Modeling and Optimization of Vehicle Routing and Arc Routing Problems

A parallel iterated tabu search heuristic for vehicle routing problems

This research presents a solution process for Periodic Arc Routing Problem with Refill Points (PARPRP). The Periodic Arc Routing Problem is a natural extension of Arc Routing Problem (ARP) and is classified as an NP-hard problem. The street tree watering problem is used as the case study. The study tackles the ARP requiring a specified time horizon to fulfill it. A refill point in the problem is a node in the graph at which the vehicle capacity can be recovered as long as the vehicle makes a stop on it. The strategy of solving the problem is first to transform the problem into a Vehicle Routing Problem. Secondly, an Ant Colony Optimization algorithm is developed to solve the PARPRP because of its remarkable capability in the establishment of network routes. A local search method is incorporated to reach the local minimum for further improvement. Two sets of benchmarks are used to verify the solving process and the computational results are provided. The outputs indicate that proposed methods can yield promising solutions within reasonable execution time. A real case regarding the street tree watering of Kaohsiung city, Taiwan, is investigated. The results suggest that while α = 1 and β = 3 (i.e. parameters to control the influence of the pheromone value allocated on and the desirability of the arc, respectively), the algorithm can yield the best solution. The number of refill points is analyzed as well and output result suggests that a system with two refill points can obtain the least route length.

A variable neighborhood descent heuristic for arc routing problems with time-dependent service costs

This article is concerned with the problem of finding optimal vehicle routes to minimize the overall travel time, with constraints on the minimum and maximum amount of time spent on each route. The problem extends previous work on the distance‐constrained vehicle routing problem by introducing lower bounds on route durations to ensure that the resulting routes are balanced. The article also explicitly addresses the situation where a solution is artificially balanced as a result of inoptimal orders of visits. The article describes alternative ways in which the restrictions on route connectivity, duration, and artificial balancing can be formulated, and introduces an exact algorithm based on cutting planes and mixed‐integer linear programming. To the best of our knowledge, this is the first exact algorithm proposed for such a problem that explicitly addresses artificially balanced routes. Computational results are presented for three versions of the exact algorithm using TSPLIB instances. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(2), 166–179 2015

SYNOPTIC ABSTRACTBranch exchange techniques, such as the well-known 2-opt and 3-opt procedures, are among the most powerful heuristics available for the solution of the classic vehicle routing problem. The imposition of time window constraints on customer delivery time within the vehicle routing problem, however, introduces several complexities that can reduce the power of these techniques. In this paper, two test data sets for the vehicle routing and scheduling problem with time window constraints are studied. Initial solutions are obtained using a variety of heuristics. These solutions are then improved using branch exchange procedures modified to incorporate the time window constraints.

This study will solve the classical vehicle routing problem, the goal is to generate k trips with the shortest distance for h customers with predetermined locations and needs.. The proposed solution to the classical vehicle routing problem is a hybrid sine cosine algorithm. The sine cosine algorithm is hybridized with the grey wolf optimizer, which is used in combination with the methods of tournament selection, opposition learning, and the mutation and crossover method to build the optimal routing plan for the means of transporting cement. To demonstrate the advantages of the developed hybrid sine cosine algorithm, this algorithm is evaluated and compared with modern algorithms such as sine cosine algorithm, dragonfly algorithm, grey wolf optimizer, ant lion optimizer, particle swarm optimization, modified hybrid particle swarm optimization, genetic algorithm, and the double-population genetic algorithm in case studies. The hybrid sine cos algorithm gives optimal results in these cases because it balances mining and exploration. Thus, the results of this study indicate that managers can use the developed hybrid sine cosine algorithm to create optimal vehicle routing plans to reduce transportation distances.

In this paper, a three-phase algorithm is designed for solving a real problem of vehicle capacity and route optimization. The proposed algorithm fulfills non-stochastic demand in a limited time window by optimally allocating vehicles of heterogeneous capacity. The pricing model of the supplier (CMMF- a popular Co-operative Milk Marketing Federation of southern India) to transport fodder from the central production facility to different destinations was not very encouraging for the vehicle owners. In CMMF’s pricing model, it is not possible to reduce the cost of transportation by vehicle capacity optimization or route optimization. CMMF was using the manual system of assignment of the vehicle to different demand locations often resulting in vehicles traveling longer distances with unused capacity. Management saw an opportunity to optimally load vehicles and fulfill various demand locations in such a way that the vehicle travels minimum distance with unused capacity. The proposed algorithm is tested on a sample 100 node network with actual demands and relevant data like demand arrival date, a connected network of demand locations, distance of demand locations from the source, and list of vehicles that are used in the existing system. A decision support system is developed to prescribe solutions to the decision-maker with different threshold unused capacity (5%, 10%, 15%, and 20%) of vehicles. Subject to the imposed constraints, a considerable reduction in the unused capacity (Kilogram-Kilometer) of vehicles is recorded.

