An Extended Neighborhood Vision for Hill-Climbing Move Strategy Design

  • Sara Tari
  • Matthieu BasseurEmail author
  • Adrien Goëffon
Part of the Operations Research/Computer Science Interfaces Series book series (ORCS, volume 62)


Many combinatorial optimization problem solvers are based on stochastic local search algorithms, which mainly differ by their move selection strategies, also called pivoting rules. In this chapter, we aim at determining pivoting rules that allow hill-climbing to reach good local optima. We propose here to use additional information provided by an extended neighborhood for an accurate selection of neighbors. In particular, we introduce the maximum expansion pivoting rule which consists in selecting a solution which maximizes the improvement possibilities at the next step. Empirical experiments on permutation-based problem instances indicate that the expansion score is a relevant criterion to attain good local optima.


Combinatorial optimization Neighborhood search Permutation problems 



The work is partially supported by the PGMO project from the Fondation Math/’ematique Jacques Hadamard.


  1. 1.
    E. Alekseeva, Y. Kochetov, A. Plyasunov, Complexity of local search for the p-median problem, in 18th Mini Euro Conference on VNS, 2005Google Scholar
  2. 2.
    M. Basseur, A. Goeffon, Hill-climbing strategies on various landscapes: an empirical comparison, in Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, GECCO ’13 (ACM, New York, 2013), pp. 479–486Google Scholar
  3. 3.
    M. Basseur, A. Goëffon, On the efficiency of worst improvement for climbing NK-landscapes, in Proceedings of the 2014 Conference on Genetic and Evolutionary Computation, GECCO ’14 (ACM, New York, 2014), pp. 413–420Google Scholar
  4. 4.
    M. Basseur, A. Goëffon, Unconventional pivoting rules for local search, in International Conference on Metaheuristics and Nature Inspired Computing (META’2014), 2014Google Scholar
  5. 5.
    M. Basseur, A. Goëffon, Climbing combinatorial fitness landscapes. Appl. Soft Comput. 30, 688–704 (2015)CrossRefGoogle Scholar
  6. 6.
    M. Basseur, A. Goëffon, F. Lardeux, F. Saubion, V. Vigneron, On the attainability of NK landscapes global optima, in Seventh Annual Symposium on Combinatorial Search, 2014Google Scholar
  7. 7.
    W. Bateson, Mendel’s Principles of Heredity (Cambridge University Press, Cambridge, 1909)CrossRefGoogle Scholar
  8. 8.
    P. Collard, S. Verel, M. Clergue, How to use the scuba diving metaphor to solve problem with neutrality? in ECAI 2004: 16th European Conference on Artificial Intelligence, 22–27 August 2004, Valencia, Spain: Including Prestigious Applications of Intelligent Systems (PAIS 2004): Proceedings, vol. 110 (IOS Press, Amsterdam, 2004), p. 166Google Scholar
  9. 9.
    P. Hansen, N. Mladenovic, First vs. best improvement: an empirical study. Discret. Appl. Math. 154(5), 802–817 (2006). {IV} ALIO/EURO Workshop on Applied Combinatorial Optimization IV ALIO/EURO Workshop on Applied Combinatorial OptimizationGoogle Scholar
  10. 10.
    S.A. Kauffman, The Origins of Order: Self-organization and Selection in Evolution (Oxford University Press, New York, 1993)Google Scholar
  11. 11.
    J.D. Knowles, R.A. Watson, D. Corne, Reducing local optima in single-objective problems by multi-objectivization, in Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization (EMO 2001), Zurich, 7–9 March 2001, pp. 269–283, 2001Google Scholar
  12. 12.
    T. Koopmans, M.J. Beckmann, Assignment problems and the location of economic activities. Cowles Foundation Discussion Papers 4, Cowles Foundation for Research in Economics, Yale University, 1955Google Scholar
  13. 13.
    J.K. Lenstra, A.H.G. Rinnooy Kan, P. Brucker, Complexity of machine scheduling problems. Ann. Discret. Math. 1, 343–362 (1977)CrossRefGoogle Scholar
  14. 14.
    K. Malan, A.P. Engelbrecht, A survey of techniques for characterising fitness landscapes and some possible ways forward. Inf. Sci. 241, 148–163 (2013)CrossRefGoogle Scholar
  15. 15.
    G. Ochoa, S. Verel, M. Tomassini, First-improvement vs. best-improvement local optima networks of NK landscapes, in Parallel Problem Solving from Nature, PPSN XI, ed. by R. Schaefer, C. Cotta, J. Koodziej, G. Rudolph. Lecture Notes in Computer Science (Springer, Berlin/Heidelberg, 2010), pp. 104–113Google Scholar
  16. 16.
    P.P.M. Pardalos, H. Wolkowicz, Quadratic Assignment and Related Problems: Dimacs Workshop 20–21 May 1993, vol. 16 (American Mathematical Society, Providence, RI, 1994)Google Scholar
  17. 17.
    F.J. Poelwijk, S. Tanase-Nicola, D.J. Kiviet, S.J. Tans, Reciprocal sign epistasis is a necessary condition for multi-peaked fitness landscapes. J. Theor. Biol. 272(1), 141–144 (2011)CrossRefGoogle Scholar
  18. 18.
    S. Sahni, T. Gonzalez, P-complete approximation problems. J. ACM 23(3), 555–565 (1976)CrossRefGoogle Scholar
  19. 19.
    É. Taillard, Benchmarks for basic scheduling problems. Eur. J. Oper. Res. 64(2), 278–285 (1993)CrossRefGoogle Scholar
  20. 20.
    E.-G. Talbi, Metaheuristics: From Design to Implementation, vol. 74 (Wiley, Hoboken, 2009)CrossRefGoogle Scholar
  21. 21.
    D. Whitley, A.E. Howe, D. Hains, Greedy or not? Best improving versus first improving stochastic local search for MAXSAT, in Proceedings of the Twenty-Seventh AAAI Conference on Artificial Intelligence, 14–18 July 2013, Bellevue, Washington (2013)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.LERIAUniversité d’AngersAngersFrance

Personalised recommendations