An Explicit Exact SDP Relaxation for Nonlinear 0-1 Programs
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
Exact Solution of the Quadratic Knapsack Problem
INFORMS Journal on Computing
Using a Mixed Integer Quadratic Programming Solver for the Unconstrained Quadratic 0-1 Problem
Mathematical Programming: Series A and B
The quadratic knapsack problem-a survey
Discrete Applied Mathematics
Improved compact linearizations for the unconstrained quadratic 0-1 minimization problem
Discrete Applied Mathematics
Solution of Large Quadratic Knapsack Problems Through Aggressive Reduction
INFORMS Journal on Computing
Linear forms of nonlinear expressions: New insights on old ideas
Operations Research Letters
Generalized quadratic multiple knapsack problem and two solution approaches
Computers and Operations Research
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The quadratic knapsack problem (QKP) has been the subject of considerable research in recent years. Despite notable advances in special purpose solution methodologies for QKP, this problem class remains very difficult to solve. With the exception of special cases, the state-of-the-art is limited to addressing problems of a few hundred variables and a single knapsack constraint. In this paper we provide a comparison of quadratic and linear representations of QKP based on test problems with multiple knapsack constraints and up to eight hundred variables. For the linear representations, three standard linearizations are investigated. Both the quadratic and linear models are solved by standard branch-and-cut optimizers available via CPLEX. Our results show that the linear models perform well on small problem instances but for larger problems the quadratic model outperforms the linear models tested both in terms of solution quality and solution time by a wide margin. Moreover, our results demonstrate that QKP instances larger than those previously addressed in the literature as well as instances with multiple constraints can be successfully and efficiently solved by branch and cut methodologies.