Complex Vehicle Routing Problems Research Articles

New features for customer classification in the Flying Sidekick Traveling Salesman Problem

The increasing interest in the deployment of truck and drone delivery systems leads to the definition of new and complex vehicle routing problems. In this context, the flying sidekick traveling salesman problem (FS-TSP) is the first truck-and-drone routing problem defined in the literature. Several variants appeared in the last years differing in the operating conditions and the structure of the hybrid truck-and-drone delivery system. Exact and heuristic solution methods have been proposed in the literature to solve these problems effectively. However, the exact solution methods can generally solve only small-size instances due to the complexity of these problems. On the other hand, heuristic solution methods are able to find feasible solutions with an acceptable computational burden but without any guarantee of the quality of the solution. This work aims to investigate the possibility of using data science and machine learning techniques to reduce the complexity of solving an FS-TSP instance. The idea is to determine a good/optimal customer-to-vehicle assignment apriori to reduce the number of decisions involved in the FS-TSP solution. The assignment is determined through the classification of customers based on a subset of features specifically defined for the FS-TSP. This information can be exploited by existing solution approaches for the FS-TSP to improve their performance. An extensive computational campaign on benchmark instances is carried out with a twofold objective. On the one hand, we aim to evaluate the impact of the features on customer classification. On the other hand, we intend to show the relationship between classification and combinatorial optimization results by observing the effect of the customer classification on the FS-TSP solution.

Learning Large Neighborhood Search for Vehicle Routing in Airport Ground Handling

Dispatching vehicle fleets to serve flights is a key task in airport ground handling (AGH). Due to the notable growth of flights, it is challenging to simultaneously schedule multiple types of operations (services) for a large number of flights, where each type of operation is performed by one specific vehicle fleet. To tackle this issue, we first represent the operation scheduling as a complex vehicle routing problem and formulate it as a mixed integer linear programming (MILP) model. Then given the graph representation of the MILP model, we propose a learning assisted large neighborhood search (LNS) method using data generated based on real scenarios, where we integrate imitation learning and graph convolutional network (GCN) to learn a destroy operator to automatically select variables, and employ an off-the-shelf solver as the repair operator to reoptimize the selected variables. Experimental results based on a real airport show that the proposed method allows for handling up to 200 flights with 10 types of operations simultaneously, and outperforms state-of-the-art methods. Moreover, the learned method performs consistently accompanying different solvers, and generalizes well on larger instances, verifying the versatility and scalability of our method.

Planning methods and decision support systems in vehicle routing problems for timber transportation: a review

ABSTRACT In the forest industry, transportation accounts for a significant part of the operational costs. Reducing transportation costs through advanced planning and improved efficiency has motivated considerable research efforts. A substantial part of the research has been devoted to planning methodology and decision support systems development to solve large complex vehicle routing problems in forest timber or roundwood transportation. This paper reviews the scientific contributions to timber transportation vehicle routing planning methodologies and decision support systems used in case studies found in the literature. The challenges of their deployment are discussed and future research opportunities are presented. Vehicle routing problems in timber transportation differ from general vehicle routing problems in many aspects. This paper also describes the industrial context, in which various timber transportation vehicle routing problems (TTVRPs) are intrinsic. Several attributes are identified that characterize the TTVRPs, for which various planning and solution methodologies have been implemented.

Open pollution routing problem of logistics distribution in medical union based on differential search algorithm

Medical care is a guarantee of people's daily life. Improving healthcare contributes to people's well-being. However, healthcare resources are characterized by uneven distribution. Financially well-off areas will have higher quality health care resources. Most of the medical resources are concentrated in public general hospitals, however, primary care institutions can hardly meet the growing needs of people. To solve this problem, Medical Union achieves efficient deployment of resources by integrating various medical institutions in the same area. In the process of logistics integration of the medical union, the scale of logistics distribution expands accordingly. Transportation vehicles have high operating costs and produce greenhouse gases in the process of distribution. The optimization of the driving path of logistics distribution vehicles can reduce the operating cost, fuel consumption and carbon emission. To solve this kind of decentralized and complex vehicle routing problem, this paper proposes a pollution routing problem model considering electrical vehicle usage, customer's soft time window expectation, open path and carbon cost. A modified Differential Search Algorithm with the comprehensive learning strategy and dynamic Cauchy variation strategy is advanced to solve the problem. Results show that the improved algorithm has good solving performance, and verifies the rationality of the proposed model, which will help to reduce carbon emissions and save the logistics and operating costs of medical devices.

