João P. Teles

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

Abstract 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.

Univariate parameterization for global optimization of mixed-integer polynomial problems

This paper presents a new relaxation technique to globally optimize mixed-integer polynomial programming problems that arise in many engineering and management contexts. Using a bilinear term as the basic building block, the underlying idea involves the discretization of one of the variables up to a chosen accuracy level (Teles, J.P., Castro, P.M., Matos, H.A. (2013). Multiparametric disaggregation technique for global optimization of polynomial programming problems. J. Glob. Optim. 55, 227–251), by means of a radix-based numeric representation system, coupled with a residual variable to effectively make its domain continuous. Binary variables are added to the formulation to choose the appropriate digit for each position together with new sets of continuous variables and constraints leading to the transformation of the original mixed-integer non-linear problem into a larger one of the mixed-integer linear programming type. The new underestimation approach can be made as tight as desired and is shown capable of providing considerably better lower bounds than a widely used global optimization solver for a specific class of design problems involving bilinear terms.

Parametric programming technique for global optimization of wastewater treatment systems

Abstract This paper presents a parametric programming technique for the optimal design of industrial wastewater treatment networks (WTN) featuring multiple contaminants. Inspired in scientific notation and powers of ten, the proposed approach avoids the non-convex bilinear terms through a piecewise decomposition scheme that combines the generation of artificial flowrate variables with a multi-parameterization of the outlet concentration variables. The general non-linear problem (NLP) formulation is replaced by a mixed-integer linear programming (MILP) model that is able to generate near optimal solutions, fast. The performance of the new approach is compared to that of global optimization solver BARON through the solution a few test cases.

OptWatNet ‐ a software for the optimal design of water-using networks with multi-contaminants

Abstract This paper presents a new user friendly software, OptWatNet, for the design of water using networks with multiple water sources and contaminants. It can handle four alternative solution strategies that differ in the initialization method used prior to the solution of the nonlinear program (NLP). OptWatNet provides an interface for easy data input, which is then converted to the GAMS format and included in the files that comprise the general linear (LP)/NLP models. Once the problem is solved, OptWatNet is able to draw the water networks corresponding to the solutions resulting from the different strategies. Overall, it is a powerful tool that can be used to easily evaluate alternative design options and compare the several strategies with respect to quality of the best solution obtained, quality of the initialization procedure and total computational effort.