On Stochastic Fitness Landscapes: Local Optimality and Fitness Landscape Analysis for Stochastic Search Operators

Abstract

Fitness landscape analysis is a well-established tool for gaining insights about optimization problems and informing about the behavior of local and evolutionary search algorithms. In the conventional definition of a fitness landscape, the neighborhood of a given solution is a set containing nearby solutions whose distance is below a threshold, or that are reachable using a deterministic local search operator. In this paper, we generalize this definition in order to analyze the induced fitness landscape for stochastic search operators, that is when neighboring solutions are reachable under different probabilities. More particularly, we give the definition of a stochastic local optimum under this setting, in terms of a probability to reach strictly improving solutions. We illustrate the relevance of stochastic fitness landscapes for enumerable combinatorial benchmark problems, and we empirically analyze their properties for different stochastic operators, neighborhood sample sizes, and local optimality thresholds. We also portray their differences through stochastic local optima networks, intending to gather a better understanding of fitness landscapes under stochastic search operators.