Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Mathematical Programming: Series A and B
Formulations and valid inequalities for the node capacitated graph partitioning problem
Mathematical Programming: Series A and B
Introduction to Dynamic Programming
Introduction to Dynamic Programming
Exact Solution of the Quadratic Knapsack Problem
INFORMS Journal on Computing
Dynamic Programming
Operations Research
Operations Research Letters
Approximation algorithms for fractional knapsack problems
Operations Research Letters
The quadratic 0-1 knapsack problem with series-parallel support
Operations Research Letters
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Quadratic knapsack problem (QKP) has a central role in integer and combinatorial optimization, while efficient algorithms to general QKPs are currently very limited. We present an approximate dynamic programming (ADP) approach for solving convex QKPs where variables may take any integer value and all coefficients are real numbers. We approximate the function value using (a) continuous quadratic programming relaxation (CQPR), and (b) the integral parts of the solutions to CQPR. We propose a new heuristic which adaptively fixes the variables according to the solution of CQPR. We report computational results for QKPs with up to 200 integer variables. Our numerical results illustrate that the new heuristic produces high-quality solutions to large-scale QKPs fast and robustly.