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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| Published in: | Information sciences Vol. 476; pp. 64 - 82 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Inc
01.02.2019
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| Subjects: | |
| ISSN: | 0020-0255, 1872-6291 |
| Online Access: | Get full text |
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| Summary: | 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. |
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| ISSN: | 0020-0255 1872-6291 |
| DOI: | 10.1016/j.ins.2018.10.009 |