A tractable Walsh analysis of SAT and its implications for genetic algorithms

  • Authors:
  • Soraya Rana;Robert B. Heckendorn;Darrell Whitley

  • Affiliations:
  • -;-;-

  • Venue:
  • AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
  • Year:
  • 1998

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Abstract

Walsh Transforms measure all sources of nonlinear interactions for functions that have a bit representation. There can be exponentially many nonlinear interactions and exactly computing all Walsh coefficients is usually intractable for non-trivial functions. In this paper we will show that SAT problems evaluated as MAXSAT functions have a highly restricted set of nonzero Walsh coefficients and those coefficients can be computed in linear time with respect to the number of clauses. This analysis suggests why standard simple genetic algorithms should perform poorly on MAXSAT problems.