American Institute of Mathematical Sciences

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January  2009, 5(1): 47-60. doi: 10.3934/jimo.2009.5.47

A Lagrangian dual and surrogate method for multi-dimensional quadratic knapsack problems

Xiaoling Sun 1, , Xiaojin Zheng 2, and  Juan Sun 2,

1. 

School of Management, Fudan University, Shanghai 200433
2. 

Department of Mathematics, Shanghai University, Shanghai 200444, China, China

Received  April 2008 Revised  October 2008 Published  December 2008

Quadratic 0-1 knapsack problems have a variety of applications in various areas such as flexible manufacturing systems, location of transportation facilities and telecommunications. In this paper we present a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems. Outer approximation and bundle method are used to compute the Lagrangian bound where the Lagrangian relaxation is solved by the maximum flow algorithm. We also present a surrogate constraint heuristic for finding feasible solutions. Preliminary computational results for small to medium size test problems are reported.
Keywords: branch-and-bound method, bundle method., outer approximation, Multi-dimensional quadratic 0-1 knapsack problem.
Mathematics Subject Classification: Primary: 90C10, 90C20; Secondary: 90C1.
Citation: Xiaoling Sun, Xiaojin Zheng, Juan Sun. A Lagrangian dual and surrogate method for multi-dimensional quadratic knapsack problems. Journal of Industrial and Management Optimization, 2009, 5 (1) : 47-60. doi: 10.3934/jimo.2009.5.47
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