Variable-fixing then subgradient optimization guided very large scale neighborhood search for the generalized assignment problem

Haddadi, Salim

doi:10.1007/s10288-018-0389-z

“…SLBLR outperforms SAVLR [17] as well, thereby demonstrating that the fast convergence offered by the novel "levelbased" stepsizing, with other things being equal, translates into better results as compared to those obtained by SAVLR, which employs the "contraction mapping" stepsizing [17]. Lastly, the methods developed in [18][19][20] specifically target GAPs, whereas the SLBLR method developed in this paper has broader applicability.…”

Section: Example 1: Generalized Assignment Problemsmentioning

confidence: 82%

“…Column Generation [19], and Very Large Scale Neighborhood Search (VLNS) [20], which to the best of the authors' knowledge are the best methods for at least one of the above instances. For completeness, comparison against Surrogate Absolute-Value Lagrangian Relaxation (SAVLR) [17], which is an improved version of Surrogate Lagrangian Relaxation (SLR) [33], is also performed.…”

Section: Example 1: Generalized Assignment Problemsmentioning

confidence: 99%

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

Bragin

¹

,

Tucker

²

2022

Preprint

1

0

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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 step-sizing formula for the fastest coordination possible to obtain near-optimal solutions in a computationally efficient manner. Unlike all previous methods to set step-sizes heuristically by adjusting hyper-parameters, the key novel way to obtain step-sizes is purely decision-based: a novel “auxiliary” constraint satisfaction problem is solved, from which the appropriate step-sizes are inferred. Testing results for large-scale Generalized Assignment Problems (GAP) 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 frequently used Branch-and-Cut (B&C). SLBLR has a major impact on the efficient resolution of complex Mixed-Integer Programming (MIP) problems arising within a variety of scientific fields.

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“…SLBLR outperforms SAVLR [17] as well, thereby demonstrating that the fast convergence offered by the novel "level-based" stepsizing, with other things being equal, translates into better results as compared to those obtained by SAVLR, which employs the "contraction mapping" stepsizing [17]. Lastly, the methods developed in [18][19][20] specifically target GAPs, whereas the SLBLR method developed in this paper has broader applicability.…”

Section: Example 1: Generalized Assignment Problemsmentioning

confidence: 83%

“…To test scalability, six instances d201600, d401600, d801600, e201600, e401600 and e801600 are considered. SLBLR is compared with Depth-First Lagrangian Branch-and-Bound Method (DFLBnB) [18], Column Generation [19], and Very Large Scale Neighborhood Search (VLNS) [20], which to the best of the authors' knowledge are the best methods for at least one of the above instances. For completeness, comparison against Surrogate Absolute-Value Lagrangian Relaxation (SAVLR) [17], which is an improved version of Surrogate Lagrangian Relaxation (SLR) [33], is also performed.…”

Section: Example 1: Generalized Assignment Problemsmentioning

confidence: 99%

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

Bragin

¹

,

Tucker

²

2022

Preprint

View full text Add to dashboard Cite

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 step-sizing formula for the fastest coordination possible to obtain near-optimal solutions in a computationally efficient manner. Unlike all previous methods to set step-sizes heuristically by adjusting hyper-parameters, the key novel way to obtain step-sizes is purely decision-based: a novel “auxiliary” constraint satisfaction problem is solved, from which the appropriate step-sizes are inferred. Testing results for large-scale Generalized Assignment Problems (GAP) 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 frequently used Branch-and-Cut (B&C). SLBLR has a major impact on the efficient resolution of complex Mixed-Integer Programming (MIP) problems arising within a variety of scientific fields.

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“…Az sayıda çalışma çok amaçlı yapıdadır ( [20]- [23]). GAP literatürü çözüm yöntemleri açısından incelendiğinde, çözüm yöntemlerinin kesin çözüm yöntemleri ( [12], [13], [18]- [20], [24], [25]) ve sezgisel/metasezgisel yöntemler ([1], [3]- [6], [8]- [10], [15]- [17], [19], [21]- [23], [25]- [29]) olarak gruplanabileceği görülmektedir.…”

Section: Gi̇ri̇ş (Introduction)unclassified

A Simulated Annealing Algorithm for the Multi Resource Generalized Assignment Problem with Eligibility Constraint

Erten

¹

,

Saraç

²

,

Özçelik

³

2021

Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım Ve Teknoloji

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Variable-fixing then subgradient optimization guided very large scale neighborhood search for the generalized assignment problem

Cited by 11 publications

References 38 publications

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

A Simulated Annealing Algorithm for the Multi Resource Generalized Assignment Problem with Eligibility Constraint

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