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 building the network and operating it optimally is globally minimized. The network has to be designed to be feasible and optimal over a given set of scenarios in which different operational conditions hold. The uncertain operational parameters in the system are the amount of contaminants generated in the process units and the extent of removal of the contaminants inside the treatment units. We optimize a superstructure that incorporates all feasible design alternatives for wastewater treatment, reuse and recycle, with a multiscenario nonconvex mixed integer nonlinear programming (MINLP) model, which is a deterministic equivalent of a two-stage stochastic programming model with recourse. These models can grow in size with the number of scenarios and often require exponential computational effort to be solved to rigorous global optimality. To effectively solve this problem, we propose a spatial branch and cut algorithm that uses Lagrangean decomposition for global optimization of the large multiscenario model. Two examples are presented to illustrate the global optimization of integrated water networks operating under uncertainty using the proposed algorithm. (C) 2007 Elsevier Ltd. All rights reserved.