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Strengthening A Linear Reformulation Of The 0-1 Cubic Knapsack Problem Via Variable Reordering, Richard Forrester, Lucas Waddell

Faculty Journal Articles

The 0-1 cubic knapsack problem (CKP), a generalization of the classical 0-1 quadratic knapsack problem, is an extremely challenging NP-hard combinatorial optimization problem. An effective exact solution strategy for the CKP is to reformulate the nonlinear problem into an equivalent linear form that can then be solved using a standard mixed-integer programming solver. We consider a classical linearization method and propose a variant of a more recent technique for linearizing 0-1 cubic programs applied to the CKP. Using a variable reordering strategy, we show how to improve the strength of the linear programming relaxation of our proposed reformulation, which ultimately …