Estimating attraction basin sizes of combinatorial optimization problems

Elorza, Anne; Hernando, Leticia; Mendiburu, Alexander; Lozano, José A.

doi:10.1007/s13748-018-0156-6

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…In this section, we illustrate the relevance of the SLO definition, and we show preliminary scenarios for analyzing stochastic fitness landscapes 5 .…”

Section: Resultsmentioning

confidence: 99%

“…For large landscapes, different methods allow one to estimate the number of local optima using uniform random sampling, biased random sampling [1,7], or the length of an adaptive walk before being trapped [11]. In addition to the number of local optima, the size, the distribution and the structure of local optima's basins of attraction is one major feature related to algorithm performance [5,8], including for problems from machine learning [3]. The basin of attraction of a local optimum x is defined as the set of solutions from which a hill-climbing algorithm h falls into:…”

Section: Preliminariesmentioning

confidence: 99%

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

Aboutaib

Vérel

Fonlupt

et al. 2020

Lecture Notes in Computer Science

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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.

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“…In this section, we illustrate the relevance of the SLO definition, and we show preliminary scenarios for analyzing stochastic fitness landscapes 5 .…”

Section: Resultsmentioning

confidence: 99%