Solving Vehicle Routing Problem Research Articles

Improved Whale Optimization Algorithm with Variable Neighbourhood Search Strategy (WOA-VNS) in Solving Vehicle Routing Problem (VRP) for Recommending Multi-days Tourist Routes in Yogyakarta

Improved Whale Optimization Algorithm with Variable Neighbourhood Search Strategy (WOA-VNS) in Solving Vehicle Routing Problem (VRP) for Recommending Multi-days Tourist Routes in Yogyakarta

An exact and metaheuristic optimization framework for solving Vehicle Routing Problems with Shipment Consolidation using population-based and Swarm Intelligence

The Vehicle Routing Problem with Shipment Consolidation (VRPSC) is a novel variation of the vehicle routing problem that involves multiple commodities, multiple dimensions, a fleet with different types of vehicles, and the challenge of consolidating shipments during the route. Exact algorithms have been suggested to solve the VRPSC problems. Besides exact algorithms, specific metaheuristic algorithms are employed to deliver solutions of superior quality, albeit not necessarily optimal. The Artificial Immune System (AIS) and Genetic Algorithm (GA) are the metaheuristic optimization techniques applied in this research. Genetic programming is included in evolutionary computing, while AIS is included in swarm intelligence. This research presents a vehicle routing model with product consolidation and different product dimensions. These criteria were selected due to their significant impact on the complexity of mathematical problem-solving in VRPSC. The results from applying these metaheuristic algorithms will be compared with those of exact algorithms to compare and analyse different VRPSC solution approaches.

Swarm intelligence and nature inspired algorithms for solving vehicle routing problems: a survey

Swarm intelligence and nature inspired algorithms for solving vehicle routing problems: a survey

Gase: graph attention sampling with edges fusion for solving vehicle routing problems

Gase: graph attention sampling with edges fusion for solving vehicle routing problems

Machine Learning to Solve Vehicle Routing Problems: A Survey

Machine Learning to Solve Vehicle Routing Problems: A Survey

Smart Routes: A System for Development and Comparison of Algorithms for Solving Vehicle Routing Problems with Realistic Constraints

Smart Routes: A System for Development and Comparison of Algorithms for Solving Vehicle Routing Problems with Realistic Constraints

Smart Routes: A System for Development and Comparison of Algorithms for Solving Vehicle Routing Problems with Realistic Constraints

The problem of route optimization with realistic constraints is becoming extremely relevant in the face of global urban population growth. While we are aware of approaches that theoretically provide an exact optimal solution, their application becomes challenging as the problem size increases because of exponential complexity. We investigate the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and compare solutions obtaining by exact solver SCIP [1] with heuristic algorithms such as LKH, 2-OPT, 3-OPT [2], the OR-Tools framework [3], and the deep learning model JAMPR [4]. We demonstrate that for problem of size 50 deep learning and classical heuristic solutions became close to SCIP exact solution but requires less time. Additionally for problems with size 100, SCIP exact methods ∼ 13 times slower that neural and classical heuristics with the same route cost and on ∼ 50% worse for the first feasible solution on the same time. To conduct experiments, we developed the Smart Routes platform for solving route optimization problems, which includes exact, heuristic, and deep learning models, and facilitates convenient integration of custom algorithms and datasets.

Smart Routes: A System for Development and Comparison of Algorithms for Solving Vehicle Routing Problems with Realistic Constraints

Задача оптимизации маршрутов с реалистичными ограничениями становится крайне актуальной в условиях глобального роста городского населения. Подходы к оптимизации маршрутов, включая точные методы, сталкиваются с проблемой экспоненциальной сложности при увеличении размера задачи оптимизации маршрутов. Вработе сравнивается точный решатель SCIP с эвристическими методами (LKH, 2-OPT, 3-OPT, ORTools) и моделью глубокого обучения JAMPR+. Для задач размером 50 глубокое обучение и классические эвристики достигают точности, сравнимой с SCIP, но требуют меньше времени. Для задач размером 100, эвристики и нейронные сети значительно опережают SCIP как по времени, так и по качеству первого найденного решения. Для проведения экспериментов разработана платформа Smart Routes для решения задачи оптимизации маршрутов, которая включает в себя точные, эвристические и нейросетевые модели и облегчает удобное интегрирование собственных алгоритмов и наборов данных.

