An improved surrogate constraints method for separable nonlinear integer programming

An improved surrogate constraints method for solving separable nonlinear integer programming problems with multiple constraints is presented. The surrogate constraints method is very effective in solving problems with multiple constraints. The method solves a succession of surrogate constraints problems having a single constraint instead of the original multiple constraint problem. A surrogate problem with an optimal multiplier vector solves the original problem exactly if there is no duality gap. However, the surrogate constraints method often has a duality gap, that is it fails to find an exact solution to the original problem. The modification proposed closes the surrogate duality gap. The modification solves a succession of target problems that enumerates all solutions hitting a particular target. The target problems are produced by using an optimal surrogate multiplier vector. The computational results show that the modification is very effective at closing the surrogate gap of multiple constraints problems.