Learning to handle parameter perturbations in Combinatorial Optimization: An application to facility location

Lodi, Andrea; Mossina, Luca; Rachelson, Emmanuel

doi:10.1016/j.ejtl.2020.100023

Cited by 17 publications

(8 citation statements)

References 10 publications

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“…A similar principle based on Support Vector Machines is also applied by Sun et al (2019). A very interesting approach has been proposed by the authors of Lodi et al (2019). They assume that instances to be solved result from a perturbation of a reference instance of the facility location problem.…”

Section: And Optimizationmentioning

confidence: 99%

“…Only a few exceptions have to be mentioned. Lodi et al (2019) assume that instances being solved for the facility location problem are random perturbations of a single reference instance, which is similar to the idea of a base instance introduced in this paper. Xavier et al (2019) assume a fixed topology of the problem structure and generate instances by altering parameters with respect to historic data.…”

Section: And Optimizationmentioning

confidence: 99%

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A machine learning-based branch and price algorithm for a sampled vehicle routing problem

et al. 2021

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Planning of operations, such as routing of vehicles, is often performed repetitively in rea-world settings, either by humans or algorithms solving mathematical problems. While humans build experience over multiple executions of such planning tasks and are able to recognize common patterns in different problem instances, classical optimization algorithms solve every instance independently. Machine learning (ML) can be seen as a computational counterpart to the human ability to recognize patterns based on experience. We consider variants of the classical Vehicle Routing Problem with Time Windows and Capacitated Vehicle Routing Problem, which are based on the assumption that problem instances follow specific common patterns. For this problem, we propose a ML-based branch and price framework which explicitly utilizes those patterns. In this context, the ML models are used in two ways: (a) to predict the value of binary decision variables in the optimal solution and (b) to predict branching scores for fractional variables based on full strong branching. The prediction of decision variables is then integrated in a node selection policy, while a predicted branching score is used within a variable selection policy. These ML-based approaches for node and variable selection are integrated in a reliability-based branching algorithm that assesses their quality and allows for replacing ML approaches by other (classical) better performing approaches at the level of specific variables in each specific instance. Computational results show that our algorithms outperform benchmark branching strategies. Further, we demonstrate that our approach is robust with respect to small changes in instance sizes.

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Section: And Optimizationmentioning

confidence: 99%

Section: And Optimizationmentioning

confidence: 99%

A machine learning-based branch and price algorithm for a sampled vehicle routing problem

et al. 2021

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“…The objective is to gain insights on the possible solution of a new unseen problem. This information can be used directly to guide decision making (as in Fischetti and Fraccaro (2019)) or can be used to increase the performance of the existing model (as in Larsen et al (2018); Xavier et alXavier et al (2019); Lodi et al (2019)).…”

Section: State Of the Artmentioning

confidence: 99%

“…the solution space and can potentially remove optimal solutions. Following notation in Lodi et al (2019), we refer to these pseudo-cuts as "learned constraints." The result of applying all learned constraints thus creates a new solution space Y � (x) .…”

Section: Learning Bounds and Constraintsmentioning

confidence: 99%

A novel solution approach with ML-based pseudo-cuts for the Flight and Maintenance Planning problem

et al. 2020

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This paper deals with the long-term Military Flight and Maintenance Planning problem. In order to solve this problem efficiently, we propose a new solution approach based on a new Mixed Integer Program and the use of both valid cuts generated on the basis of initial conditions and learned cuts based on the prediction of certain characteristics of optimal or near-optimal solutions. These learned cuts are generated by training a Machine Learning model on the input data and results of 5000 instances. This approach helps to reduce the solution time with little losses in optimality and feasibility in comparison with alternative matheuristic methods. The obtained experimental results show the benefit of a new way of adding learned cuts to problems based on predicting specific characteristics of solutions.

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“…These concepts, applicable to situations in which the future number of facilities is uncertain, have parallels to the broader class of models for optimization under uncertainty. More recently, a body of research has arisen examining linkages between combinatorial optimization (such as the facility location models of [10]) and machine learning methods, e.g., [12], which explicitly considered facility location problems as an application area in which machine learning methods could be used to address uncertainties in input parameters.…”

mentioning

confidence: 99%

Nested-solution facility location models

McGarvey

Thorsen

2021

Optim Lett

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Classical facility location models can generate solutions that do not maintain consistency in the set of utilized facilities as the number of utilized facilities is varied. We introduce the concept of nested facility locations, in which the solution utilizing p facilities is a subset of the solution utilizing q facilities, for all i ≤ p < q ≤ j, given some lower limit i and upper limit j on r, the number of facilities that will be utilized in the future. This approach is demonstrated with application to the p-median model, with computational testing showing these new models achieve reductions in both average regret and worst-case regret when r = p facilities are actually utilized.

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Learning to handle parameter perturbations in Combinatorial Optimization: An application to facility location

Cited by 17 publications

References 10 publications

A machine learning-based branch and price algorithm for a sampled vehicle routing problem

A machine learning-based branch and price algorithm for a sampled vehicle routing problem

A novel solution approach with ML-based pseudo-cuts for the Flight and Maintenance Planning problem

Nested-solution facility location models

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