxClique is NP- Complete”, manuscript, 1992.Google Scholar
- Kann, V.: “ On the Approximability of NP-Complete Optimisation Problems”, Phd Thesis, Royal Institute of Technology Stockolm, 1992.Google Scholar