Direct Statistical Estimation of GA Landscape Properties

Abstract

This chapter derives some probability distributions for quantities that can be measured in repeated application of heuristic search methods. It then describes how this can be used to provide direct statistical estimates of the number of attractors using maximum likelihood methods. The chapter also discusses practical questions of numerical estimation, provides some illustrations of how the method works in the case of a genetic algorithm (GA), and discusses some implications of the assumptions made in deriving the estimates. A variety of predictive measures are suggested for assessing how difficult it might be to solve a particular problem instance using a particular algorithm. However, most of these measures are indirect. For neighborhood search methods, one direct indicator of problem difficulty is the number of local optima that exist in the problem landscape. Whether one speaks of local optima or attractors, estimating their number is not an easy problem.