Variants of VRP to Optimize Logistics Management Problems

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.

The vehicle routing problem (VRP), as a classic combinatorial optimization problem, has always been a hot research topic in operations research. In order to gain a deeper understanding of the VRP problem, this work uses the knowledge graph to comprehensively analyze and summarize the literature related to VRP from 1959 to 2022 in the Web of Science (WoS) database. Firstly, according to the basic statistical information of the literature, the annual publications, the authors, their institutions and countries, the keyword co-occurrence, and the literature co-citation network are analyzed to comprehensively summarize and generalize the research on VRP and predict its future development trend. The results show that, in the past 60 years, there have been abundant changes in the research on VRP. The United States and China have made the most important contributions in the field of VRP. According to the WoS literature retrieval results and classification methods, the VRP models and their solutions are comprehensively classified, and the model solving algorithms are divided into exact algorithms, heuristic algorithms, metaheuristic algorithms, hyper-heuristic algorithms, machine learning, etc. The results show that the development of information computing technology plays an important role in research on the VRP problem, and dynamic VRP, hyper-heuristic algorithms, deep reinforcement learning, etc. are the future development directions of the VRP model and its optimization. The results of this research can provide help and guidance for beginners and scholars outside the industry to comprehensively understand the development and research hotspots of VRP.

In response to the rapid increase in e-commerce, distribution services, and smart technology, businesses need to solve the vehicle routing problem (VRP) and its variants to improve service quality and cut operating costs. In this paper, we introduce the VRP with time windows and time costs (VRPTWTC), which is a new but practical VRP variant that adds time windows of customers and time costs of service constraints into the optimization of the traditional VRP problem. Furthermore, we propose a masking algorithm and combine it into our proposed end-to-end and data-driven deep reinforcement learning framework to solve the VRPTWTC. Experimental results show a shorter tour length and reasonable processing time than benchmarks both on a simulated dataset and a real enterprise-level dataset. Besides, violation of time window and total time cost, which is one of the most important criterions in our problem formulation, never occurred in our experiment under the real road connection conditions when using a real map API. To the best of our knowledge, our framework is the first to effectively and efficiently solve a VRP variant problem with practical time windows and time costs constraints with a real map API to calculate routes of VRP considering real road connection conditions on an enterprise-level dataset.

Metaheuristics like ant colony optimization (ACO) can be used to solve combinatorial optimization problems. In this paper we refer to its successful application to the vehicle routing problem (VRP). At the beginning, we introduce the VRP and some of its variants. The variants of VRP were designed to reproduce the kind of situations faced in the real-world. Further, we introduce the fundamentals of ant colony optimization, and we present in few words its application to the solution of the VRP. At the end, we discuss the applications of ACO to a number of real-world problems: a VRP with time windows for a major supermarket chain in Switzerland; a VRP with pickup and delivery for a leading distribution company in Italy and an on-line VRP in the city of Lugano, Switzerland, where clients' orders arrive during the delivery process.

Nowadays, the continuous increase in traffic makes the management of road flows increasingly difficult. Hence, transportation network and delivery problems are becoming a real priority. To solve this complexity of situation we call on Vehicle Routing Problem (VRP). When we have capacity constraints, we talk about Capacitated Vehicle Routing Problem (CVRP) considered as a variant of Vehicle Routing Problem (VRP). Due to the increasing of supply chain complexity, new optimization techniques in additional to new technologies give a great development, and so new Information and Communications Technologies (ICT) are implemented as support to the transportation and logistics management. This paper develops an optimization algorithm to solve CVRP of goods. We give an example of delivery distribution of BIM Stores in El Jadida city in Morocco. The aim is to deliver goods to the different points of Bim stores for a minimum cost while never exceeding the capacity of trucks to optimize the trucks tour. For that, we use an algorithm of operational research using Python language: The Guided Local Search. The results obtained represent the optimal path for delivering goods to different points of BIM stores in El Jadida city.

With the current economic improvement, the logistics industries have been developed quickly. The logistics distribution of inter-city has been widely used in people's life. To shorten the delivery time and improve the economic benefits, how to choose the right path for the delivery personnel has become the most urgent problem. To solve this problem, the model of Vehicle Routing Problem (VRP) was proposed. Many researchers have applied various algorithms to solve VRP problems. However, because of the NP-hard characteristics of VRP problems, there is still have some room to improve the algorithms under the criteria of quality and time solutions. At the same time, there are many branches of VRP subproblems, among which the most common one is the VRP problem with capacity constraint (CVRP). As the CVRP problem belongs to the Combinatorial Optimization Problems (COPs), we select the ant colony algorithm to improve the CVRP. In this paper, based on the Max-Min Ant System (MMAS) algorithm, the utilization of mining information is strengthened by the elite ant path. The adaptive parameters are added to adjust the exploration and exploitation ability of the algorithm. Moreover, some appropriate constraints are added to the pheromone of the ant system to ensure the effectiveness of the algorithm. Based on the above strategy, the Adaptive Parameter for Max-Min Elite Ant System (APMMEAS) algorithm is proposed in this paper. The experimental results from the CVRP benchmark showed that the proposed APMMEAS algorithm is more competitive in quality and time solutions than in other ant colony series algorithms.

