Surrogate “Level-Based” Lagrangian Relaxation for mixed-integer linear programming
Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from combinatorial complexity . Because of integer decision variables, as the problem size increases, the n...
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| Vydáno v: | Scientific reports Ročník 12; číslo 1; s. 22417 - 12 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
London
Nature Publishing Group UK
27.12.2022
Nature Publishing Group Nature Portfolio |
| Témata: | |
| ISSN: | 2045-2322, 2045-2322 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines and within areas of strategic importance to society. The MILP problems, however, suffer from
combinatorial complexity
. Because of integer decision variables, as the problem size increases, the number of possible solutions increases
super-linearly
thereby leading to a drastic increase in the computational effort. To efficiently solve MILP problems, a “price-based” decomposition and coordination approach is developed to exploit 1. the super-linear reduction of complexity upon the decomposition and 2. the geometric convergence potential inherent to Polyak’s stepsizing formula for the fastest coordination possible to obtain near-optimal solutions in a computationally efficient manner. Unlike all previous methods to set stepsizes heuristically by adjusting hyperparameters, the key novel way to obtain stepsizes is purely decision-based: a novel “auxiliary” constraint satisfaction problem is solved, from which the appropriate stepsizes are inferred. Testing results for large-scale Generalized Assignment Problems demonstrate that for the majority of instances, certifiably optimal solutions are obtained. For stochastic job-shop scheduling as well as for pharmaceutical scheduling, computational results demonstrate the two orders of magnitude speedup as compared to Branch-and-Cut. The new method has a major impact on the efficient resolution of complex Mixed-Integer Programming problems arising within a variety of scientific fields. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 content type line 23 |
| ISSN: | 2045-2322 2045-2322 |
| DOI: | 10.1038/s41598-022-26264-1 |