Optimized Crossover-Based Genetic Algorithms for the Maximum Cardinality and Maximum Weight Clique Problems

  • Authors:
  • Egon Balas;William Niehaus

  • Affiliations:
  • Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA 15213;SRA International, Fairfax, VA

  • Venue:
  • Journal of Heuristics
  • Year:
  • 1998

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Abstract

In Balas and Niehaus (1996), we have developed a heuristic for generating large cliques in anarbitrary graph, by repeatedly taking two cliques and finding amaximum clique in the subgraph induced by the union of theirvertex sets, an operation executable in polynomial time throughbipartite matching in the complement of the subgraph. Aggarwal, Orlin and Tai (1997) recognized thatthe latter operation can be embedded into the framework of agenetic algorithm as an optimized crossover operation. Inspiredby their approach, we examine variations of each element of thegenetic algorithm—selection, population replacement andmutation—and develop a steady-state genetic algorithm thatperforms better than its competitors on most problems.