Multi-objective based scheduling algorithm for sudden drinking water contamination incident

doi:10.1016/j.swevo.2020.100674

Swarm and Evolutionary Computation

Volume 55, June 2020, 100674

https://doi.org/10.1016/j.swevo.2020.100674 Get rights and content

Abstract

In recent years, drinking water contamination incidents have been occurring at an increasingly frequent rate, leading to significant economic losses and social issues. Establishing and improving emergency disposal mechanisms for water contamination incidents is an important issue that has become a foremost concern globally. In this study, we first perform a theoretical analysis on an optimal scheduling problem and then prove that the scheduling of the valve and hydrant is NP-complete. Subsequently, we propose a multi-objective optimization model for contaminant response and primarily investigate two conflicting objectives: first, to minimize the volume of contaminated water exposed to the public; and second, to minimize the operational costs of the hydrant and valves. Finally, a customized multi-objective non-dominated sorted genetic algorithm-II (NSGA-II) coupling with an EPANET simulation is proposed and two different sizes of water distribution networks are employed to demonstrate the validity of the proposed model and methodology. Furthermore, we investigate the impact of different parameters on the performance of our proposed algorithm.

Introduction

In recent decades, the safety of drinking water has become a widespread concern. The “Scientific American” has reported 202 unregulated chemicals found in 45 states in the U.S. [1]. To reduce the risk of contamination, water quality monitoring sensors should be deployed in water distribution systems (WDSs) to enable real-time contamination detection. Once any sensor gives an alarm, the authority should conduct effective emergency responses. The primary responses include (1) identifying the source of contamination by using certain algorithms, and (2) scheduling valves and hydrants. Some appropriate valve closures are chosen to isolate the contaminated water, and some hydrants are opened to flush and drain the contaminated water.

For example, a typical simple water distribution network is shown in Fig. 1. When a contamination event occurs, there will be severe contamination diffusion if the valve scheduling is not timely and reasonable. As shown in Fig. 1(a), contaminated water passes through most of the pipes (red line). However, when reasonable scheduling is performed, that is, closing the valves and opening the hydrant (red solid triangle is a sensor, blue solid triangle is a valve, and black solid square is a hydrant), the contamination situation can be controlled as shown in Fig. 1(b).

However, it is quite challenging to schedule appropriate valve closures and hydrants in complex water distribution systems. Several studies have applied integer programming, genetic algorithms (GAs), and evolution strategies to identify strategies for operating hydrants and valves to minimize the time required for detection, the amount of contaminant at terminal nodes, and the impact on public health [2,3].

As multiple optimization goals exist for scheduling valves and hydrants, some researchers used multi-objective optimization to trade-off different conflicting goals, i.e., the number of polluted nodes, cost of operations, public health impacts, and service interruptions. In this study, we investigate a multi-objective optimization model comprehensively and propose a customized NSGA-II based algorithm (C-NSGA-II). More specifically, the objective of this study is regarding three aspects:\def\itemwd{$bullet$}

∙
We first reduce the optimal scheduling of valves and hydrants to a Knapsack problem and then prove that it is NP-Complete.
∙
We establish a bi-objective optimization model; one objective is the minimization of the volume of contaminated water exposed to the public, the other is the minimization of operational cost. These two goals are conflicting as the lower the operational cost is, the more volume of contaminated water will be exposed to the public.
∙
We design a C-NSGA-II to solve this bi-objective optimization problem. By employing a medium and a larger-sized water distribution network, we provide a comprehensive impact analysis with respect to hydrant flow rate, contamination source, and location of the control center in our proposed model and algorithm.

The remainder of this paper is organized as follows. Section 2 provides a brief introduction of response actions and the state-of-the-art multi-objective evolutionary algorithms (MOEAs). Section 3 presents the system model and formulates the optimal scheduling problem; by means of the Knapsack problem, we also prove that the optimization problem is NP-complete. In section 4, we investigate a multi-objective optimization model. According to the characteristic of this problem, section 5 presents a C-NSGA-II algorithm. Section 6 validates the efficiency and robustness of our algorithm. Section 7 concludes our work and puts forward some issues that must be highlighted in future work.

Section snippets

Related work

In this section, we perform a survey of the MOEAs and then present their applications in WDSs. Specially, we present some works on the scheduling of valves and hydrants for the emergency response to sudden drinking water pollution.

