Abstract
According to worst-case complexity analysis, difficult combinatorial problems are those for which no polynomial-time algorithms are known (see, for instance, [15]). Thus, according to this point of view, large enough instances of these problems cannot be solved in reasonable time. The mathematical analysis is primarily based on decision problems, i.e. those that require a yes/no answer [7, 15], but the theory can readily be extended to optimization problems [16], roughly speaking, those in which we seek a solution with an associated minimum or maximum cost, which are the ones that will be dealt with here.
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References
Barthélemy, M., Barrat, A., Pastor-Satorras, R., Vespignani, A.: Characterization and modeling of weighted networks. Physica A 346, 34–43 (2005)
Clauset, A., Newman, M.E.J., Moore, C.: Finding community structure in very large networks. Physical Review EÂ 70(6), 66111 (2004)
Daolio, F., Tomassini, M., Vérel, S., Ochoa, G.: Communities of minima in local optima networks of combinatorial spaces. Physica A 390, 1684–1694 (2011)
Daolio, F., Vérel, S., Ochoa, G., Tomassini, M.: Local optima networks of the quadratic assignment problem. In: IEEE Congress on Evolutionary Computation, CEC 2010, pp. 3145–3152. IEEE Press (2010)
Derrida, B.: Random energy model: an exactly solvable model of disordered systems. Phys. Rev. BÂ 24, 2613 (1981)
Fortunato, S.: Community detection in graphs. Physics Reports 486, 75–174 (2010)
Garey, M.R., Johnson, D.S.: Computers and Intractability. Freeman, San Francisco (1979)
Garnier, J., Kallel, L.: Efficiency of local search with multiple local optima. SIAM Journal on Discrete Mathematics 15(1), 122–141 (2001)
Jones, T.: Evolutionary algorithms, fitness landscapes and search. PhD thesis. The University of New Mexico (1995)
Kallel, L., Naudts, B., Rogers, A. (eds.): Theoretical Aspects of Evolutionary Computing. Springer, Heidelberg (2001)
Kauffman, S.A.: The Origins of Order. Oxford University Press, New York (1993)
Knowles, J.D., Corne, D.W.: Instance Generators and Test Suites for the Multiobjective Quadratic Assignment Problem. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 295–310. Springer, Heidelberg (2003)
Newman, M.E.J.: Networks: An Introduction. Oxford University Press, Oxford (2010)
Ochoa, G., Tomassini, M., Vérel, S., Darabos, C.: A study of NK landscapes’ basins and local optima networks. In: Genetic and Evolutionary Computation Conference, GECCO 2008, pp. 555–562. ACM (2008)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)
Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Englewood Cliffs (1982)
Reichardt, J., Bornholdt, S.: Statistical mechanics of community detection. Physical Review EÂ 74(1), 16110 (2006)
Reidys, C.M., Stadler, P.F.: Combinatorial landscapes. SIAM Review 44(1), 3–54 (2002)
Taillard, E.D.: Comparison of iterative searches for the quadratic assignment problem. Location Science 3(2), 87–105 (1995)
Talbi, E.-G.: Metaheuristics: From Design to Implementation. Wiley, Hoboken (2009)
Tomassini, M., Vérel, S., Ochoa, G.: Complex-network analysis of combinatorial spaces: The NK landscape case. Phys. Rev. E 78(6), 066114 (2008)
Vérel, S., Ochoa, G., Tomassini, M.: Local optima networks of NK landscapes with neutrality. IEEE Trans. Evol. Comp. 15(6), 783–797 (2011)
Weinberger, E.D.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biological Cybernetics 63, 325–336 (1990)
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Tomassini, M., Daolio, F. (2013). A Complex-Networks View of Hard Combinatorial Search Spaces. In: Tantar, E., et al. EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation. Studies in Computational Intelligence, vol 447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32726-1_6
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