Global optimization of multiscenario mixed integer nonlinear programming models arising in the synthesis of integrated water networks under uncertainty

The problem of optimal synthesis of an integrated water system is addressed in this work, where water using processes and water treatment operations are combined into a single network such that the total cost of designing the network and operating it optimally is globally minimized. The network design has to be feasible and optimal over a given set of scenarios in which different operational conditions hold. We propose a superstructure whose optimization is formulated as a multiscenario non-convex Mixed Integer NonLinear Programming (MINLP) problem. A Lagrangean decomposition based algorithm is proposed for the global optimization of such large multiscenario models. An example is presented for the global optimization of an integrated network operating under uncertainty using the proposed algorithm.