A Relation-Algebraic View on Evolutionary Algorithms for Some Graph Problems
We take a relation-algebraic view on the formulation of evolutionary algorithms in discrete search spaces. First, we show how individuals and populations can be represented as relations and formulate some standard mutation and crossover operators for this representation using relation-algebra. Evaluating a population with respect to their constraints seems to be the most costly step in one generation for many important problems. We show that the evaluation process for a given population can be sped up by using relation-algebraic expressions in the process. This is done by examining the evaluation of possible solutions for three of the best-known NP-hard combinatorial optimization problems on graphs, namely the vertex cover problem, the computation of maximum cliques, and the determination of a maximum independent set. Extending the evaluation process for a given population to the evaluation of the whole search space we get exact methods for the considered problems, which allow to evaluate the quality of solutions obtained by evolutionary algorithms.
KeywordsEvolutionary Algorithm Random Graph Crossover Operator Vertex Cover Relational Algebra
Unable to display preview. Download preview PDF.
- 8.Kehden, B., Neumann, F., Berghammer, R.: Relational Implementation of Simple Parallel Evolutionary Algorithms. In: Proc. of the 8th International Conference on Relational Methods in Computer Science (RelMiCS 8), pp. 137–146 (2005)Google Scholar
- 9.Leoniuk, B.: ROBDD-based implementation of relational algebra with applications (in German). Diss., Univ. Kiel (2001)Google Scholar
- 11.Milanese, U.: On the implementation of a ROBDD-based tool for the manipulation and visualization of relations (in German). Diss., Univ. Kiel (2003)Google Scholar
- 15.Soak, S.-M., Corne, D.W., Ahn, B.-H.: A Powerful New Encoding for Tree-Based Combinatorial Optimisation Problems. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 430–439. Springer, Heidelberg (2004)CrossRefGoogle Scholar