Quantitative measure of nonconvexity for black-box continuous functions

Metaheuristic algorithms usually aim to solve nonconvex optimization problems in black-box and high-dimensional scenarios. Characterizing and understanding the properties of nonconvex problems is therefore important for effectively analyzing metaheuristic algorithms and their development, improvemen...

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Veröffentlicht in:Information sciences Jg. 476; S. 64 - 82
Hauptverfasser: Tamura, Kenichi, Gallagher, Marcus
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.02.2019
Schlagworte:
Black-box functions
Complexity
Fitness landscape analysis
Large problems
Metaheuristics
Monte Carlo integral
Monte Carlo integral
Black-box functions
Metaheuristics
Large problems
Fitness landscape analysis
Complexity
ISSN:0020-0255, 1872-6291
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Zusammenfassung:Metaheuristic algorithms usually aim to solve nonconvex optimization problems in black-box and high-dimensional scenarios. Characterizing and understanding the properties of nonconvex problems is therefore important for effectively analyzing metaheuristic algorithms and their development, improvement and selection for problem solving. This paper establishes a novel analysis framework called nonconvex ratio analysis, which can characterize nonconvex continuous functions by measuring the degree of nonconvexity of a problem. This analysis uses two quantitative measures: the nonconvex ratio for global characterization and the local nonconvex ratio for detailed characterization. Midpoint convexity and Monte Carlo integral are important methods for constructing the measures. Furthermore, as a practical feature, we suggest a rapid characterization measure that uses the local nonconvex ratio and can characterize certain black-box high-dimensional functions using a much smaller sample. Throughout this paper, the effectiveness of the proposed measures is confirmed by numerical experiments using the COCO function set.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2018.10.009