A robustness division based multi-population evolutionary algorithm for solving vehicle routing problems with uncertain demand

The vehicle routing problem with uncertain demand (VRPUD) is an extension of capacitated vehicle routing problem (CVRP), where the demand of each customer is unknown when dispatching the vehicles to service customers. Since it is more practical than CVRP, the VRPUD has aroused wide attention. Although the evolutionary algorithms (EAs) have demonstrate its promising performance on solving VRPUD, the most of EAs only consider the robustness of solution after generating offspring, which limit the quality of solutions found by EAs. To this end, in this paper, a robustness division based multi-population evolutionary algorithm (RDMPEA) is developed for VRPUDs, where the robustness is considered before, during and after offspring. Specifically, before generating offspring, the RDMPEA first divides the individuals into different subpopulations according to their robustness level, and only the individuals within the same subpopulation can match each other and generate offspring. During generating offspring, the RDMPEA employs a route based crossover operator to generate offspring, where the routes with higher robustness have a greater probability of being inherited by the offspring. After generating offspring, a dedicated environment selection strategy is applied to survive the individuals with better robustness and travel cost. In the experiments, the proposed RDMPEA is compared to three state-of-the-art heuristic methods tailored for VRPUDs on a variety of instances obtained by using three widely used vehicle routing problem benchmarks. The experimental results indicate that the proposed RDMPEA is superior to three compared algorithms, and can find solutions with better travel cost and robustness.

Learning Feature Embedding Refiner for Solving Vehicle Routing Problems.

While the encoder-decoder structure is widely used in the recent neural construction methods for learning to solve vehicle routing problems (VRPs), they are less effective in searching solutions due to deterministic feature embeddings and deterministic probability distributions. In this article, we propose the feature embedding refiner (FER) with a novel and generic encoder-refiner-decoder structure to boost the existing encoder-decoder structured deep models. It is model-agnostic that the encoder and the decoder can be from any pretrained neural construction method. Regarding the introduced refiner network, we design its architecture by combining the standard gated recurrent units (GRU) cell with two new layers, i.e., an accumulated graph attention (AGA) layer and a gated nonlinear (GNL) layer. The former extracts dynamic graph topological information of historical solutions stored in a diversified solution pool to generate aggregated pool embeddings that are further improved by the GRU, and the latter adaptively refines the feature embeddings from the encoder with the guidance of the improved pool embeddings. To this end, our FER allows current neural construction methods to not only iteratively refine the feature embeddings for boarder search range but also dynamically update the probability distributions for more diverse search. We apply FER to two prevailing neural construction methods including attention model (AM) and policy optimization with multiple optima (POMO) to solve the traveling salesman problem (TSP) and the capacitated VRP (CVRP). Experimental results show that our method achieves lower gaps and better generalization than the original ones and also exhibits competitive performance to the state-of-the-art neural improvement methods.

Skewed general variable neighborhood search to solve the multi-compartment vehicle routing problem

Skewed General Variable Neighborhood Search (SGVNS) is shown to be a powerful and robust methodology for solving vehicle routing problems. In this paper we suggest new SGVNS for solving the multi-compartment vehicle routing problem (MCVRP). The problem of multi-compartment vehicle routing is of practical importance in the petrol and food delivery and waste collection industries. A comparison between our algorithm and the memetic algorithm and the tabu search is provided. It was clear that the proposed algorithm is capable of solving the available instances. Skewed General Variable Neighborhood Search was used because it makes it easy to explore the space of realizable solutions for MCVRP. As a result, the SGVNS is much faster and more effective. It is able to solve 50 to 484 customers from the literature.

Deep Reinforcement Learning for Solving Vehicle Routing Problems With Backhauls.

The vehicle routing problem with backhauls (VRPBs) is a challenging problem commonly studied in computer science and operations research. Featured by linehaul (or delivery) and backhaul (or pickup) customers, the VRPB has broad applications in real-world logistics. In this article, we propose a neural heuristic based on deep reinforcement learning (DRL) to solve the traditional and improved VRPB variants, with an encoder-decoder structured policy network trained to sequentially construct the routes for vehicles. Specifically, we first describe the VRPB based on a graph and cast the solution construction as a Markov decision process (MDP). Then, to identify the relationship among the nodes (i.e., linehaul and backhaul customers, and the depot), we design a two-stage attention-based encoder, including a self-attention and a heterogeneous attention for each stage, which could yield more informative representations of the nodes so as to deliver high-quality solutions. The evaluation on the two VRPB variants reveals that, our neural heuristic performs favorably against both the conventional and neural heuristic baselines on randomly generated instances and benchmark instances. Moreover, the trained policy network exhibits a desirable capability of generalization to various problem sizes and distributions.

