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A heuristic-based branch and bound algorithm for unconstrained quadratic zero-one programming

Ein auf Heuristiken fußendes Branch- and Bound-Verfahren zur quadratischen 0–1 Optimierung

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Abstract

In this paper we describe a branch and bound algorithm for solving the unconstrained quadratic 0–1 programming problem. The salient features of it are the use of quadratic programming heuristics in the transformation of subproblems and exploiting some classes of facets of the polytope related to the quadratic problem in deriving upper bounds on the objective function. We develop facet selection procedures that form a basis of the bound computation algorithm. We present computational experience on four series of randomly generated problems and 14 real instances of a quadratic problem arising in design automation. We remark that the same ideas can also be applied to some other combinatorial optimization problems.

Zusammenfassung

In diesem Artikel beschreiben wir einen “Branch and Bound”-Algorithmus zur Lösung von quadratischen Optimierungsaufgaben in 0–1 Variablen und ohne Restriktionen. Das Verfahren verwendet Heuristiken zur Transformation von Teilproblemen. Zur Bestimmung oberer Schranken für die Zielfunktion werden gewiesse Klassen von Facetten des zugehörigen Polyeders verwendet. Weiters werden Auswahlalgorithmen für Facetten angegeben, die die Grundlage der Schrankenberechnungen bilden. Es werden Rechenergebnisse für vier zufällig generierte Aufgabenserien vorgestellt, wie auch von 14 realen Anwendungen aus dem Bereich der automatisierten Projektierung. Es wird betont, daß dieselben Ideen auch auf andere kombinatorische Optimierungsprobleme angewandt werden können.

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  1. Department of Practical Informatics, Kaunas University of Technology, Studentu St. 50, 3028, Kaunas, Lithuania

    G. Palubeckis

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  1. G. Palubeckis
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Palubeckis, G. A heuristic-based branch and bound algorithm for unconstrained quadratic zero-one programming. Computing 54, 283–301 (1995). https://doi.org/10.1007/BF02238228

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  • DOI: https://doi.org/10.1007/BF02238228

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