Computational Evaluation of Data Driven Local Search for MIP Decompositions

Basso, Saverio; Ceselli, Alberto

doi:10.1007/978-3-030-34960-8_19

Cited by 1 publication

(10 citation statements)

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“…Even if our preliminary investigations showed data driven methods to be promising in specific tasks, the results of [21,22] are not directly applicable as a full computational tool. In detail, [21] shows how to rank decompositions in terms of distance from the Pareto front on the space of bound and computing time, but the problem of actually generating and selecting a specific decomposition of good rank in an overall optimization framework is only sketched.…”

Section: Introductionmentioning

confidence: 89%

“…We found them to be able to predict bound and computing time for other random decompositions over the same set of MIP instances, or limited perturbations of them [21]. Second, we used these models for choosing how to improve decompositions by simple local changes [22]. We found them effective.…”

Section: Introductionmentioning

confidence: 94%

“…In this paper we fill the gap between the concepts of [21,22] and their actual use in a full decomposition-based MIP resolution framework, proving its effectiveness in realistic contexts. We also describe and share a library of more than 31 thousands decompositions of MIPLIB instances, generated by a randomized greedy algorithm and scored by their root node computation.…”

Section: Introductionmentioning

confidence: 96%

“…Preliminary investigations. In two preparatory workshop papers [21,22] we have experimented the potential of machine learning tools in this context. We have mainly focused on two very specific tasks.…”

Section: Introductionmentioning

confidence: 99%

“…In detail, [21] shows how to rank decompositions in terms of distance from the Pareto front on the space of bound and computing time, but the problem of actually generating and selecting a specific decomposition of good rank in an overall optimization framework is only sketched. Neither the results of [22] are sufficient to be directly integrated in an overall framework, the main drawback being the computing time: the algorithms of [22] might take as long as the optimization phase itself. Further integration issues are not discussed, such as which combinations of data driven models, training techniques, decomposition generation and improvement methods work well together.…”

Section: Introductionmentioning

confidence: 99%

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A data driven Dantzig–Wolfe decomposition framework

Basso

Ceselli

2022

Math. Prog. Comp.

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We face the issue of finding alternative paradigms for the resolution of generic Mixed Integer Programs (MIP), by considering the perspective option of general purpose solvers which switch to decomposition methods when pertinent. Currently, the main blocking factor in their design is the problem of automatic decomposition of MIPs, that is to produce good MIP decompositions algorithmically, looking only at the algebraic structure of the MIP instance. We propose to employ Dantzig–Wolfe reformulation and machine learning methods to obtain a fully data driven automatic decomposition framework. We also design strategies and introduce algorithmic techniques in order to make such a framework computationally effective. An extensive experimental analysis shows our framework to grant substantial improvements, in terms of both solutions quality and computing time, with respect to state-of-the-art automatic decomposition techniques. It also allows us to gain insights into the relative impact of different techniques. As a side product of our research, we provide a dataset of more than 31 thousand random decompositions of MIPLIB instances, with 121 features, including computations of their root node relaxation.

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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%