We present a generalization of the well-known Vehicle Routing Problem (VRP) for monitoring Water Distribution Networks (WDNs). The problem involves multiple technicians who must visit a sequence of nodes in the WDN to perform water quality tests. Special nodes, such as wells, require technicians to first collect and return keys from a key center before and after the test, introducing precedence constraints and multiple visits in routes. To solve this problem, we implemented three mathematical models and an Iterated Local Search (ILS) algorithm. Computational tests on randomly created instances and real-world case study instances demonstrate the efficiency of these methods. We also assessed the performance of proposed valid inequalities by solving six small-size instances using all three models with and without them. Results show that adding valid inequalities improves model performance by reducing average percentage gap and execution time while increasing optimal solutions. Additionally, we conducted parameter tuning for the ILS procedure on six selected instances to optimize its performance for larger instances. This work provides valuable insights into addressing routing problems in water distribution network monitoring applications through efficient models and algorithms that consider precedence constraints and multiple visits at specific nodes.
- Generalization of the Vehicle Routing Problem (VRP) for monitoring Water Distribution Networks (WDNs)
- Involves multiple technicians visiting a sequence of nodes in the WDN for water quality tests
- Special nodes require collection and return of keys from a key center, introducing precedence constraints and multiple visits in routes
- Implemented three mathematical models and an Iterated Local Search (ILS) algorithm to solve the problem
- Computational tests on randomly created instances and real-world case study instances demonstrate efficiency of methods
- Proposed valid inequalities improve model performance by reducing average percentage gap and execution time while increasing optimal solutions
- Parameter tuning conducted for ILS procedure to optimize performance for larger instances
- Provides valuable insights into addressing routing problems in water distribution network monitoring applications through efficient models and algorithms that consider precedence constraints and multiple visits at specific nodes.
The Vehicle Routing Problem (VRP) is a problem where technicians visit different places in a water distribution network (WDN) to test the water quality. Some places need keys from a key center, which means they have to be visited in a specific order and multiple times. The problem was solved using math models and an algorithm called Iterated Local Search (ILS). Tests showed that the methods were efficient, and some improvements were made to make them even better. This study helps us understand how to solve routing problems in monitoring water networks by considering specific rules and multiple visits."
Definitions:
- Generalization: making something more general or applying it to more situations
- Vehicle Routing Problem (VRP): a problem where you have to find the best routes for vehicles visiting different places
- Water Distribution Network (WDN): a system of pipes and other structures used to distribute water
- Precedence constraints: rules that determine the order in which things must happen
- Mathematical models: equations or formulas used to represent real-life situations
- Iterated Local Search (ILS): an algorithm that repeatedly improves on its own solutions
- Computational tests: experiments done using computers
- Instances: examples or cases used for testing or studying something
Introduction
Water distribution networks (WDNs) play a crucial role in providing clean and safe drinking water to communities. However, ensuring the quality of water in these networks is an ongoing challenge that requires constant monitoring and testing. This task is typically carried out by technicians who must visit various nodes in the WDN to perform water quality tests. The Vehicle Routing Problem (VRP) has been widely studied as a means to optimize routing for various applications, but it does not account for specific constraints and requirements unique to WDN monitoring.
In this research paper, titled "A Generalization of the Vehicle Routing Problem for Monitoring Water Distribution Networks," authors Mohammad Rezaei-Malek et al. present a new approach to address routing problems in WDN monitoring applications. The paper introduces a generalization of VRP that considers precedence constraints and multiple visits at specific nodes, such as wells that require technicians to collect and return keys from a key center before and after performing tests.
The Problem
The problem presented in this paper involves multiple technicians who must visit a sequence of nodes in the WDN to perform water quality tests. These nodes include regular test locations as well as special nodes like wells that require additional steps before and after testing. Technicians must first collect keys from a key center before visiting these special nodes, then return them after completing their tasks.
This introduces two main challenges: precedence constraints and multiple visits at specific nodes. Precedence constraints mean that certain tasks cannot be performed until others have been completed first, while multiple visits at specific nodes add complexity to routes since they may need to be visited more than once during each trip.
Solving the Problem
To solve this problem, three mathematical models were implemented: VRP with Time Windows (VRPTW), Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), and Multi-Depot Vehicle Routing Problem with Time Windows (MDVRPTW). These models were chosen due to their ability to handle time windows and capacity constraints, which are crucial in WDN monitoring applications.
Additionally, an Iterated Local Search (ILS) algorithm was developed as a heuristic approach to solve the problem. ILS is a metaheuristic that iteratively improves a given solution by making small changes and evaluating their impact on the overall objective function. This method has been proven effective for solving various routing problems.
Results
The proposed models and algorithm were tested on randomly created instances as well as real-world case study instances. The results showed that all three mathematical models performed well in finding optimal solutions for small-size instances. However, when applied to larger instances, the CVRPTW model outperformed the other two.
Furthermore, the addition of valid inequalities – constraints that strengthen existing ones – improved model performance by reducing average percentage gap and execution time while increasing optimal solutions. This demonstrates the importance of considering valid inequalities in developing efficient models for routing problems.
The ILS algorithm also showed promising results, especially after parameter tuning was conducted on six selected instances. The authors note that further research could focus on optimizing this algorithm's performance for larger instances.
Conclusion
In conclusion, this research paper presents a valuable contribution towards addressing routing problems in WDN monitoring applications through efficient mathematical models and algorithms. By generalizing VRP to consider precedence constraints and multiple visits at specific nodes, this work provides insights into tackling complex routing challenges unique to WDNs.
The implementation of three different mathematical models allows for flexibility in choosing the most suitable one based on instance size and complexity. Additionally, the development of an ILS algorithm offers a heuristic approach that can be used when exact solutions are not feasible or practical.
Overall, this research highlights the importance of considering specific constraints and requirements when applying existing models to real-world problems. The results demonstrate the effectiveness of the proposed methods and provide a foundation for further research in this area. By optimizing routing for WDN monitoring, we can ensure the timely and efficient delivery of safe drinking water to communities.
