Global optimization based on subspaces elimination: Applications to generalized pooling and water management problems

Abstract

A global optimization strategy based on the partition of the feasible region in boxed subspaces defined by the partition of specific variables into intervals is described. Using a valid lower bound model, we create a master problem that determines several subspaces where the global optimum may exist, disregarding the others. Each subspace is then explored using a global optimization methodology of choice. The purpose of the method is to speed up the search for a global solution by taking advantage of the fact that tighter lower bounds can be generated within each subspace. We illustrate the method using the generalized pooling problem and a water management problem, which is a bilinear problem that has proven to be difficult to solve using other methods. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2336–2345, 2012