Building Blocks as Experiences in Dynamic Capacitated Arc Routing Problems

A multi-start local search matheuristic for the capacitated arc routing problem with irregular services

Multi-depot periodic capacitated arc routing problem with intermediate facilities for waste collection

A hierarchical integrated exact algorithm for multi-level capacitated arc routing problem in waste collection

An orchard spraying application of the split-delivery capacitated arc routing problem

ABSTRACT The gradual growth of road infrastructure worldwide has heightened the importance of sustainable roadside management for preserving adjacent ecosystems and maintaining critical ecosystem services. Although the Arc Routing Problem (ARP) presents a promising framework for optimising operations carried out along an arc, its application to roadside management remains unexplored despite its advantages over traditional routing problems. This study presents a comprehensive systematic literature review to analyse how ARPs have been applied across various real‐world scenarios and to identify relevant features for roadside management applications. The presented analysis is conducted in two stages. First, a bibliometric analysis introduces the context of the ARP scientific domain. Then, a deeper analysis is based on a detailed examination of model characteristics, network configurations, and sustainability challenges across different application domains. The findings reveal a predominance of theoretical work with few real‐life applications but highlight significant opportunities for adapting existing ARP frameworks to roadside management, particularly in integrating sustainability criteria and local context considerations. However, crucial gaps in current ARP applications are identified, notably the limited incorporation of sustainable and regenerative practices in model formulation. This review provides a structured decision support framework for researchers and practitioners, outlining specific directions for developing ARP models tailored to sustainable roadside management while emphasising the need to balance operational efficiency with sustainable objectives.

Neural solvers (NSs) based on the attention mechanism have demonstrated remarkable effectiveness in solving routing problems like traveling salesman problems (TSPs) and vehicle routing problems (VRPs). However, in the generalization process, we find a phenomenon of the dispersion of attention scores in existing NSs, which leads to poor performance. To improve the generalization ability of NSs, this article proposes a distance-aware attention reshaping (DAR) method. Specifically, without increasing any parameter of the neural network (NN), we utilize the distance information between nodes to adjust attention scores. This enables an NS trained on small-scale instances with a certain distribution to make rational choices when solving large-scale problems with different distributions. Its effectiveness is verified both theoretically and empirically. Extensive experiments on the TSP, asymmetric TSP (ATSP), capacitated VRP (CVRP), VRP with time windows (VRPTW), capacitated arc routing problem (CARP), and knapsack problem (KP) demonstrate the advantages of our method. Our code is available at https://github.com/ftwangyang/DAR.

In urban areas with many commercial facilities, patrolling by police officers or security guards is essential for crime prevention, in addition to the use of surveillance cameras. To address the challenge of planning effective patrol routes, Tohyama and Tomisawa introduced the Police Officer Patrolling Problem (POPP), an arc routing problem that allows for visual monitoring from intersections and is proven to be NP-complete. Building on this work, we propose the Generalized POPP (GPOPP), a more realistic bi-objective combinatorial optimization model. This model simultaneously minimizes the total patrol route length and maximizes the coverage of surveillance areas. The contributions of this paper are threefold: (1) we formulate the GPOPP by incorporating practical constraints, such as mandatory patrolling of high-security roads and visibility-based coverage from intersections; (2) we develop a novel hybrid heuristic method that combines a multi-objective evolutionary algorithm (MoEA-HSS) with an improved Jaya algorithm to solve the GPOPP effectively; and (3) we conduct comprehensive computational experiments using benchmark instances to evaluate the effectiveness and competitiveness of the proposed method. These contributions demonstrate the practicality and efficiency of our approach for addressing realistic urban patrolling problems.

A biased-randomised iterated local search for the team orienteering arc routing problem allowing different origin and destination

An adaptive large neighborhood search method for the drone–truck arc routing problem

Abstract This paper introduces a novel heuristic method, the smart selective navigator (SSN), for addressing arc routing problems (ARPs) with a focus on integrating hard turn restrictions in urban winter operations. Addressing a significant gap in existing ARP methodologies, SSN seamlessly incorporates common side constraints, such as vehicle characteristics and road priorities, while strictly adhering to turn restrictions. Mathematically, the approach involves representing urban road networks as directed multigraphs. SSN's effectiveness was demonstrated through a case study on winter road maintenance in the City of Oshawa, which showed improved operation times. This study not only fills a crucial research gap in ARP but also offers a versatile solution applicable to various urban routing challenges, with potential applications extending beyond winter operations. Future research directions include exploring dynamic weighting models further and replacing classical optimization methods with machine learning for real‐time route generation.

