A Note on Problem Difficulty Measures in Black-Box Optimization: Classification, Realizations and Predictability

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Colleges, School and Institutes


Various methods have been defined to measure the hardness of a fitness function for evolutionary algorithms and other black-box heuristics. Examples include fitness landscape analysis, epistasis, fitness-distance correlations etc., all of which are relatively easy to describe. However, they do not always correctly specify the hardness of the function. Some measures are easy to implement, others are more intuitive and hard to formalize. This paper rigorously defines difficulty measures in black-box optimization and proposes a classification. Different types of realizations of such measures are studied, namely exact and approximate ones. For both types of realizations, it is proven that predictive versions that run in polynomial time in general do not exist unless certain complexity-theoretical assumptions are wrong.


Original languageEnglish
Pages (from-to)435-443
Number of pages9
JournalEvolutionary Computation
Issue number4
Publication statusPublished - 1 Dec 2007


  • satisfiability problem, problem difficulty measure, evolutionary algorithm, running time, black-box optimization