A Lagrangian dual and surrogate method for multi-dimensional
quadratic knapsack problems
Xiaoling Sun - School of Management, Fudan University, Shanghai 200433, China (email)
Abstract: 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: Multi-dimensional quadratic
0-1 knapsack problem, branch-and-bound method, outer approximation,
Received: April 2008; Revised: October 2008; Published: December 2008.
2011 Impact Factor.66