Modeling and Optimization: Theory and Applications: Selected Contributions from the MOPTA 2012 Conference PDF
Preview Modeling and Optimization: Theory and Applications: Selected Contributions from the MOPTA 2012 Conference
Springer Proceedings in Mathematics & Statistics Luis F. Zuluaga Tamás Terlaky Editors Modeling and Optimization: Theory and Applications Selected Contributions from the MOPTA 2012 Conference Springer Proceedings in Mathematics & Statistics Volume 62 Forfurthervolumes: http://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, includingORandoptimization.Inadditiontoanoverallevaluationoftheinterest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematicalandstatisticalresearchtoday. Luis F. Zuluaga • Tamás Terlaky Editors Modeling and Optimization: Theory and Applications Selected Contributions from the MOPTA 2012 Conference 123 Editors LuisF.Zuluaga TamásTerlaky DepartmentofIndustrial DepartmentofIndustrial andSystemsEngineering andSystemsEngineering LehighUniversity LehighUniversity Bethlehem,PA,USA Bethlehem,PA,USA ISSN2194-1009 ISSN2194-1017(electronic) ISBN978-1-4614-8986-3 ISBN978-1-4614-8987-0(eBook) DOI10.1007/978-1-4614-8987-0 SpringerNewYorkHeidelbergDordrechtLondon LibraryofCongressControlNumber:2013953702 MathematicsSubjectClassification:49-06,49Mxx,65Kxx,90-06,90Bxx,90Cxx ©SpringerScience+BusinessMediaNewYork2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface This volume contains a selection of papers that were presented at the Modeling and Optimization:Theory and Applications(MOPTA) Conferenceheld at Lehigh University in Bethlehem, Pennsylvania, USA, between July 30 and August 1, 2012. MOPTA 2012 aimed to bring together a diverse group of researchers and practitioners, working on both theoretical and practical aspects of continuous or discrete optimization. The goal was to host presentations on the exciting devel- opments in different areas of optimization and at the same time provide a setting for close interaction among the participants. The topics covered at MOPTA 2012 varied from algorithms for solving convex, combinatorial, nonlinear, and global optimizationproblemsandaddressedtheapplicationofoptimizationtechniquesin finance,electricitysystems,healthcare,andotherimportantfields.Thefivepapers contained in this volume represent a sample of these topics and applications and illustratethebroaddiversityofideasdiscussedattheconference.Below,webriefly introduceeachofthem. The paper by Anjos provides a comprehensive review of the mathematical optimization models that have been proposed to address the Unit Commitment problem.Thisisafundamentalproblemintheoperationofpowersystemsthatseeks to find the optimal way to generate a power production schedule, while ensuring demand satisfaction and the safe and reliable operation of the system. The Unit Commitment problem is becoming increasingly important and challenging. This is mainly due to the transition to low-carbon, sustainable, and renewable energy sources (e.g., wind and solar energy) and the need to reliably satisfy increasing energy demands in a scarce resource, highly competitive, and interconnected economy. ThepaperbyLejeuneconsidersanovelwaytotakeintoaccountuncertaintyin the key problem of optimal portfolio allocation. Furthermore, the paper provides algorithmictechniquestoaddressthesolutionoflarge-scaleproblemsinthisclass withpracticallyrelevantfeaturesthatmaketheirsolutionmorechallenging.Namely, heconsiderstheportfolioallocationproblemswithfeaturessuchasfixedtransaction costsand diversification,cardinality,and buy-inthresholdconstraints.Large-scale v vi Preface problems in this category become difficult to solve by commercially available optimization solvers. Thus, the focus is to obtain optimal or close to optimal solutionstotheprobleminafastmanner. The paper by Regis considers black-box optimization problems for which the dependance between the objective function and the decision variables is not available in explicit functional form. Instead, values of the problems’ objective can only be computed for given values of the decision variables through compu- tationally