# American Institute of Mathematical Sciences

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

 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.
Citation: Xiaoling Sun, Xiaojin Zheng, Juan Sun. A Lagrangian dual and surrogate method for multi-dimensional quadratic knapsack problems. Journal of Industrial & Management Optimization, 2009, 5 (1) : 47-60. doi: 10.3934/jimo.2009.5.47
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