ABSTRACT
We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces (Doye, 2002). We use the well-known family of $NK$ landscapes as an example. In our case the inherent network is the graph where the vertices are all the local maxima and edges mean basin adjacency between two maxima. We exhaustively extract such networks on representative small NK landscape instances, and show that they are 'small-worlds'. However, the maxima graphs are not random, since their clustering coefficients are much larger than those of corresponding random graphs. Furthermore, the degree distributions are close to exponential instead of Poissonian. We also describe the nature of the basins of attraction and their relationship with the local maxima network.
- A-L. Barabasi and R. Albert, Emergence of scaling in random networks, Science 286 (1999), 509--512.Google ScholarCross Ref
- K. D. Boese, A. B. Kahng, and S. Muddu, A new adaptive multi-start technique for combinatorial global optimizations, Operations Research Letters 16 (1994), 101--113.Google ScholarDigital Library
- C. Cotta and J.-J. Merelo, Where is evolutionary computation going? A temporal analysis of the EC community, Genetic Programming and Evolvable Machines 8 (2007), 239--253. Google ScholarDigital Library
- S. N. Dorogovtsev and J. F. F. Mendes, Evolution of networks, Oxford University Press, Oxford, New York, 2003.Google Scholar
- J. P. K. Doye, The network topology of a potential energy landscape: a static scale-free network, Phys. Rev. Lett. 88 (2002), 238701.Google ScholarCross Ref
- J. P. K. Doye and C. P. Massen, Characterizing the network topology of the energy landscapes of atomic clusters, J. Chem. Phys. 122 (2005), 084105.Google ScholarCross Ref
- W. Feller, An introduction to probability theory and its applications, Wiley, New York, 1968.Google Scholar
- J. Garnier and L. Kallel, Efficiency of local search with multiple local optima, SIAM Journal on Discrete Mathematics 15 (2001), no. 1, 122--141. Google ScholarDigital Library
- M. Giacobini, M. Preuss, and M. Tomassini, Effects of scale-free and small-world topologies on binary coded self-adaptive CEA, Evolutionary Computation in Combinatorial Optimization -- EvoCOP 2006 (Budapest), LNCS, vol. 3906, Springer Verlag, 2006, pp. 85--96. Google ScholarDigital Library
- M. Giacobini, M. Tomassini, and A. Tettamanzi, Takeover time curves in random and small-world structured populations, Genetic and Evolutionary Computation Conference, GECCO 2005, Proceedings, ACM, 2005, pp. 1333--1340. Google ScholarDigital Library
- S. A. Kauffman, The origins of order, Oxford University Press, New York, 1993.Google Scholar
- L.Luthi, M. Tomassini, M. Giacobini, and W. B. Langdon, The genetic programming collaboration network and its communities, Genetic and Evolutionary Computation Conference, GECCO 2007, Proceedings, London, England, UK (Hod Lipson et al., ed.), ACM, 2007, pp. 1643--1650. Google ScholarDigital Library
- P. Merz and B. Freisleben, Memetic algorithms and the fitness landscape of the graph bi-partitioning problem, Parallel Problem Solving from Nature V (A. E. Eiben, T. Back, M. Schoenauer, and H.-P. Schwefel, eds.), Lecture Notes in Computer Science, vol. 1498, Springer-Verlag, 1998, pp. 765--774. Google ScholarDigital Library
- M. E. J. Newman, The structure and function of complex networks, SIAM Review \textbf45 (2003), 167--256.Google Scholar
- J. L. Payne and M. J. Epstein, Takeover times on scale-free topologies, Genetic and Evolutionary Computation Conference, GECCO 2007, Proceedings, London, England, UK (Hod Lipson et al., ed.), ACM, 2007, pp. 308--315. Google ScholarDigital Library
- C. R. Reeves, Landscapes, operators and heuristic search, Annals of Operations Research 86 (1999), 473--490.Google ScholarCross Ref
- D. L. Stein, Disordered systems: mostly spin glasses, Lectures in the Sciences of Complexity (D. L. Stein, ed.), Addison-Wesley, 1989, pp. 301--353.Google Scholar
- F.H. Stillinger, A topographic view of supercooled liquids and glass formation, Science 267 (1995), 1935--1939.Google ScholarCross Ref
- M. Tomassini, M. Giacobini, and C. Darabos, Evolution of small-world networks of automata for computation, Parallel Problem Solving from Nature -- PPSN VIII (Birmingham, UK), LNCS, vol. 3242, Springer-Verlag, 2004, pp. 672--681.Google Scholar
- D. J. Watts, The "new" science of networks, Annual Review of Sociology 30 (2004), 243--270.Google ScholarCross Ref
- D. J. Watts and S. H. Strogatz, Collective dynamics of "small-world" networks, Nature 393 (1998), 440--442.Google ScholarCross Ref
Index Terms
- A study of NK landscapes' basins and local optima networks
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