Representations and Evolutionary Operators for the Scheduling of Pump Operations in Water Distribution Networks

Manuel López-Ibáñez,T Devi Prasad,Ben Paechter

doi:10.1162/evco_a_00035

Abstract

Reducing the energy consumption of water distribution networks has never had more significance. The greatest energy savings can be obtained by carefully scheduling the operations of pumps. Schedules can be defined either implicitly, in terms of other elements of the network such as tank levels; or explicitly, by specifying the time during which each pump is on/off. The traditional representation of explicit schedules is a string of binary values with each bit representing pump on/off status during a particular time interval. In this paper, we formally define and analyze two new explicit representations based on time-controlled triggers, where the maximum number of pump switches is established beforehand and the schedule may contain fewer than the maximum number of switches. In these representations, a pump schedule is divided into a series of integers with each integer representing the number of hours for which a pump is active/inactive. This reduces the number of potential schedules compared to the binary representation, and allows the algorithm to operate on the feasible region of the search space. We propose evolutionary operators for these two new representations. The new representations and their corresponding operations are compared with the two most-used representations in pump scheduling, namely, binary representation and level-controlled triggers. A detailed statistical analysis of the results indicates which parameters have the greatest effect on the performance of evolutionary algorithms. The empirical results show that an evolutionary algorithm using the proposed representations is an improvement over the results obtained by a recent state of the art hybrid genetic algorithm for pump scheduling using level-controlled triggers.

Highlights

Water Distribution Networks (WDNs) ensure the supply of water with adequate pressure to consumers at demand nodes
Our goal is to study the effect of several representations and their corresponding evolutionary operators, hopefully minimising the influence of other algorithmic factors
We have formally proposed two new representations based on the concept of time-controlled triggers, and evolutionary operators suited for these new representations

Summary

Introduction

Water Distribution Networks (WDNs) ensure the supply of water with adequate pressure to consumers at demand nodes. To accomplish this task, often, water must be pumped to overcome frictional losses and to store it at a higher elevation. Pumps lift water from a treatment plant into an elevated tank, where water is stored temporarily before supplying it to consumers. The cost of energy consumed by pumps is a significant proportion of the total operational cost of a WDN. Pumps need to be repaired and replaced, incurring additional costs. Scheduling pump operations may reduce the total pump operational cost, which includes pumping cost and maintenance cost, while guaranteeing a competent service

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