Strengthening a linear reformulation of the 0-1 cubic knapsack problem via variable reordering

The 0-1 cubic knapsack problem (CKP), a generalization of the classical quadratic problem, is an extremely challenging NP-hard combinatorial optimization problem. An effective exact solution strategy for CKP to reformulate nonlinear into equivalent linear form that can then be solved using standard mixed-integer programming solver. We consider linearization method and propose variant more recent technique linearizing programs applied CKP. Using variable reordering strategy, we show how improve strength relaxation our proposed reformulation, which ultimately leads reduced overall times. In addition, develop simple heuristic obtaining good-quality solutions used provide warm start Computational tests demonstrate effectiveness both method.