Multiobjective optimization of industrial water networks with contaminants

This paper presents a multiobjective MILP formulation for optimizing industrial water networks. By expressing balance equations in terms of partial mass flows instead of total mass flows and concentrations, and because the contaminant mass flow (ppm) is very small compared to the water mass flow (T.h-1), the problem becomes linear. The integer variables are related to the interconnections into the network. The biobjective optimization of the fresh water flow rate at the network entrance and the water flow rate at regeneration unit inlets, parameterized by the number of interconnections, is carried out according to a lexicographic procedure. A monocontaminant network involving ten processes and one regeneration unit illustrates the approach. Even if the results are specific, the methodology guide can be applied to a large panel of networks. On the one hand, this example shows that the Pareto front is a straight line where each point is a feasible solution, when the number of connections is maximal (120). On the other hand, the Pareto front is reduced with the number of connections (11) and constituted by isolated points located mainly on a straight line with the same slope as for 120 connections, but no feasible solution exists between these points