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Theorems Supporting r-flip Search for Pseudo-Boolean Optimization

Author

Listed:
  • Bahram Alidaee

    (University of Mississippi, USA)

  • Gary Kochenberger

    (University of Colorado Denver, USA)

  • Haibo Wang

    (Texas A&M International University, USA)

Abstract

Modern metaheuristic methodologies rely on well defined neighborhood structures and efficient means for evaluating potential moves within these structures. Move mechanisms range in complexity from simple 1-flip procedures where binary variables are “flipped” one at a time, to more expensive, but more powerful, r-flip approaches where “r” variables are simultaneously flipped. These multi-exchange neighborhood search strategies have proven to be effective approaches for solving a variety of combinatorial optimization problems. In this paper, we present a series of theorems based on partial derivatives that can be readily adopted to form the essential part of r-flip heuristic search methods for Pseudo-Boolean optimization. To illustrate the use of these results, we present preliminary results obtained from four simple heuristics designed to solve a set of Max 3-SAT problems.

Suggested Citation

  • Bahram Alidaee & Gary Kochenberger & Haibo Wang, 2010. "Theorems Supporting r-flip Search for Pseudo-Boolean Optimization," International Journal of Applied Metaheuristic Computing (IJAMC), IGI Global, vol. 1(1), pages 93-109, January.
    • Handle: RePEc:igg:jamc00:v:1:y:2010:i:1:p:93-109
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    Cited by:

    1. Bahram Alidaee & Haibo Wang, 2017. "A note on heuristic approach based on UBQP formulation of the maximum diversity problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 102-110, January.

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