Memetic algorithms and the fitness landscape of the graph bi-partitioning problem

  • Peter Merz
  • Bernd Freisleben
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1498)


In this paper, two types of fitness landscapes of the graph bipartitioning problem are analyzed, and a memetic algorithm — a genetic algorithm incorporating local search — that finds near-optimum solutions efficiently is presented. A search space analysis reveals that the fitness landscapes of geometric and non-geometric random graphs differ significantly, and within each type of graph there are also differences with respect to the epistasis of the problem instances. As suggested by the analysis, the performance of the proposed memetic algorithm based on Kernighan-Lin local search is better on problem instances with high epistasis than with low epistasis. Further analytical results indicate that a combination of a recently proposed greedy heuristic and Kernighan-Lin local search is likely to perform well on geometric graphs. The experimental results obtained for non-geometric graphs show that the proposed memetic algorithm (MA) is superior to any other heuristic known to us. For the geometric graphs considered, only the initialization phase of the MA is required to find (near) optimum solutions.


Genetic Algorithm Local Search Problem Instance Travel Salesman Problem Memetic Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    R. Battiti and A. Bertossi. Differential Greedy for the 0–1 Equicut Problem. In D.Z. Du and P.M. Pardalos, editors, Proceedings of the DIMACS Workshop on Network Design: Connectivity and Facilities Location. Amer. Math. Soc., 1997.Google Scholar
  2. 2.
    R. Battiti and A. Bertossi. Greedy, Prohibition, and Reactive Heuristics for Graph-Partitioning. IEEE Transactions on Computers, 1997, to appear.Google Scholar
  3. 3.
    K.D. Boese. Cost versus Distance in the Traveling Salesman Problem. Technical Report TR-950018, UCLA CS Department, 1995.Google Scholar
  4. 4.
    T. N. Bui and B. R. Moon. Genetic Algorithm and Graph Partitioning. IEEE Transactions on Computers, 45(7):841–855, 1996.zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    R. Dawkins. The Selfish Gene. Oxford University Press, Oxford, 1976.Google Scholar
  6. 6.
    L. J. Eshelman and J. D. Schaffer. Preventing Premature Convergence in Genetic Algorithms by Preventing Incest. In Proceedings of the 4th Int. Conference on Genetic Algorithms, pages 115–122. Morgan Kaufmann, 1991.Google Scholar
  7. 7.
    L.J. Eshelman. The CHC Adaptive Search Algorithm: How to Have Safe Search When Engaging in Nontraditional Genetic Recombination. In G. J. E. Rawlings, editor, Foundations of Genetic Algorithms, pages 265–283. Kaufmann, 1991.Google Scholar
  8. 8.
    C. M. Fiduccia and R. M. Mattheyses. A Liner-Time Heuristic for Improving Network Partitions. In Proceedings of the 19th ACM/IEEE Design Automation Conference DAC 82, pages 175–181, 1982.Google Scholar
  9. 9.
    B. Freisleben and P. Merz. A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesman Problems. In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation, pages 616–621. IEEE Press, 1996.Google Scholar
  10. 10.
    B. Freisleben and P. Merz. New Genetic Local Search Operators for the Traveling Salesman Problem. In H.-M. Voigt, W. Ebeling, I. Rechenberg, and H.-P. Schwefel, editors, Proceedings of the 4th Conference on Parallel Problem Solving from Nature — PPSN IV, pages 890–900. Springer, 1996.Google Scholar
  11. 11.
    M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York, 1979.zbMATHGoogle Scholar
  12. 12.
    D. S. Johnson, C. R. Aragon, L. A. McGeoch, and C. Schevon. Optimization by Simulated Annealing; Part I, Graph Partitioning. Operations Research, 37:865–892, 1989.zbMATHCrossRefGoogle Scholar
  13. 13.
    T. Jones and S. Forrest. Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms. In L. J. Eshelman, editor, Proceedings of the 6th Int. Conference on Genetic Algorithms, pages 184–192, Kaufman, 1995.Google Scholar
  14. 14.
    S. A. Kauffman. The Origins of Order: S elf-Organization and Selection in Evolution. Oxford University Press, 1993.Google Scholar
  15. 15.
    S. A. Kauffman and S. Levin. Towards a General Theory of Adaptive Walks on Rugged Landscapes. Journal of Theoretical Biology, 128:11–45, 1987.MathSciNetGoogle Scholar
  16. 16.
    B. Kernighan and S. Lin. An Efficient Heuristic Procedure for Partitioning Graphs. Bell Systems Journal, 49:291–307, 1972.Google Scholar
  17. 17.
    P. Merz and B. Freisleben. On the Effectiveness of Evolutionary Search in High-Dimensional NK-Landscapes. In Proceedings of the 1998 IEEE International Conference on Evolutionary Computation, pages 741–745, IEEE Press, 1998.Google Scholar
  18. 18.
    P. Merz and B. Freisleben. A Genetic Local Search Approach to the Quadratic Assignment Problem. In T. Bäck, editor, Proceedings of the 7th International Conference on Genetic Algorithms, pages 465–472, Morgan Kaufmann, 1997.Google Scholar
  19. 19.
    P. Merz and B. Freisleben. Genetic Local Search for the TSP: New Results. In Proceedings of the 1997 IEEE International Conference on Evolutionary Computation, pages 159–164, IEEE Press, 1997.Google Scholar
  20. 20.
    P. Moscato. On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts: Towards Memetic Algorithms. Technical Report No. 790, Caltech Concurrent Computation Program, California Institue of Technology, USA, 1989.Google Scholar
  21. 21.
    P. Moscato and M. G. Norman. A Memetic Approach for the Traveling Salesman Problem Implementation of a Computational Ecology for Combinatorial Optimization on Message-Passing Systems. In M. Valero, E. Onate, M. Jane, J. L. Larriba, and B. Suarez, editors, Parallel Computing and Transputer Applications, pages 177–186, IOS Press, 1992.Google Scholar
  22. 22.
    A. G. Steenbeek, E. Marchiori, and A. E. Eiben. Finding Balanced Graph Bi-Partitions Using a Hybrid Genetic Algorithm. In Proceedings of the IEEE International Conference on Evolutionary Computation ICEC'98, pages 90–95, IEEE press, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Peter Merz
    • 1
  • Bernd Freisleben
    • 1
  1. 1.Department of Electrical Engineering and Computer Science (FB 12)University of SiegenSiegenGermany

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