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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Veröffentlicht in:Scientific reports Jg. 12; H. 1; S. 22417 - 12
Hauptverfasser: Bragin, Mikhail A., Tucker, Emily L.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: London Nature Publishing Group UK 27.12.2022
Nature Publishing Group
Nature Portfolio
Schlagworte:
639/166
639/705
692/700
Computer applications
Decomposition
Humanities and Social Sciences
Integer programming
Linear programming
multidisciplinary
Programming, Linear
Science
Science (multidisciplinary)
ISSN:2045-2322, 2045-2322
Online-Zugang:Volltext
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Zusammenfassung: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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ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-022-26264-1