Title: Computationally attractive non-linear models for combinatorial optimisation

Authors: Bahram Alidaee, Gary A. Kochenberger, Karen Lewis, Mark Lewis, Haibo Wang

Addresses: MIS/POM Department, School of Business Administration, University of Mississippi, University, MS 38677, USA. ' Decision Science Department, School of Business Administration, University of Colorado, Denver, CO 80217, USA. ' 5 Tara Drive Street, St Joseph, MO 64507, USA. ' Management Department, School of Professional Studies, Missouri Western State University, St Joseph, MO 64507, USA. ' IB&TS Division, College of Business Administration, Texas A&M International University, Laredo, TX 78041, USA

Abstract: A common approach to many combinatorial problems is to model them as 0/1 linear programs. This approach enables the use of standard linear program-based optimisation methodologies that are widely employed by the operation research community. While this methodology has worked well for many problems, it can become problematic in cases where the linear programs generated become excessively large. In such cases, linear models can lose their computational viability. In recent years, several articles have explored the computational attractiveness of non-linear alternatives to the standard linear models typically adopted to represent such problems. In many cases, comparative computational testing yields results favouring the non-linear models by a wide margin. In this article, we summarise some of these successes in an effort to encourage a broader view of model construction than the conventional wisdom, i.e. linear modelling, typically affords.

Keywords: integer programming; nonlinear modelling; combinatorial optimisation.

DOI: 10.1504/IJMOR.2009.022873

International Journal of Mathematics in Operational Research, 2009 Vol.1 No.1/2, pp.9 - 19

Published online: 31 Jan 2009 *

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