Superstructure decomposition and parametric optimization approach for the synthesis of distributed wastewater treatment networks

Simultaneous design techniques for the synthesis of distributed wastewater treatment networks rely on the solution of nonconvex mathematical models, which give rise to multiple suboptimal solutions and often cause standard local optimization techniques to fail. A superstructure decomposition and parametric optimization approach is presented in this paper for the synthesis of distributed wastewater treatment networks with no stream recycles or recirculations. Within the developed methodology, a typical complex network superstructure for simultaneous design is decomposed into a set of basic network superstructures, which partitions the design search space. The best treatment network design embedded in each of the basic network superstructures is determined by solving a set of linear programming problems that is generated from a structured nonconvex mathematical model by fixing a small number of key problem variables. Under the most generally accepted assumptions, the systematic exploration of the parametric space defined by the key problem variables renders, from the solution space spanned by the basic network superstructures, a most certainly globally optimal network design. Indeed, the best network design of a problem involving one treatment unit can be obtained by solving a single linear programming problem. The best designs of systems containing two and three treatment units can be obtained by carrying out the parametric optimization over only one and three key problem variables, respectively. The application of the proposed methodology is illustrated with the detailed solution of several design problems.