System architecture

To ensure the safety of consumers, it is crucial to monitor water quality and operate the valves or the hydrants. In recent years, most water distribution systems have equipped SCADA (Supervisory Control And Data Acquisition) system to facilitate water management. Smart water management mainly includes two functions; one is to monitor portable water, the other is aiming to monitor the water supply distribution, which includes control of water flow, speed, rate, and condition of tubes.

In a smart

Multi-objective optimization model for drinking water contamination incident

In this part, we establish a bi-objective optimization model, and the first goal is to minimize the volume of contaminant exposed to the public which is opposite to the maximization of the draining of polluted water, the other goal is to minimize the operational cost. The detailed optimization objective function is as follows.

Customized NSGA-II approach for the bi-criterion scheduling problem

For this bi-criteria scheduling problem, we propose a C-NSGA-II algorithm, which determines a trade-off between contaminant exposure (f₁) and the operational costs of valves and hydrants (f₂). The whole algorithm consists of three steps:

First, a random parent population is created, each chromosome in the population is initialized, the length of the binary chromosome is the number of valves and hydrants. Subsequently, fitness function f₁ and f₂ are evaluated and a fast non-dominated sorting is

Parameter setting

In our study, two typical water distribution networks are employed to illustrate the solution methodology. The first is provided by the organizers of the Battle of Water Sensor Networks (BWSN) [38]. The network has 126 nodes, one constant head source, two tanks, and 168 pipe links, as shown in Fig. 3. The second is a larger-sized WDN KY5 [39] shown in Fig. 8, which comprises 409 nodes, four reservoirs, four tanks, and 498 pipes.

For the parameters of the algorithm, we set the population size to

Conclusion

In this paper, we first argue that the scheduling of valves and hydrants is an NP-complete problem. Then, a multi-objective model is proposed to improve the response to a drinking water contamination event. Subsequently, C-NSGA-II is employed to find a trade-off between two conflicting objectives: minimization of contaminated water exposed to the public and minimization of operational costs of valves and hydrants. Finally, we study the influence of the hydrant flow rate, contamination source,

CRediT authorship contribution statement

Chengyu Hu: Conceptualization, Methodology, Data curation, Formal analysis, Funding acquisition. Xuesong Yan: Funding acquisition. Wenyin Gong: Writing - original draft, Writing - review & editing. Xiaobo Liu: Writing - original draft, Writing - review & editing. Ling Wang: Writing - original draft, Writing - review & editing. Liang Gao: Writing - original draft, Writing - review & editing.

Declaration of competing interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “Multi-objective based Scheduling Algorithm for Sudden Drinking Water Contamination Incident”.

Acknowledgment

This research was partially supported by the NSF of China (Grant No. U1911205) and NSF for Distinguished Young Scholars of China (61525304), supported by Hubei Key Laboratory of Intelligent Geo-Information Processing, China University of Geosciences (Wuhan), supported by the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) and the State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology (

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Multi-objective based scheduling algorithm for sudden drinking water contamination incident

Abstract

Introduction

Section snippets

Related work

System architecture

Multi-objective optimization model for drinking water contamination incident

Customized NSGA-II approach for the bi-criterion scheduling problem

Parameter setting

Conclusion

CRediT authorship contribution statement

Declaration of competing interest

Acknowledgment

Inf. Sci.

Knowl. Base Syst.

Swarm Evol. Comput.

Energy

Swarm Evol. Comput.

Eur. J. Oper. Res.

Swarm Evol. Comput.

Swarm Evol. Comput.

J. Hydrol.

Water Res.

Environ. Model. Software

Procedia Eng.

U.s. drinking water widely contaminated

Finding multiple roots of nonlinear equation systems via a repulsion-based adaptive differential evolution

IEEE Trans. Syst., Man, Cybern.

Solving nonlinear equations system with dynamic repulsion-based evolutionary algorithms

IEEE Trans. Syst. Man Cybern. Syst.

Multi-objective migrating birds optimization algorithm for stochastic lot-streaming flow shop scheduling with blocking

IEEE Access

A discrete artificial bee colony algorithm incorporating differential evolution for the flow-shop scheduling problem with blocking

Eng. Optim.

Effective hybrid discrete artificial bee colony algorithms for the total flowtime minimization in the blocking flowshop problem

Int. J. Adv. Manuf. Technol.