Surrogate duality in a branch-and-bound procedure for integer programming

Abstract

The existence of efficient techniques such as subgradient search for solving Lagrangean duals has led to some very successful applications of Lagrangean duality in solving specially structured discrete problems. While surrogate duals have been theoretically shown to provide stronger bounds, the complexity of surrogate dual multiplier search has discouraged their employment in solving integer programs. We have recently suggested a new strategy for computing surrogate dual values that allows us to directly use established Lagrangean search methods for exploring surrogate dual multipliers. This paper considers the problem of incorporating surrogate duality within a branch-and-bound procedure for solving integer programming problems. Computational experience with randomly generated multiconstraint knapsack problems is also reported.