Elementary Landscape Decomposition of the Hamiltonian Path Optimization Problem,

  • Darrell Whitley
  • Francisco Chicano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8600)

Abstract

There exist local search landscapes where the evaluation function is an eigenfunction of the graph Laplacian that corresponds to the neighborhood structure of the search space. Problems that display this structure are called “Elementary Landscapes” and they have a number of special mathematical properties. The problems that are not elementary landscapes can be decomposed in a sum of elementary ones. This sum is called the elementary landscape decomposition of the problem. In this paper, we provide the elementary landscape decomposition for the Hamiltonian Path Optimization Problem under two different neighborhoods.

Keywords

Landscape theory elementary landscapes hamiltonian path optimization quadratic assignment problem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Agarwala, R., Applegate, D.L., Maglott, D., Schuler, G.D.: A fast and scalable radiation hybrid map construction and integration strategy. Genome Research 10(3), 350–364 (2000)CrossRefGoogle Scholar
  2. 2.
    Burkard, R.E.: Quadratic Assignment Problems. In: Handbook of Combinatorial Optimization, 2nd edn., pp. 2741–2815. Springer (2013)Google Scholar
  3. 3.
    Chen, W., Whitley, D., Hains, D., Howe, A.: Second order partial derivatives for NK-landscapes. In: Proceeding of GECCO, pp. 503–510. ACM (2013)Google Scholar
  4. 4.
    Chicano, F., Alba, E.: Exact computation of the expectation curves of the bit-flip mutation using landscapes theory. In: Proc. of GECCO, pp. 2027–2034 (2011)Google Scholar
  5. 5.
    Chicano, F., Alba, E.: Exact computation of the fitness-distance correlation for pseudoboolean functions with one global optimum. In: Hao, J.-K., Middendorf, M. (eds.) EvoCOP 2012. LNCS, vol. 7245, pp. 111–123. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  6. 6.
    Chicano, F., Whitley, L.D., Alba, E.: A methodology to find the elementary landscape decomposition of combinatorial optimization problems. Evolutionary Computation 19(4), 597–637 (2011)CrossRefGoogle Scholar
  7. 7.
    Grover, L.K.: Local search and the local structure of NP-complete problems. Operations Research Letters 12, 235–243 (1992)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Hains, D., Whitley, D., Howe, A., Chen, W.: Hyperplane initialized local search for MAXSAT. In: Proceeding of GECCO, pp. 805–812. ACM (2013)Google Scholar
  9. 9.
    Lawler, E.L.: The quadratic assignment problem. Manage. Sci. 9, 586–599 (1963)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Parsons, R., Forrest, S., Burks, C.: Genetic algorithms, operators, and DNA fragment assembly. Machine Learning 21, 11–33 (1995)Google Scholar
  11. 11.
    Reidys, C.M., Stadler, P.F.: Combinatorial landscapes. SIAM Review 44(1), 3–54 (2002)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Sutton, A.M., Chicano, F., Whitley, L.D.: Fitness function distributions over generalized search neighborhoods in the q-ary hypercube. Evol. Comput. 21(4) (2013)Google Scholar
  13. 13.
    Sutton, A.M., Whitley, D., Howe, A.E.: Mutation rates of the (1+1)-EA on pseudo-boolean functions of bounded epistasis. In: Proc. of GECCO, pp. 973–980 (2011)Google Scholar
  14. 14.
    Sutton, A.M., Whitley, L.D., Howe, A.E.: Computing the moments of k-bounded pseudo-boolean functions over hamming spheres of arbitrary radius in polynomial time. Theoretical Computer Science 425, 58–74 (2011)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Whitley, D., Chen, W.: Constant time steepest descent local search with lookahead for NK-landscapes and MAX-kSAT. In: Proc. of GECCO, pp. 1357–1364 (2012)Google Scholar
  16. 16.
    Whitley, D., Sutton, A.M., Howe, A.E.: Understanding elementary landscapes. In: Proc. of GECCO, pp. 585–592 (2008)Google Scholar
  17. 17.
    Whitley, L.D., Sutton, A.M.: Partial neighborhoods of elementary landscapes. In: Proc. of GECCO, pp. 381–388 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Darrell Whitley
    • 1
  • Francisco Chicano
    • 2
  1. 1.Dept. of Computer ScienceColorado State UniversityFort CollinsUSA
  2. 2.Dept. de Lenguajes y Ciencias de la ComputaciónUniversity of MálagaSpain

Personalised recommendations