A self-adaptive local search algorithm for the classical vehicle routing problem

The adoption of electric vehicles (EVs) has gained significant momentum in recent years as a sustainable alternative to traditional internal combustion engine vehicles. However, the efficient utilization of batteries in EVs, coupled with the growing demand for sustainable transportation, has posed complex challenges for battery management in the context of electric vehicle routing problems in a broad sense, which includes vehicle routing problems, team orienteering problems, and arc routing problems, all of them using EVs. This paper presents a comprehensive review of the state-of-the-art approaches, methodologies, and strategies for battery management in each of the aforementioned optimization problems. We explore the relevant factors influencing battery performance and the interplay between routing, charging, and energy management in the context of EVs. The paper also discusses the advances in optimization algorithms, vehicle-to-grid integration, and intelligent decision-making techniques aimed at enhancing the range, reliability, and sustainability of EV operations. Key findings indicate a paradigm shift towards addressing uncertainties, dynamic conditions, and synchronization challenges inherent in large-scale and dynamic routing problems within the context of EVs that require efficient battery management.

The problem of vehicle routing optimization is researched, to improve the efficiency of vehicle scheduling. With the increasing complexity of the traffic network, the vehicle will face the interference of accident and congestion, this situation is random and cannot be predicted. The traditional vehicle routing planning model lack of analysis of the interference risk, accurate model cannot be established, the vehicle scheduling operating efficiency is bad. In order to avoid these defects, the vehicle routing optimization method is proposed based on hybrid algorithm. According to the theory of traffic information feedback method, the feedback model of road information is established. It provides basis for vehicle routing optimization. The ant colony algorithm and extreme optimization algorithm are combined, the hybrid algorithm is obtained. According to the theory of hybrid algorithm, the vehicle routing optimization model is constructed, and related vehicle data is input in the model. The vehicle routing optimization processing is realized. The experiment results show that this algorithm can improve the scheduling efficiency, so as to meet the actual demand of traffic management.

Vehicle routing problems (VRPs) are a fundamental class of combinatorial optimization problems (COPs) in computer science and operations research, with diverse real-world applications in logistics, transportation, and manufacturing. The intrinsic NP-hard nature makes VRPs exponentially expensive to be solved by exact solvers. As an alternative, heuristic solvers deliver suboptimal solutions within reasonable time but require extensive hand-crafted rules and domain expertise tailored to each specific problem. Recently, neural combinatorial optimization (NCO), which leverages machine learning to learn heuristics in a data-driven manner, has gained significant attention. These neural solvers demonstrate strong performance while reducing computational overhead and reliance on domain expertise compared to traditional solvers. However, they face significant generalization challenges. For example, their performance may degrade substantially when applied to instances with different data distributions, problem scales, or constraints than those encountered during training. This generalization issue severely limits their practical applicability. This thesis aims to systematically address these challenges and advance the development of generalizable neural solvers for VRPs. The thesis begins by enhancing the cross-distribution generalization of neural VRP solvers through an adversarial training approach. We introduce an ensemble-based Collaborative Neural Framework (CNF) that adversarially trains multiple models in a collaborative manner, promoting robustness against adversarial attacks while also boosting performance on clean instances. In this framework, an attacker generates hard instances by perturbing the data distribution, challenging the models to adapt and thereby strengthening cross-distribution generalization. Additionally, a neural router is designed to efficiently distribute training instances among the models, thereby improving load balancing and collaborative efficacy. Extensive experiments on two classic routing problems -- the travelling salesman problem (TSP) and the capacitated vehicle routing problem (CVRP) -- demonstrate the effectiveness and versatility of CNF in enhancing the cross-distribution generalization. Next, the thesis further expands neural solvers to simultaneously address both cross-size and cross-distribution generalization challenges. We propose Omni-VRP, a generic meta-learning framework that enables effective training of an initial model with the capacity for rapid adaptation to new tasks during inference, where each task corresponds to a set of instances with the same problem scale and data distribution. Additionally, we introduce a simple yet efficient approximation method to reduce the training overhead associated with second-order derivative calculations. Extensive experiments on both synthetic and benchmark instances of TSP and CVRP validate the effectiveness of our approach. Finally, the thesis pioneers the study of cross-problem generalization, pushing the boundaries of neural VRP solvers in learning generalizable representations across diverse constraints. We propose MVMoE, a unified neural solver capable of solving 16 VRP variants simultaneously in a zero-shot manner through attribute composition. To efficiently enhance model capacity, we employ a mixture-of-experts architecture with a hierarchical gating mechanism, striking a balance between empirical performance and computational complexity. Experimentally, our method significantly promotes zero-shot generalization on 10 unseen VRP variants, and showcases decent results on the few-shot setting and real-world benchmark instances. Overall, this thesis represents a pioneering exploration and substantial advancement in developing generalizable neural solvers for VRPs. It investigates innovative designs across various components, including model architectures, training algorithms, and problem settings, to enhance the generalization of neural solvers across diverse contexts such as varying data distributions, problem scales, and constraints. These contributions encourage neural solvers to learn more robust and generalizable representations, paving the way for the first generation of foundation models capable of addressing a wide range of COPs. Ultimately, the insights gained here not only propel the field of NCO forward but also enrich the broader landscape of learning-based optimization methods.

