Exploiting surrogate constraint analysis for fixing variables in both bounds for multidimensional knapsack problems

The exploitation by Osorio et al. (2002) of surrogate constraints and constraint pairing is strengthened to give better results in multidimensional knapsack problems, by excluding simple bounding constraints as component constraints. The surrogate constraint is obtained by weighting the original problem constraints by their associated dual values in the LP relaxation of the problem. This surrogate constraint is paired with the objective function to obtain a combined constraint where negative variables are replaced by complemented variables and the resulting constraint used to fix variables to zero or one.