Phase Transition and Landscape Properties of the Number Partitioning Problem
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This paper empirically studies basic properties of the fitness landscape of random instances of number partitioning problem, with a focus on how these properties change with the phase transition. The properties include number of local and global optima, number of plateaus, basin size and its correlation with fitness. The only two properties that were found to change when the problem crosses the phase transition are the number of global optima and the number of plateaus, the rest of the properties remained oblivious to the phase transition. This paper, also, studies the effect of different distributions of the weights and different neighbourhood operators on the problem landscape.
Keywordscombinatorial optimisation phase transition partitioning problem makespan scheduling fitness landscape
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- 3.Fu, Y.: The use and abuse of statistical mechanics in computational complexity. In: Stein, D.L. (ed.) Lectures in the Sciences of Complexity, vol. 1, pp. 815–826. Addison-Wesley, Reading (1989)Google Scholar
- 4.Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of books in the mathematical sciences. W.H. Freeman (1979)Google Scholar
- 6.Hartmann, A.K., Weigt, M.: Phase Transitions in Combinatorial Optimization Problems. John Wiley & Sons (2006)Google Scholar
- 7.Kallel, L., Naudts, B., Reeves, C.R.: Properties of fitness functions and search landscapes. Theoretical Aspects of Evolutionary Computing, 175–206 (2001)Google Scholar
- 12.Stadler, P.F., Hordijk, W., Fontanari, J.F.: Phase transition and landscape statistics of the number partitioning problem. Physical Review E 67(5), 056701 (2003)Google Scholar
- 14.Tayarani, M., Prugel-Bennett, A.: On the landscape of combinatorial optimisation problems. IEEE Transactions on Evolutionary Computation PP(99) (2013)Google Scholar