VRPSolverEasy: A Python Library for the Exact Solution of a Rich Vehicle Routing Problem

The optimization community has made significant progress in solving vehicle routing problems (VRPs) to optimality using sophisticated branch-cut-and-price (BCP) algorithms. VRPSolver is a BCP algorithm with excellent performance in many VRP variants. However, its complex underlying mathematical model makes it hardly accessible to routing practitioners. To address this, VRPSolverEasy provides a Python interface to VRPSolver that does not require any knowledge of mixed integer programming modeling. Instead, routing problems are defined in terms of familiar elements, such as depots, customers, links, and vehicle types. VRPSolverEasy can handle several popular VRP variants and arbitrary combinations of them. History: Accepted by Ted Ralphs, Area Editor for Software Tools. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Software Tools for Vehicle Routing. Funding: This work was supported by Faperj [Grant E-26/202.887/2017] and Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 305684/2022-1]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0103 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0103 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Metaheuristic link prediction (MLP) using AI based ACO-GA optimization model for solving vehicle routing problem

Metaheuristic link prediction (MLP) using AI based ACO-GA optimization model for solving vehicle routing problem

An Overview of Algorithms for Solving Vehicle Routing Problems in the Quantum-Classical Cloud

Introduction. The hope of solving the problem of the avalanche-like growth of requirements for computing power, essential for solving complex routing problems and other problems of combinatorial optimization, relies on the latest quantum computers, in the development of which governments and corporations invest multi-billion investments. The article examines modern routing algorithms and performs their analysis and verification, if the authors of the algorithm provided appropriate test programs. The purpose of the article is to review the current state of development in the field of development of routing algorithms for hybrid quantum-classical clouds, analyze them and propose a classification of algorithms. Results. Modern quantum computers (QCs) make it possible to find approximate solutions to some of mathematical problems faster than classical computers. The inaccuracy of the solutions obtained by the QC is a consequence of physical and technological limitations: calculation errors are caused by thermal noise, a small number of computational elements - qubits and connections between them, which requires the decomposition of the problem and the use of heuristic algorithms. The analysis of approaches to the solution of optimization problems on QC allows us to single out: quantum response and variational search of eigenvalues based on quantum logic gates as the general directions of development of the vast majority of algorithms for solving routing problems. The considered algorithms reduce the vehicle routing problem to a quadratic unconstrained binary optimization problem, which is isomorphic to the Hamilton-Ising model. In this form, the problem is suitable for embedding in QC, which finds an approximate solution that has the best statistical reliability or corresponds to the quantum state with the lowest energy. As a separate class, vehicle routing algorithms for classical computers that use quantum computing to accelerate problem solving can be distinguished. For example, neural networks that calculate weighting factors using QC or an ant algorithm that calculates a pheromone trail in a hybrid cloud. It should be mentioned the quantum-inspired algorithms, which are based on software tools for the simulation of QC and the corresponding libraries and allow creating an effective class of algorithms for solving problems of vehicle routing. Conclusions. Combining hardware quantum annealing with a number of software tools for calculating optimization problems for classical computers in a hybrid quantum-classical cloud service allows to obtain advantages in speed and accuracy of some types of complex optimization problems of a commercial scale, in particular, routing vehicles, which is already bringing substantial profits to a number of corporations. Keywords: vehicle routing problem, quantum computer, annealing, combinatorial optimization, traveling salesman problem, clustering, qubit.

Solving Vehicle Routing Problem Using Quantum Approximate Optimization Algorithm

Intelligent transportation systems (ITS) are a critical component of Industry 4.0 and 5.0, particularly having applications in logistic management. One of their crucial utilization is in supply-chain management and scheduling for optimally routing transportation of goods by vehicles at a given set of locations. This paper discusses the broader problem of vehicle traffic management, more popularly known as the Vehicle Routing Problem (VRP), and investigates the possible use of near-term quantum devices for solving it. For this purpose, we give the Ising formulation for VRP and some of its constrained variants. Then, we present a detailed procedure to solve VRP by minimizing its corresponding Ising Hamiltonian using a hybrid quantum-classical heuristic called Quantum Approximate Optimization Algorithm (QAOA), implemented on the IBM Qiskit platform. We compare the performance of QAOA with classical solvers such as CPLEX on problem instances of up to 15 qubits. We find that performance of QAOA has a multifaceted dependence on the classical optimization routine used, the depth of the ansatz parameterized by p, initialization of variational parameters, and problem instance itself.

