Multi-Objective Optimization of Semi-Continuous Water Networks

There is an increasing interest in complex optimization of resource utilization in industrial processes, like energy and utilities such as water or steam. Traditionally, optimization of water networks (WNs) was performed using mono-objective functions (freshwater consumption, investment and/or operating costs etc). Lately, multi-objective function optimization was used in order to get a set of solutions (Pareto front - PF) from which to choose using non-quantifiable criteria. In the present paper, we used a complex two level optimization. The outer level optimizes the schedule of the water using units (WUs) according to their windows of opportunity with respect to the freshwater consumption, while the inner level uses a dual-objective function to optimize the topology of the semi-continuous WN: a) the freshwater consumption and b) the combined investment and operating cost of the pipe network, designed for the optimum diameter. The targeted schedule should ensure a maximum wastewater reuse between the discontinuous WUs and a minimum quantity of water for storage. The WN has N discontinuous WUs with respect to the processed raw materials, but continuous with respect to water flow, each handling at most K contaminants, and one storage tank (ST) of limited capacity. A single freshwater source is available. For each time interval, the network (the overlapping WUs) is abstracted as an oriented graph having the WUs and the ST as nodes and the flow pipes as arches. The WUs operating within a time interval are ranked also according to their maximum critical outlet concentration of contaminants. Therefore, water reuse is allowed from the WUs having lower maximum outlet concentrations to the ones with higher limits. The mathematical model consists of total and partial mass balance equations for each WU and the ST. Multi-objective genetic algorithm was the method of choice for optimization, as implemented in Matlab (TM). The same synthetic case study optimized for minimum freshwater consumption was used to test this new approach. The results are analyzed and discussed with respect to the mono-objective optimization as well.