We aim to suggest a simple genetic algorithm (GA) and other four hybrid GAs (HGAs) for solving the asymmetric distance-constrained vehicle routing problem (ADVRP), a variant of vehicle routing problem (VRP). The VRP is a difficult NP-hard optimization problem that has numerous real-life applications. The VRP aims to find an optimal tour that has least total distance (or cost) to provide service to n customers (or nodes or cities) utilizing m vehicles so that every vehicle starts journey from and ends journey at a depot (headquarters) and visits every customer only once. The problem has many variations, and we consider the ADVRP for this study, where distance traveled by every vehicle must not exceed a predefined maximum distance. The proposed GA uses random initial population followed by sequential constructive crossover and swap mutation. The HGAs enhance the initial solution using 2-opt search method and incorporate a local search technique along with an immigration procedure to obtain effective solution to the ADVRP. Experiments have been conducted among the suggested GAs by solving several restricted and unrestricted ADVRP instances on asymmetric TSPLIB utilizing several vehicles. Our experiments claim that the suggested HGAs using local search methods are very effective. Finally, we reported a comparative study between our best HGA and a state-of-the-art algorithm on asymmetric capacitated VRP and found that our algorithm is better than the state-of-the-art algorithm for the instances.

Solving the vehicle routing problem (VRP) is one of the best-known optimization issues in the TLS (transport, logistic, spedition) branch market. Various variants of the VRP problem have been presented and discussed in the literature for many years. In most cases, batch versions of the problem are considered, wherein the complete data, including customers’ geographical distribution, is well known. In real-life situations, the data change dynamically, which influences the decisions made by optimization systems. The article focuses on the aspect of geopositioning updates and their impact on the effectiveness of optimization algorithms. Such updates affect the distance matrix, one of the critical datasets used to optimize the VRP problem. A demonstration version of the optimization system was developed, wherein updates are carried out in integration with both open source routing machine and GPS tracking services. In the case of a dynamically changing list of destinations, continuous and effective updates are required. Firstly, temporary values of the distance matrix based on the correction of the quasi-Euclidean distance were generated. Next, the impact of update progress on the proposed optimization algorithms was investigated. The simulation results were compared with the results obtained “manually” by experienced planners. It was found that the upload level of the distance matrix influences the optimization effectiveness in a non-deterministic way. It was concluded that updating data should start from the smallest values in the distance matrix.

The Vehicle Routing Problem (VRP) is a well-known combinatorial optimization problem where a number of customers must be served with a fleet of vehicles. The classical variation of the VRP is the Capacicated Vehicle Routing Problem (CVRP) with the additional constraint that each vehicle must have uniform capacity. Many Decision Support Systems (DSS) have been implemented to solve real life problems of the VRP and its’ variants, but they do not allow multiple decision makers to explore several scenarios of a given problem simultaneously and collaborate with each other in order to find the best possible solution. In this paper, we extend our previous work [35] and incorporate in our spatial DSS four variants of the CVRP: (i) Distance Constrained Vehicle Routing Problem (DVRP), (ii) Vehicle Routing Problem with Time Windows (VRPTW), (iii) Vehicle Routing Problem with Backhauls (VRPB), and (iv) Vehicle Routing Problem With Pickup and Delivery (VRPPD). This extension allows decision makers to solve specific routing problems according to their needs. The proposed collaborative spatial DSS allows two decision makers to collaborate with each other in order to find the best possible solution through a tangible interface. The locations are added through interactive Google Maps and other parameters through user-friendly forms that can be manipulated via tangible interfaces. The proposed DSS has been implemented using Java, TUIO protocol, jsprit, and Google Maps.

