Journal of Applied Mathematics and Decision Sciences
Volume 2005 (2005), Issue 2, Pages 113-121

A new modeling and solution approach for the number partitioning problem

Bahram Alidaee,1 Fred Glover,2 Gary A. Kochenberger,3 and Cesar Rego1

1Hearin Center for Enterprise Science, School of Business Administration, University of Mississippi, 38677, MS, USA
2Leeds School of Business, University of Colorado at Boulder, Boulder 80309-0419, CO, USA
3School of Business, University of Colorado at Denver and Health Sciences Center, Denver 80217-3364, CO, USA

Received 24 November 2003; Revised 9 May 2004

Copyright © 2005 Bahram Alidaee et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The number partitioning problem has proven to be a challenging problem for both exact and heuristic solution methods. We present a new modeling and solution approach that consists of recasting the problem as an unconstrained quadratic binary program that can be solved by efficient metaheuristic methods. Our approach readily accommodates both the common two-subset partition case as well as the more general case of multiple subsets. Preliminary computational experience is presented illustrating the attractiveness of the method.