One-pass heuristics for large-scale unconstrained binary quadratic problems Fred Glover * , Bahram Alidaee, C esar Rego, Gary Kochenberger Hearin Center for Enterprise Science, University of Mississippi, University, MS 38677, USA Abstract Many signi®cant advances have been made in recent years for solving unconstrained binary quadratic programs UQP).Asaresult,thesizeofprobleminstancesthatcanbeecientlysolvedhasgrownfromahundredorsovariables afewyearsagoto2000or3000variablestoday.Theseadvanceshavemotivatednewapplicationsofthemodelwhich, inturn,havecreatedtheneedtosolveevenlargerproblems.Inresponsetothisneed,weintroduceseveralnew``one- pass'' heuristics for solving very large versions of this problem. Our computational experience on problems of up to 9000variablesindicatesthatthesemethodsarebothecientandeectiveforverylargeproblems.Thesigni®canceof problemsofthissizeisthattheynotonlyopenthedoortosolvingamuchwiderarrayofrealworldproblems,butalso thatthestandardlinearmixedintegerformulationsofthenonlinearmodelsinvolveover40,000,000variablesandthree times that many constraints. Our approaches can be used as stand-alone solution methods, or they can serve as pro- cedures for quickly generating high quality starting points for other, more sophisticated methods. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Unconstrained binary quadratic optimization; One-pass heuristics 1. Introduction The unconstrained quadratic program can be written in the form: UQP : min f x xQx; where Q isan n n matrixofconstantsand x isan n-vectorofbinaryvariables.UQPisnotableforits ability to represent a wide variety of important problems as well as its NP-hard diculty. Appli- cations have been reported in many dierent set- tings including social psychology [14], ®nancial analysis[18,20],computeraideddesign[17],trac management [7,27], machine scheduling [1], cellu- lar radio channel allocation [6], and molecular conformation[25].Moreover,manycombinatorial optimization problems pertaining to graphs such as determining maximum cliques, maximum cuts, maximum vertex packing, minimum coverings, European Journal of Operational Research 137 2002) 272±287 www.elsevier.com/locate/dsw * Corresponding author. E-mail addresses: fglover@bus.olemiss.edu F. Glover), balidaee@bus.olemiss.edu B. Alidaee), crego@bus.olemiss.edu C. Rego), gkochenberger@bus.olemiss.edu G. Kochenber- ger). 0377-2217/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII:S0377-221701)00209-0