In order to promote the cost reduction and efficiency improvement of the logistics distribution process and to guarantee the safety of goods transportation, this paper studies the portfolio optimization of goods loading and the problem of simultaneous pickup and delivery vehicle routing. A balanced loading constraint was introduced to restrict loading through two aspects of axle weight bearing and lateral center-of-gravity offset. With the shortest total route length as the objective, this paper constructs a simultaneous pickup and delivery vehicle routing model with three-dimensional (3D) balanced loading constraints (3BL-VRPSPD). Additionally, a hybrid tabu search (TS) algorithm embedded loading test was proposed to solve this problem. Firstly, a heuristic insertion method was applied to determine the initial routing scheme, and the node swapping and relocation operators were designed to construct the tabu neighborhood scheme for routing optimization. On this basis, the 3D balanced loading was incorporated into the routing iteration process. A balanced loading algorithm, combining multiple-indicator ordering and maximum space division strategies (MOMD), was formulated to develop a 3D-balanced loading plan for goods with a pickup and delivery vehicle routing scheme. Finally, standard instances verified the effectiveness of the method. The results show that the proposed method can effectively optimize 3BL-VRPSPD and outperform other algorithms.

We consider a natural probabilistic variation of the classical vehicle routing problem (VRP), in which demands are stochastic. Given only a probabilistic description of the demand we need to design routes for the VRP. Motivated by applications in strategic planning and distribution systems, rather than resolving the problem when the demand becomes known, we propose to construct an a priori sequence among all customers of minimal expected total length. We analyze the problem using a variety of theoretical approaches. We find closed-form expressions and algorithms to compute the expected length of an a priori sequence under general probabilistic assumptions. Based on these expressions we find upper and lower bounds for the probabilistic VRP and the VRP re-optimization strategy, in which we find the optimal route at every instance. We propose heuristics and analyze their worst case performance as well as their average behavior using techniques from probabilistic analysis. Our results suggest that our approach is a strong and useful alternative to the strategy of re-optimization in capacitated routing problems.

SummaryWith advanced information technologies and industrial intelligence, Industry 4.0 has been witnessing a large scale digital transformation. Intelligent transportation plays an important role in the new era and the classic vehicle routing problem (VRP), which is a typical problem in providing intelligent transportation, has been drawing more attention in recent years. In this article, we study multidepot VRP (MDVRP) that considers the management of the vehicles and the optimization of the routes among multiple depots, making the VRP variant more meaningful. In addressing the time efficiency and depot cooperation challenges, we apply the artificial bee colony (ABC) algorithm to the MDVRP. To begin with, we degrade MDVRP to single‐depot VRP by introducing depot clustering. Then we modify the ABC algorithm for single‐depot VRP to generate solutions for each depot. Finally, we propose a coevolution strategy in depot combination to generate a complete solution of the MDVRP. We conduct extensive experiments with different parameters and compare our algorithm with a greedy algorithm and a genetic algorithm (GA). The results show that the ABC algorithm has a good performance and achieve up to 70% advantage over the greedy algorithm and 3% advantage over the GA.

A visual interactive approach to classical and mixed vehicle routing problems with backhauls