Global optimization of water networks design using multiparametric disaggregation

We propose new mixed-integer linear programming models for the optimal design of water-using and wastewater treatment networks. These replace the original non-convex, nonlinear problems following parameterization of the concentration variables appearing in the bilinear terms resulting from the contaminant mass balances. The difference between the models lies in the numeric system used for the parameterization. We show how to perform the transformation for a generic coding and give the results for the decimal and binary systems. While the resulting MILPs are approximations of the original NLP, any desired accuracy level can be set, being the proposed models exact in the limit of an infinite number of significant digits. Through the solution of several test cases taken from the literature, we show that the value of the objective function rapidly approaches the global optimal solution. The models can also be used to initialize the NLP when solved with local optimization solvers.

► We show how to approximate nonlinear problems featuring bilinear terms with a mixed-integer linear program.
► Any desired accuracy level can be set in terms of number of significant digits.
► The higher the number, the closer the solution will be to the real optimal solution.
► We illustrate the method with decimal and binary numeric systems.
► The estimated optimality gap can be significantly lower than the one from the global optimization solver BARON.