This paper presents an overview of recent advances in the field of the vehicle routing problem (VRP), based on papers published in high-quality journals during the period from January 2015 to July 2017. A distinctive feature of the presented survey is its focus on new versions of the VRP, which have recently emerged or gained momentum, and the corresponding new solution methods, with particular emphasis on computational intelligence (CI) approaches. The list of newly proposed or currently popular VRP formulations include last mile and same day delivery, crowdshipping, bike sharing systems, post-disaster response plans, local routing in large production or cargo plants, customer-centric VRP, autonomous delivery, unnamed aerial vehicle delivery, green VRP, waste collection VRP, rich VRP, or VRP with backhauls. Simultaneously, an adequate increase of interest in the application of traditional CI methods (e.g., genetic, memetic, ant colony or particle swarm optimization, simulated annealing, or their various hybrid versions) can be observed in the VRP domain. At the same time, approaches proven efficient in other optimization areas (e.g., hyperheuristics, methods based on Monte Carlo simulations, algorithms rooted in game theory and bi-level optimization-Stackelberg games, or cognitively motivated methods) have lately entered the VRP field and become a viable alternative to more traditional techniques. Since VRP is one of the fastest growing fields in the operations research area, we believe that an analysis of the recently published VRP papers from the perspective of their novelty in problem formulation and/or applied solution method can provide a true value for the CI community, especially young researchers entering the field and seeking challenges in this interesting and fast developing research area.

This paper proposes an efficient algorithm, with a reduced number of parameters, for solving the two‐dimensional loading‐capacitated vehicle routing problem (2L‐CVRP). This problem combines two of the most important issues in logistics, that is, vehicle routing and packing problems. Our approach contemplates unrestricted loading including the possibility of applying 90° rotations to each rectangular‐shaped item while loading it into the vehicle, which is a realistic assumption seldom considered in the existing literature. The algorithm uses a multistart approach that is designed to avoid local minima and also to make the algorithm an easily parallelizable one. At each restart, a biased randomization of a savings‐based routing algorithm is combined with an enhanced version of a classical packing heuristic to produce feasible good solutions for the 2L‐CVRP. The proposed algorithm has been compared with the classical benchmarks for two different 2L‐CVRP variants, that is, with and without item rotations. Experimental results show that our approach outperforms several best‐known solutions from previous work, both in terms of quality and the computational time needed to obtain them.

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.

Traditional vehicle routing problems implicitly assume that only one crew operates a vehicle for the entirety of its journey. However, this assumption is violated in many applications arising in humanitarian and military logistics. This paper considers a joint vehicle and crew routing and scheduling problem in which crews are able to interchange vehicles, resulting in space and time interdependencies between vehicle routes and crew routes. The problem is formulated as a mixed integer programming (MIP) model and a constraint programming (CP) model that overlay crew routing constraints over a standard vehicle routing problem. The constraint program uses a novel optimization constraint to detect infeasibility and to bound crew objectives. This paper also explores methods using large neighborhood search over the MIP and CP models. Experimental results indicate that modeling the vehicle and crew routing problems jointly and supporting vehicle interchanges for crews may bring significant benefits in cost reduction compared with a method that sequentializes these decisions.

Mobilidade urbana é tema que está sempre em alta desde o surgimento das grandes metrópoles. Dentre os diversos fatores geradores de tráfego, podemos destacar os polos geradores de viagens (PGVs), locais que concentram os destinos ou origens de grande quantidade de pessoas, como centros comerciais, parques industriais e grandes condomínios. O objetivo deste trabalho é definir o Problema de Roteamento de Veículos para o Transporte Contínuo (CommuteVRP, do inglês Commute Vehicle Routing Problem), que descreve o deslocamento diário de pessoas a um PGV, e verificar se algoritmos já propostos na literatura são capazes de solucionar o problema com instâncias de escala próxima à demanda real do mercado. Definimos o CommuteVRP como uma variante dos problemas de roteamento de veículos que busca pela criação de rotas economicamente lucrativas com conforto e preços acessíveis aos passageiros. Trata-se de um problema de otimização diferente dos problemas clássicos de roteamento de veículos e transporte de pessoas encontrados na literatura, pois tem como foco a otimização do ponto de vista mercadológico, cuja solução é composta de rotas economicamente viáveis e lucrativas que não necessariamente atendam a todas as pessoas envolvidas. Foi possível solucionar o problema em tempo razoável utilizando a heurística do princípio ruin and recreate que nos permite a computação paralela para a geração de rotas. Foram alcançados resultados lucrativos para todas as instâncias testadas, e foram comparadas diferentes configurações de execução.

The Vehicle Routing Problem (VRP) is a known optimization problems falling under the category of NP-Hard set of problems. VRP, along with its variations, continue to be extensively explored by the research community due to their large domain of application (environment, agriculture, industry, etc.) and economic impact on improving the overall performance, Quality of Services and reducing the operational cost. In this paper, we focus on VRPMTW; a variant of VRP with Multiple Time Windows constraints. We introduce a novel Hybrid Genetic Variable Neighborhood Search (HGVNS) based heuristic for the optimization of VRPMTW. The proposed framework uses genetic cross-over operators on a list of best parents and new implementations of local search operators. Computational results on benchmark data show substantial performance improvement when using the newly introduced heuristic.