Comparison of global optimization algorithms for the design of water-using networks

We address a special class of bilinear process network problems with global optimization algorithms iterating between a lower bound provided by a mixed-integer linear programming (MILP) formulation and an upper bound given by the solution of the original nonlinear problem (NLP) with a local solver. Two conceptually different relaxation approaches are tested, piecewise McCormick envelopes and multiparametric disaggregation, each considered in two variants according to the choice of variables to partition/parameterize. The four complete MILP formulations are derived from disjunctive programming models followed by convex hull reformulations. The results on a set of test problems from the literature show that the algorithm relying on multiparametric disaggregation with parameterization of the concentrations is the best performer, primarily due to a logarithmic as opposed to linear increase in problem size with the number of partitions. The algorithms are also compared to the commercial solvers BARON and GloMIQO through performance profiles.

► Global optimization algorithms are proposed.
► Lower bounding formulations use the novel concept of multiparametric disaggregation.
► Derived from disjunctive programming models and convex hull reformulations.
► Significantly better performance than piecewise McCormick relaxation.
► Competitive performance with respect to commercial solvers.