Detecting and Handling Reflection Symmetries in Mixed-Integer (Nonlinear) Programming
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909201596416000 |
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| author | Hojny, Christopher |
| author_facet | Hojny, Christopher |
| contents | Symmetries in mixed-integer (nonlinear) programs (MINLP), if not handled appropriately, are known to negatively impact the performance of (spatial) branch-and-bound algorithms. Usually one thus tries to remove symmetries from the problem formulation or is relying on a solver that automatically detects and handles symmetries. While modelers of a problem can handle various kinds of symmetries, automatic symmetry detection and handling is mostly restricted to permutation symmetries. This article therefore develops techniques such that also black-box solvers can automatically detect and handle a broader class of symmetries.
Inspired from geometric packing problems such as the kissing number problem, we focus on reflection symmetries of MINLPs. We develop a generic and easily applicable framework that allows to automatically detect reflection symmetries for MINLPs. To handle this broader class of symmetries, we discuss generalizations of state-of-the-art methods for permutation symmetries, and develop dedicated symmetry handling methods for special reflection symmetry groups. Our symmetry detection framework has been implemented in the open-source solver SCIP and we provide a comprehensive discussion of the implementation. The article concludes with a detailed numerical evaluation of our symmetry handling methods when solving MINLPs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Detecting and Handling Reflection Symmetries in Mixed-Integer (Nonlinear) Programming Hojny, Christopher Optimization and Control Symmetries in mixed-integer (nonlinear) programs (MINLP), if not handled appropriately, are known to negatively impact the performance of (spatial) branch-and-bound algorithms. Usually one thus tries to remove symmetries from the problem formulation or is relying on a solver that automatically detects and handles symmetries. While modelers of a problem can handle various kinds of symmetries, automatic symmetry detection and handling is mostly restricted to permutation symmetries. This article therefore develops techniques such that also black-box solvers can automatically detect and handle a broader class of symmetries. Inspired from geometric packing problems such as the kissing number problem, we focus on reflection symmetries of MINLPs. We develop a generic and easily applicable framework that allows to automatically detect reflection symmetries for MINLPs. To handle this broader class of symmetries, we discuss generalizations of state-of-the-art methods for permutation symmetries, and develop dedicated symmetry handling methods for special reflection symmetry groups. Our symmetry detection framework has been implemented in the open-source solver SCIP and we provide a comprehensive discussion of the implementation. The article concludes with a detailed numerical evaluation of our symmetry handling methods when solving MINLPs. |
| title | Detecting and Handling Reflection Symmetries in Mixed-Integer (Nonlinear) Programming |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2405.08379 |