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ABSTRACT

This paper introduces the concept of a critical backbone as a minimal set of variable or part of the solution necessary to be within the basin of attraction of the global optimum. The concept is illustrated with a new class of test problems Backbone in which the critical backbone structure is completely transparent. The performance of a number of standard heuristic search methods is measure for this problem. It is shown that a hybrid genetic algorithm that incorporates a descent algorithm solves this problem extremely efficiently. Although no rigorous analysis is given the problem is sufficiently transparent that this result is easy to understand. The paper concludes with a discussion of how the emergence of a critical backbone may be the salient feature in a phase transition from typically easy to typically hard problems.

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INDEX TERMS

Primary Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY

General Terms:
Algorithms, Theory

Keywords:
backbones, genetic algorithms, optimization