{"title":"Learning to handle parameter perturbations in Combinatorial Optimization: An application to facility location","authors":"Andrea Lodi , Luca Mossina , Emmanuel Rachelson","doi":"10.1016/j.ejtl.2020.100023","DOIUrl":null,"url":null,"abstract":"<div><p>We present an approach to couple the resolution of Combinatorial Optimization problems with methods from Machine Learning. Specifically, our study is framed in the context where a reference discrete optimization problem is given and there exist data for many variations of such reference problem (historical or simulated) along with their optimal solution. Those variations can be originated by disruption but this is not necessarily the case. We study how one can exploit these to make predictions about an unseen new variation of the reference instance.</p><p>The methodology is composed by two steps. We demonstrate how a classifier can be built from these data to determine whether the solution to the reference problem still applies to a perturbed instance. In case the reference solution is only partially applicable, we build a regressor indicating the magnitude of the expected change, and conversely how much of it can be kept for the perturbed instance. This insight, derived from <em>a priori</em> information, is expressed via an additional constraint in the original mathematical programming formulation.</p><p>We present the methodology through an application to the classical facility location problem and we provide an empirical evaluation and discuss the benefits, drawbacks and perspectives of such an approach.</p><p>Although it cannot be used in a black-box manner, i.e., it has to be adapted to the specific application at hand, we believe that the approach developed here is general and explores a new perspective on the exploitation of past experience in Combinatorial Optimization.</p></div>","PeriodicalId":45871,"journal":{"name":"EURO Journal on Transportation and Logistics","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.ejtl.2020.100023","citationCount":"21","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EURO Journal on Transportation and Logistics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2192437620301539","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 21
Abstract
We present an approach to couple the resolution of Combinatorial Optimization problems with methods from Machine Learning. Specifically, our study is framed in the context where a reference discrete optimization problem is given and there exist data for many variations of such reference problem (historical or simulated) along with their optimal solution. Those variations can be originated by disruption but this is not necessarily the case. We study how one can exploit these to make predictions about an unseen new variation of the reference instance.
The methodology is composed by two steps. We demonstrate how a classifier can be built from these data to determine whether the solution to the reference problem still applies to a perturbed instance. In case the reference solution is only partially applicable, we build a regressor indicating the magnitude of the expected change, and conversely how much of it can be kept for the perturbed instance. This insight, derived from a priori information, is expressed via an additional constraint in the original mathematical programming formulation.
We present the methodology through an application to the classical facility location problem and we provide an empirical evaluation and discuss the benefits, drawbacks and perspectives of such an approach.
Although it cannot be used in a black-box manner, i.e., it has to be adapted to the specific application at hand, we believe that the approach developed here is general and explores a new perspective on the exploitation of past experience in Combinatorial Optimization.
期刊介绍:
The EURO Journal on Transportation and Logistics promotes the use of mathematics in general, and operations research in particular, in the context of transportation and logistics. It is a forum for the presentation of original mathematical models, methodologies and computational results, focussing on advanced applications in transportation and logistics. The journal publishes two types of document: (i) research articles and (ii) tutorials. A research article presents original methodological contributions to the field (e.g. new mathematical models, new algorithms, new simulation techniques). A tutorial provides an introduction to an advanced topic, designed to ease the use of the relevant methodology by researchers and practitioners.