Abstract
An empirical study is performed on the local-optimum space in graph bipartitioning. We examine some statistical features of the fitness landscape and the local properties of the landscape. They include the distributions of local optima, their cost-distance correlations, their attraction powers, the properties around the central area of local optima, etc. The study reveals some new notable results about the properties of the fitness landscape. For example, the central area yielded good quality in local-optimum space, the local-optimum space had the self-similar structure of global convexity, local optima showed clusters in more than one place, etc. We also provide a simple experiment on whether it is worth to exploit the area around the Euclidean center of the problem space.
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References
Battiti, R. and A. Bertossi. (1998). “Differential Greedy for the 0-1 Equicut Problem.” In D.Z. Du and P.M. Pardalos (eds.), Network Design: Connectivity and Facilities Location. American Mathematical Society. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 40, 3-21.
Battiti, R. and A. Bertossi. (1999). “Greedy, Prohibition, and Reactive Heuristics for Graph Partitioning.” IEEE Trans. on Computers 48(4), 361–385.
Boese, K.D. and A.B. Kahng. (1994). “Best-so-far vs. Where-you-are: Implications for Optimal Finite-Time Annealing.” Systems and Control Letters 22(1), 71–78.
Boese, K.D., A.B. Kahng, and S. Muddu. (1994). “A New Adaptive Multi-Start Technique for Combinatorial Global Optimizations.” Operations Research Letters 15, 101–113.
Bui, T.N. and B.R. Moon. (1996). “Genetic Algorithm and Graph Partitioning.” IEEE Trans. on Computers 45(7), 841–855.
Dutt, S. and W. Deng. (1996). “A Probability-Based Approach to VLSI Circuit Partitioning.” In Design Automation Conference, pp. 100-105.
Fiduccia, C. and R. Mattheyses. (1982). “A Linear Time Heuristics for Improving Network Partitions.” In 19th ACM/IEEE Design Automation Conference, pp. 175-181.
Ford, L.R. Jr. and D.R. Fulkerson. (1962). Flows in Networks. Princeton University Press.
Fukunaga, A.S., J.H. Huang, and A.B. Kahng. (1996). “On Clustered Kick Moves for Iterated-Descent Netlist Partitioning.” In IEEE Int'l Symp. on Circuits and Systems, vol. 4, pp. 496–499.
Garey, M. and D.S. Johnson. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco: Freeman.
Hong, I., A.B. Kahng, and B.R. Moon. (1997). “Improved Large-Step Markov Chain Variants for the Symmetric TSP.” Journal of Heuristics 3(1), 63–81.
Johnson, D.S. (1990). “Local Optimization and the Traveling Salesman Problem.” In 17th Colloquium onAutomata, Languages, and Programming. Springer-Verlag, pp. 446-461.
Johnson, D.S., C. Aragon, L. McGeoch, and C. Schevon. (1989). “Optimization by Simulated Annealing: An Experimental Evaluation, Part 1, Graph Partitioning.” Operations Research 37, 865–892.
Jones, T. and S. Forrest. (1995). “Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms.” In Sixth International Conference on Genetic Algorithms, pp. 184-192.
Kauffman, S. (1989). “Adaptation on Rugged Fitness Landscapes.” Lectures in the Science of Complexity, pp. 527-618.
Kernighan, B. and S. Lin. (1970). “An Efficient Heuristic Procedure for Partitioning Graphs.” Bell Systems Technical Journal 49, 291–307.
Kim, Y.H. and B.R. Moon. (2004). “Lock-Gain Based Graph Partitioning.” Journal of Heuristics 10(1), 37–57.
Kirkpatrick, S., C.D. Gelatt Jr., and M.P. Vecchi. (1983). “Optimization by Simulated Annealing.” Science 220(4598), 671–680.
Lim, A. and Y.M. Chee. (1991). “Graph Partitioning Using Tabu Search.” In IEEE Int'l Symp. Circuits and Systems, pp. 1164-1167.
Manderick, B., M. de Weger, and P. Spiessens. (1991). “The Genetic Algorithm and the Structure of the Fitness Landscape.” In International Conference on Genetic Algorithms, pp. 143-150.
Martin, O.C., S.W. Otto, and E.W. Felten. (1991). “Large-Step Markov Chain for the Traveling Salesman Problem.” Complex Systems 5(3), 299–326.
Merz, P. and B. Freisleben. (1998). “Memetic Algorithms and the Fitness Landscape of the Graph Bi-Partitioning Problem.” In Proceedings of the 5th International Conference on Parallel Problem Solving From Nature, Springer-Verlag. Lecture Notes in Computer Science, 1498, 765-774.
Moon, B.R. and C.K. Kim. (1997). “A Two-Dimensional Embedding of Graphs for Genetic Algorithms.” In International Conference on Genetic Algorithms, pp. 204-211.
Saab, Y.G. (1995).“A Fast and Robust Network Bisection Algorithm.” IEEE Trans. on Computers 44(7), 903–913.
Sorkin, G.B. (1991). “Efficient Simulated Annealing on Fractal Landscapes.” Algorithmica 6, 367–418.
Steenbeek, A.G., E. Marchiori, and A.E. Eiben. (1998). “Finding Balanced Graph Bi-Partitions Using a Hybrid Genetic Algorithm.” In IEEE International Conference on Evolutionary Computation, pp. 90-95.
Weinberger, E.D. (1991). “Fourier and Taylor Series on Fitness Landscapes.” Biological Cybernetics 65, 321–330.
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Kim, YH., Moon, BR. Investigation of the Fitness Landscapes in Graph Bipartitioning: An Empirical Study. Journal of Heuristics 10, 111–133 (2004). https://doi.org/10.1023/B:HEUR.0000026263.43711.44
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DOI: https://doi.org/10.1023/B:HEUR.0000026263.43711.44
- cost surface
- cost-distance correlation
- central point
- graph bipartitioning
- heuristic algorithm