Quasi-elementary Landscapes and Superpositions of Elementary Landscapes

  • Darrell Whitley
  • Francisco Chicano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7219)


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 term “Quasi-elementary landscapes” is introduced to describe landscapes that are “almost” elementary; in quasi-elementary landscapes there exists some efficiently computed “correction” that captures those parts of the neighborhood structure that deviate from the normal structure found in elementary landscapes. The “shift” operator, as well as the “3-opt” operator for the Traveling Salesman Problem landscapes induce quasi-elementary landscapes. A local search neighborhood for the Maximal Clique problem is also quasi-elementary. Finally, we show that landscapes which are a superposition of elementary landscapes can be quasi-elementary in structure.


Local Search Travel Salesman Problem Auxiliary Function Neighborhood Structure Neighborhood Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

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

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