Fast Late Acceptance Local Search for Mixed Capacitated Arc Routing Problems

Mixed integer linear programming model for a multi-depot arc routing problem with different arc types and flexible assignment of end depot

This article introduces an advanced solution to optimize street sweeping operations by extending a multi-depot arc routing problem. The key enhancement involves flexible end depot assignments, where vehicles start and conclude shifts at designated depots. A notable constraint requires subsequent shifts to begin from the destination depot of the preceding shift. The problem involves servicing highway exclusively during night shifts, while other arc types can be addressed during both day and night. The objective is to identify optimal shifts meeting practical criteria while adhering to constraints like maximum shift duration. To address this, a mixed-integer linear programming (MILP) model is presented. It aims to minimize the number of shifts and total travel time. Given the computational complexity of large instances, an adaptive large neighbourhood search (ALNS) metaheuristic was developed. This approach incorporates specialized operators that address unique attributes such as arc type and depot assignments, ensuring arcs are repositioned based on their type and proximity to depots. This tailored approach provides a distinct advantage over classical ALNS operators, as numerical tests indicate that the specialized operators are more efficient in comparison. The approach is evaluated on larger and a real-world instances, demonstrating notable performance in solution quality and computational efficiency.

The min max multi-trip drone location arc routing problem

Evaluating Meta-Heuristic Algorithms for Dynamic Capacitated Arc Routing Problems Based on a Novel Lower Bound Method

As cities continue to grow, thus will the size of the routing problems necessary to the functioning of all cities. Applications such as waste collection, road maintenance, or winter gritting span over an entire city, therefore algorithms must be designed to solve large-scale problems. The Capacitated Arc Routing Problem (CARP) is an important combinatorial optimization problem that is typically used to model these applications. Classical algorithms for CARP struggle to find quality solutions for large-scale instances with thousands of services within a reasonable computational budget. To address the issue of scalability, several divide-and-conquer heuristics have recently been proposed. In this paper, we propose to integrate divide-and-conquer heuristics into a memetic algorithm by adapting these as an initialization method and as a mutation operator. The resulting algorithm, which we call Memetic Algorithm with Divide-and-Conquer Mutation (MADCoM), outperforms state-of-the-art algorithms on large-scale instances and new best solutions are found for 17 instances of MCARP, 2 of which are optimal solutions, and for 23 large-scale CARP instances. These results demonstrate the potential of the integration of divide-and-conquer heuristics into metaheuristics as a strategy to efficiently solve large-scale problems.

An improved variable neighborhood search algorithm embedded temporal and spatial synchronization for vehicle and drone cooperative routing problem with pre-reconnaissance

The drone arc routing problem (DARP) is one of the arc routing problems (ARPs) that has been studied by researchers recently. Unlike traditional ARPs, drones can travel directly between any two points in the graph. Due to the flexibility of drones, it is possible to use edges not defined in the graphs when deadheading the edges. This advantage of drones makes this problem more challenging than any other ARP. With this study, the energy capacities of drones are considered in a DARP. Thus, a novel DARP called the drone arc routing problem with deadheading demand (DARP-DD) is addressed in this study. Drone capacities are used both when servicing the edges and when deadheading the edges in the DARP-DD. A special case of the DARP-DD, called the multiple service drone arc routing problem with deadheading demand (MS-DARP-DD), is also discussed, where some critical required edges may need to be served more than once. To solve these challenging problems, a simulated annealing algorithm is used, and the components of the algorithm are designed. Additionally, novel neighbor search operators are developed in this study. The computational results show that the proposed algorithm and its components are effective and useful in solving the DARP-DD and MS-DARP-DD.

Genetic programming has been successfully used to evolve routing policies that can make real-time routing decisions for uncertain arc routing problems. Although the evolved routing policies are highly effective, they are typically very large and complex, and hard to be understood and trusted by real users. Existing studies have attempted to improve the interpretability by developing new genetic programming approaches to evolve both effective and interpretable (e.g., with smaller program size) routing policies. However, they still have limitations due to the trade-off between effectiveness and interpretability. To address this issue, we propose a new post-hoc explanation approach to explaining the effective but complex routing policies evolved by genetic programming. The new approach includes a local ranking explanation and a global explanation module. The local ranking explanation uses particle swarm optimisation to learn an interpretable linear model that accurately explains the local behaviour of the routing policy for each decision situation. Then, the global explanation module uses a clustering technique to summarise the local explanations into a global explanation. The experimental results and case studies on the benchmark datasets show that the proposed method can obtain accurate and understandable explanations of the routing policies evolved for uncertain arc routing problems. Our explanation approach is not restricted to uncertain arc routing, but has a great potential to be generalised to other optimisation and machine learning problems such as learning classifier systems and reinforcement learning.