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Ìâ Ä¿£ºLinear Reformulation of Polynomial Discrete Programming for Fast computation
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Polynomial discrete programming problems are commonly faced but hard to solve. Treating the nonconvex cross-product terms is the key. State-of-the-art methods usually convert such a problem into a 0-1 mixedinteger linear programming problem and then adopt the branch-and-bound scheme to ?nd an optimal solution. Much effort has been spent on reducing the required numbers of variables and linear constraints as well as on avoiding unbalanced branch-and-bound trees. This study presents a set of equations that linearize the discrete cross-product terms in an extremely effective manner. It is shown that embedding the proposed ¡°equations for linearizing discrete products¡± into those state-of-the-art methods in the literature not only signi?cantly reduces the required number of linear constraints from O4h3n35 to O4hn5 for a cubic polynomial discrete program with n variables in h possible values but also tighten these methods with much more balanced branch-and-bound trees. Numerical experiments con?rm a two-order (102-times) reduction in computational time for some randomly generated cubic polynomial discrete programming problems.
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