Solving the capacitated vehicle routing problem with time windows via graph convolutional network assisted tree search and quantum-inspired computing

Vehicle routing problems are a class of NP-hard combinatorial optimization problems which attract a lot of attention, as they have many practical applications. In recent years there have been new developments solving vehicle routing problems with the help of machine learning, since learning how to automatically solve optimization problems has the potential to provide a big leap in optimization technology. Prior work on solving vehicle routing problems using machine learning has mainly focused on auto-regressive models, which are connected to high computational costs when combined with classical exact search methods as the model has to be evaluated in every search step. This paper proposes a new method for approximately solving the capacitated vehicle routing problem with time windows (CVRPTW) via a supervised deep learning-based approach in a non-autoregressive manner. The model uses a deep neural network to assist finding solutions by providing a probability distribution which is used to guide a tree search, resulting in a machine learning assisted heuristic. The model is built upon a new neural network architecture, called graph convolutional network, which is particularly suited for deep learning tasks. Furthermore, a new formulation for the CVRPTW in form of a quadratic unconstrained binary optimization (QUBO) problem is presented and solved via quantum-inspired computing in cooperation with Fujitsu, where a learned problem reduction based upon the proposed neural network is applied to circumvent limitations concerning the usage of quantum computing for large problem instances. Computational results show that the proposed models perform very well on small and medium sized instances compared to state-of-the-art solution methods in terms of computational costs and solution quality, and outperform commercial solvers for large instances.

An improved artificial bee colony with perturbation operators in scout bees’ phase for solving vehicle routing problem with time windows

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>An example of a combinatorial problem is the vehicle routing problem with time windows (VRPTW), which focuses on choosing routes for a limited number of vehicles to serve a group of customers in a restricted period. Meta-heuristics algorithms are successful techniques for VRPTW, and in this study, existing modified artificial bee colony (MABC) algorithm is revised to provide an improved solution. One of the drawbacks of the MABC algorithm is its inability to execute wide exploration. A new solution that is produced randomly and being swapped with best solution when the previous solution can no longer be improved is prone to be trapped in local optima. Hence, this study proposes a perturbed MABC known as pertubated (P-MABC) that addresses the problem of local optima. P-MABC deploys five types of perturbation operators where it improvises abandoned solutions by changing customers in the solution. Experimental results show that the proposed P-MABC algorithm requires fewer number of vehicles and least amount of travelled distance compared with MABC. The P-MABC algorithm can be used to improve the search process of other population algorithms and can be applied in solving VRPTW in domain applications such as food distribution.</span></p></div></div></div>

Origin-Oriented Shuffled Frog Leaping Vehicle Routing Multiobjective Optimization Algorithm

Shuffled frog leaping algorithm is a biological swarm intelligent optimization algorithm and improved into capacity-limited vehicle routing problem. However, the optimization performance is limited with improvement strategies in major of the improvement algorithm. A novel framework of algorithm is proposed to solve capacity-limited vehicle routing problem, including three modules such as origin oriented shuffled frog leaping algorithm strategy, origin oriented shuffled frog leaping vehicle routing multiobjective optimization algorithm strategy, and output module. The frog individuals gather near the origin with the maximum probability and in the area circle, with the frog leaping radius or frog-oriented radius, as the neighborhood. The negative value of the maximum entropy and the shortest total path length of the vehicle are selected as the fitness. The performance test shows that it overcomes the defect of slow convergence compared with other five algorithms. It performs well to solve vehicle routing problems.

From School Buses to Carpooling: A Multifaceted Approach to Solving Vehicle Routing Problems in People Transportation

This paper delves into the complex realm of vehicle routing problems (VRPs) with a specific focus on the transportation of people, highlighting the nuanced challenges and optimization opportunities distinct from those associated with goods transportation. Among these, the Dial-a-Ride Problem (DARP) is emphasized as a pivotal area of study. DARP caters to providing personalized, accessible transportation services, particularly for individuals unable to use standard transit options, such as the elderly and handicapped. This research meticulously explores the mathematical formulation of DARP, and operational challenges and extends the discourse to encompass related VRPs in people transportation, thereby broadening the scope of investigation. Operational intricacies of DARP include managing time windows for pickups and deliveries, adhering to vehicle capacity limits, and ensuring tailored transportation solutions that optimally satisfy both operational costs and customer convenience. The paper reviews a wide spectrum of heuristic and metaheuristic solution methods developed over the years, tracing the evolution of these algorithms from their inception to the sophisticated techniques currently employed to address DARP's dynamic, static, and stochastic variants. Additionally, the research extends to related problems such as the School Bus Routing Problem (SBRP), which emphasizes the efficient and timely transportation of students, and the Carpooling Problem, focusing on organizing shared rides to reduce vehicle kilometers and enhance mobility. Demand Responsive Transportation (DRT) problems are also discussed, highlighting their importance in areas where fixed-route services are inefficient. Conclusively, the paper discusses the future scope of research in this domain, underscoring the necessity for novel solution concepts to address the growing complexity and scale of transportation demands. The integration of intermodal aspects, combining public transportation with demand-responsive services, and the advancement of hybrid algorithms are identified as key areas for future exploration. This comprehensive study not only contributes to the academic discourse on optimizing vehicle routing for people transportation but also aims to inform the development of more efficient, accessible, and customer-oriented transportation systems.