A multi-objective and multi-criteria approach for district metered area design: water operation and quality analysis

Water distribution network (WDN) operation may be improved by district metered area (DMA) design [1]. A first step to create DMAs uses graph theory and non-supervised learning, where physical features of the WDN, such as node coordinates, elevation and demand, are used for clustering purposes [2]. A second step is related to the necessary isolation of the clustered elements. For isolation purposes, it is important to determine the DMA entrances and, consequently, the needed cut-off valves. Closure of pipes and definition of DMA entrances can be set as an optimization problem with the costs associated to the valves, which are linked to pipe diameters, as a primary objective. However, placement and operation of pressure reducing valves (PRVs) change the hydraulic conditions, and the optimization process should respect operation limits, such as minimum and maximum pressure and minimum and maximum tank levels. Constrained problems are frequently handled by using penalty functions. However, as discussed in [3], penalty approaches modify the search space, impairing the search process by the creation of new local minima. To solve this problem, a bio-inspired algorithm widely applied in water distribution problems [4], adapted for a multi-objective approach, is applied. In this context, constraints become objectives to be reached, which turns the problem unconstrained. Moreover, as observed in [5], such crucial water distribution parameters as resilience, pressure uniformity and water quality strongly depend on DMA configurations. These parameters are known to depend on pressures and water tank levels and, together with cost, will be the other objectives of our optimization. A multi-objective approach gives a set of solutions, the so-called Pareto front. To select, within that front, which non-dominated solution will be implemented may be hard task. To help this process, this work presents: a) multi-level optimization process for entrance location and set point definition of PRVs, and b) a post-processing based on a multi-criteria method, which ranks the non-dominated solutions based on the relative importance of the said four main objectives: implementation cost, resilience, pressure uniformity and water quality. Among the wide range of MCDM (multi-criteria decision-making) methods used in the literature, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) effectively works across various application areas [6]. Such a technique was developed by Hwang and Yoon [7] as a simple way to solve decision-making problems by means of the ranking of various decision alternatives [8,9]. In this context, the objective of the TOPSIS application to the multi-objective problem consists in selecting the solution representing the best trade-off (among the set of optimal solutions belonging to the Pareto front) under the perspective of the considered evaluation criteria.