Abstract
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.
Preview
Unable to display preview. Download preview PDF.
References
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.
R. Battiti and A. Bertossi. Greedy, Prohibition, and Reactive Heuristics for Graph-Partitioning. IEEE Transactions on Computers, 1997, to appear.
K.D. Boese. Cost versus Distance in the Traveling Salesman Problem. Technical Report TR-950018, UCLA CS Department, 1995.
T. N. Bui and B. R. Moon. Genetic Algorithm and Graph Partitioning. IEEE Transactions on Computers, 45(7):841–855, 1996.
R. Dawkins. The Selfish Gene. Oxford University Press, Oxford, 1976.
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.
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.
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.
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.
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.
M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York, 1979.
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.
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.
S. A. Kauffman. The Origins of Order: S elf-Organization and Selection in Evolution. Oxford University Press, 1993.
S. A. Kauffman and S. Levin. Towards a General Theory of Adaptive Walks on Rugged Landscapes. Journal of Theoretical Biology, 128:11–45, 1987.
B. Kernighan and S. Lin. An Efficient Heuristic Procedure for Partitioning Graphs. Bell Systems Journal, 49:291–307, 1972.
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.
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.
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.
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.
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.
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.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Merz, P., Freisleben, B. (1998). Memetic algorithms and the fitness landscape of the graph bi-partitioning problem. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, HP. (eds) Parallel Problem Solving from Nature — PPSN V. PPSN 1998. Lecture Notes in Computer Science, vol 1498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0056918
Download citation
DOI: https://doi.org/10.1007/BFb0056918
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65078-2
Online ISBN: 978-3-540-49672-4
eBook Packages: Springer Book Archive