American Institute of Mathematical Sciences

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April  2007, 3(2): 223-232. doi: 10.3934/jimo.2007.3.223

An exact algorithm for 0-1 polynomial knapsack problems

Xiaoling Sun 1, , Hongbo Sheng 2, and  Duan Li 3,

1. 

Department of Management Science, School of Management, Fudan University, Shanghai 200433, P. R., China
2. 

Department of Elementary Education, Tongling University, Tongling, Anhui 244000, P. R., China
3. 

Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China

Received  August 2006 Revised  January 2007 Published  April 2007

In this paper we propose an exact method for the 0-1 polynomial knapsack problem. The algorithm seeks the exact optimal solution of the problem by a back-tracking branch-and-bound procedure. The upper bounds are computed by a Lagrangian dual search where the Lagrangian relaxations are solved by the maximum-flow method. Heuristic procedures are derived to search for feasible solutions and thus to improve the performance of the algorithm. Promising computational results are reported for test problems with both single constraint and multiple constraints.
Keywords: Lagrangian relaxation, branch-and-bound method, 0-1 polynomial knapsack problem, maximum-flow algorithm..
Mathematics Subject Classification: Primary: 90C09; 90C10; Secondary: 90C3.
Citation: Xiaoling Sun, Hongbo Sheng, Duan Li. An exact algorithm for 0-1 polynomial knapsack problems. Journal of Industrial & Management Optimization, 2007, 3 (2) : 223-232. doi: 10.3934/jimo.2007.3.223
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