A Model-Based Search Strategy for Exhaustive Identification of Alternative Water Network Designs

Abstract

A systematic procedure is proposed in this paper to identify all optimal single-contaminant water-using networks by solving a series of three mathematical programming models. In particular, a linear programming (LP) model is adopted in this procedure to minimize the operating costs incurred from freshwater consumption and wastewater treatment, and a mixed-integer linear program (MILP) is then utilized for minimizing the total number of interconnections in the network while keeping the total operating cost at its lowest level. The third model is also a MILP model, which is used to minimize the total throughput and generate all alternative designs under the conditions of fixed minimum operating costs and interconnection number. Notice that, since the nonlinear mass-balance constraints are all converted to linear form in the proposed models according to the necessary conditions of optimality (Savelski and Bagajewicz, 2000), the convergence of the corresponding optimization processes can always be guaranteed. The solution pool technique provided by the CPLEX II solver within GAMS environment has been adopted to search for all optima. Four examples are presented in this paper to demonstrate the effectiveness of the proposed approach.