expensive simulations. For this class of problems, the paper proposes an initialization strategy that can be effectively used to substantially improve the performance of solution algorithms for black-box optimization problems. This is shown by presentingcorrespondingcomputationalresults on problemswith up to onethousandvariables.Inparticular,instancesofablack-boxoptimizationproblem arisinginthemanagementofgroundwaterbioremediationareconsidered. ThepaperbyBensonandSag˘lamconsidersthesolutionofmixed-integersecond- order cone optimization (MISOCO) problems using a combination of nonlinear, branch-and-bound, and outer approximation techniques. A key of their approach is that it allows for warmstarting when solving the continuous relaxation of the problem.TheperformanceoftheirproposedtechniquesisinvestigatedonMISOCO problems arising in portfolio allocation problems. Currently, MISOCO problems appear in many engineering, healthcare, and finance applications, as well as in the general context of robust optimization. Thus, this paper contributes to the development of specific algorithmic techniques for this very important class of problems. The paper by Li and Terlaky investigates the duality relationship between two keystone algorithms to solve linear feasibility problems, namely, the perceptron andthevonNeumannalgorithms.Thisapproachallowstointerpretvariantsofthe perceptronalgorithmasvariantsofthevonNeumannalgorithmandviceversaand transitthecomplexityresultsfromonefamilytotheother.Advancesrelatedtothis classofinexpensivealgorithmsarekey,giventhegrowingneedtosolveextremely largeoptimizationproblemsinmostcurrentpracticalapplications. Thesearticles addressthetwofocusareasoftheMOPTAConference,namely,the rolethatmodelingplaysinthesolutionofanoptimizationproblemandadvancesin optimizationalgorithms,theory,andapplications. We end this preface by thanking the sponsors of MOPTA 2012, namely, AIMMS(http://business.aimms.com/), GuRoBiOptimization(http://www.gurobi. com/),IBM(http://www.research.ibm.com/),Mosek(http://www.mosek.com/),and SAS (http://www.sas.com/).We also thankthe host, LehighUniversity,as well as the rest of the organizing committee: Frank E. Curtis, Eugene Perevalov, Ted K. Ralphs,KatyaScheinberg,LarryV.Snyder,RobertH.Storer,andAurélieThiele. Bethlehem,PA,USA LuisF.Zuluaga TamásTerlaky Contents RecentProgressinModelingUnitCommitmentProblems ................. 1 MiguelF.Anjos PortfolioOptimizationwithCombinatorialandDownside ReturnConstraints............................................................... 31 MiguelA.Lejeune An Initialization Strategy for High-Dimensional Surrogate-BasedExpensiveBlack-BoxOptimization........................ 51 RommelG.Regis Smoothing and Regularization for Mixed-Integer Second-Order Cone Programming with Applications inPortfolioOptimization........................................................ 87 HandeY.BensonandÜmitSag˘lam The Duality Between the Perceptron Algorithm andthevonNeumannAlgorithm .............................................. 113 DanLiandTamásTerlaky vii Recent Progress in Modeling Unit Commitment Problems MiguelF.Anjos Abstract Theunitcommitmentproblemisafundamentalproblemintheoperation of power systems. The purpose of unit commitment is to minimize the system- wide cost of power generation by finding an optimal power production schedule foreachgeneratorwhileensuringthatdemandismetandthatthesystemoperates safely and reliably. This problem can be formulated as a mixed-integer nonlinear optimization problem, and finding global optimal solutions is important not only becauseofthesignificantoperationalcostsbutalsobecauseincompetitivemarket environments,different near-optimal solutions can produce considerably different financialsettlements.Atthesametime,thetimeavailabletosolvetheproblemisa hardconstraintinpractice.Henceunitcommitmentisanimportantandchallenging optimization problem. This article provides an introduction to the basic problem from the point of view of optimization, summarizes several related modeling developmentsin the recentliterature while providingsome possible directionsfor future research, and concludes with a brief mention of extensions to the basic problemthathavegreatpracticalimportanceandaredrivingmuchcurrentresearch. Keywords Optimization • Unitcommitment • Mixed-integerlinearprogramming 1 Introduction Electricity is a critical source of energy used by both individuals and industry on a daily basis. With increasing demand for electricity and various constraints on the development of new generation capacity, it is imperative to increase the overall efficiency of the power system. This need has motivated the concept of M.F.Anjos((cid:2)) CanadaResearchChairinDiscreteNonlinearOptimizationinEngineering, GERADandÉcolePolytechniquedeMontréal,Montreal,QC,CanadaH3C3A7 e-mail:[email protected] L.F.ZuluagaandT.Terlaky(eds.),ModelingandOptimization:TheoryandApplications, 1 SpringerProceedingsinMathematics&Statistics62,DOI10.1007/978-1-4614-8987-0__1, ©SpringerScience+BusinessMediaNewYork2013 2 M.F.Anjos smartgrids.Asmartgridisanext-generationelectricalpowersystemthatcombines thepowerdistributionsystemwithatwo-waycommunicationbetweensuppliersand consumerstooptimizethegeneration,transportation,anddistributionofelectrical energy. Smart grids are expected to deliver energy savings, cost reductions, and increased reliability and security by enabling new strategies to manage the power system. For example, a smart grid will in principle supporta two-way interaction withindividualhomestoachievesystem-sideobjectives[14]. Smartgridsarea popularresearchareaatpresent.TheIEEErecentlylaunched a new journal dedicated to it, and multiple research initiatives are underway aroundtheworld.TheMOPTA 2012conferencefeaturedfivesessionsof talkson electricitysystemsandsmartgrids;moreover,theAIMMS(cid:2)c competitionproblem wasconcernedwithschedulinginsmartgrids. Thisarticleisaboutoneofthefundamentaloptimizationproblemsinthisarea, namely,theunitcommitment(UC)problem.ThepurposeofsolvingUCproblemsis tominimizethesystem-widecostofpowergenerationwhileensuringthatdemandis metandthatthesystemoperatessafelyandreliably.TheUCmodelswereoriginally proposedandappliedinmonopolisticcontextsandhavebeenextendedtogenerate productionschedulesinacompetitivemarketenvironment(see,e.g.,[2,10,21]). Becauseoftheoperatingconstraintsofthegeneratorsandthebehaviorofpower flows,thecompleteUCproblemisamixed-integernonlinearoptimizationproblem. Thefirstmixed-integerlinearprogramming(MILP)formulationofthebasictrade- offs in UC was proposed more than 50years ago [4]. A vast literature has been dedicatedtodevelopingsolutiontechniquesforUC(see,e.g.,[45,61]).TheMILP approach is among the few techniques that can provide provably global optimal UC solutions. Global optima matter in competitive markets because different near-optimal solutions may yield considerably different payments to generator owners[52]. Realistic instances of the UC problem are typically large scale and require significant computationaltime to solve. Moreover, in the context of system oper- ations, the time available to solve a UC modelis a hard limitation, restricting the size and scope of UC formulations. As a result, practitioners sometimes have to settle for solutions that are not globally optimal. Nevertheless, the value of the MILP approach for solving UC problems is well recognized; for example, PJM InterconnectionhasbeenusingMILPsince2005andithascontributedtoimportant efficiencygains[43]. The objectivesof this article are to providean introductionto the UC problem from the point of view of mathematical optimization and to collect a number of recent developments in the modeling of the basic UC problem that are likely to have a significant impact on the ability to solve large-scale instances of UC in practice. The problem of UC incorporating all actual operational requirements is called security-constrained unit commitment (SCUC) (see, e.g., [48, Chap.8]). Security-constrainedUCincludesmanyfeaturesthatare notincludedinourbasic UCmodel.Wealsodonotexplicitlyaddressissuesarisingfromthebroadersmart gridcontext,suchasmanagingbidirectionalflowsofpower,integratingrenewable energysourcessuchaswindandsolar,accountingforforecastinguncertainties,and
The list of books you might like