VeRoViz: A Vehicle Routing Visualization Toolkit

VeRoViz is an open-source vehicle routing visualization package consisting of both Python and web-based components. It was developed to streamline the workflow for vehicle routing researchers by simplifying and automating many of the tedious tasks associated with generating realistic test problems. VeRoViz also provides new functionality to produce customizable visualizations of complex vehicle routing problems. These visualization tools—including Gantt charts, static maps, and dynamic 3-D videos—assist researchers in validating models and communicating results. Additionally, a comprehensive collection of utility functions within VeRoViz provides researchers with useful tools to assess features of their problems. This paper provides an overview of VeRoViz and highlights the flexibility and ease-of-use of the toolkit. Summary of Contribution: This paper describes an open-source software package designed to assist vehicle routing researchers. The software package, named VeRoViz (vehicle routing visualization), streamlines the process of collecting and visualizing data relevant to vehicle routing research. This includes capturing road network travel times (and distances) between locations, displaying turn-by-turn vehicle routes, generating Gantt charts of vehicle assignments, and producing 3-D “movies” of vehicle routing solutions. The VeRoViz suite consists of three components. First, a web-based interface allows researchers (and instructors) to quickly “sketch” elements of a vehicle routing problem, providing visual representations of nodes and arcs on a map. Second, the VeRoViz Python package provides an extensive collection of functions that assist operations researchers in collecting data and displaying solutions. Finally, an HTML/JavaScript plugin is available for displaying time-dynamic 3-D visualization of vehicle routes. VeRoViz is not a vehicle routing solver; it is a software suite that complements and supports researchers who are developing solution approaches to increasingly realistic vehicle routing problems (e.g., problems related to drone delivery, electric vehicles, or dynamic delivery requests).

Comparision of the walk techniques for fitness state space analysis in vehicle routing problem

The Vehicle Routing Problem (VRP) is a highly researched discrete optimization task. The first article dealing with this problem was published by Dantzig and Ramster in 1959 under the name Truck Dispatching Problem. Since then, several versions of VRP have been developed. The task is NP difficult, it can be solved only in the foreseeable future, relying on different heuristic algorithms. The geometrical property of the state space influences the efficiency of the optimization method. In this paper, we present an analysis of the following state space methods: adaptive, reverse adaptive and uphill-downhill walk. In our paper, the efficiency of four operators are analysed on a complex Vehicle Routing Problem. These operators are the 2-opt, Partially Matched Crossover, Cycle Crossover and Order Crossover. Based on the test results, the 2-opt and Partially Matched Crossover are superior to the other two methods.

Hierarchical Reinforcement Learning for Vehicle Routing Problems with Time Windows

Vehicle routing problem with time windows (VRPTW) is a practical and complex vehicle routing problem (VRP) which is faced by thousands of companies in logistics and transportation. Usually, VRP is solved by traditional heuristic algorithms. Recently, deep learning models under the reinforcement learning (RL) framework have been proposed to solve variants of VRP. In our study, we propose to use the hierarchical RL to find an optimal policy for generating optimal routes in VRPTW. The hierarchical RL structure includes a low level which generates feasible solutions and a high level which further searches for an optimal solution. Experimental results show that the proposed hierarchical RL model outperforms the non-hierarchical RL model and the heuristic algorithms Google OR-Tools. The proposed model also shows generalization capability in three different scenarios: varied time window constraints, from small-scale to large-scale problems, and generalization across different datasets. The flexible framework of hierarchical RL can also be applied to solve other complex VRPs with multiple objectives.

An Attraction Map Framework of a Complex Multi-Echelon Vehicle Routing Problem with Random Walk Analysis

The paper aims to investigate the basin of attraction map of a complex Vehicle Routing Problem with random walk analysis. The Vehicle Routing Problem (VRP) is a common discrete optimization problem in field of logistics. In the case of the base VRP, the positions of one single depot and many customers (which have product demands) are given. The vehicles and their capacity limits are also fixed in the system and the objective function is the minimization of the length of the route. In the literature, many approaches have appeared to simulate the transportation demands. Most of the approaches are using some kind of metaheuristics. Solving the problems with metaheuristics requires exploring the fitness landscape of the optimization problem. The fitness landscape analysis consists of the investigation of the following elements: the set of the possible states, the fitness function and the neighborhood relationship. We use also metaheuristics are used to perform neighborhood discovery depending on the neighborhood interpretation. In this article, the following neighborhood operators are used for the basin of attraction map: 2-opt, Order Crossover (OX), Partially Matched Crossover (PMX), Cycle Crossover (CX). Based on our test results, the 2-opt and Partially Matched Crossover operators are more efficient than the Order Crossover and Cycle Crossovers.

Vehicle Routing Optimisation in Humanitarian Operations: A Survey on Modelling and Optimisation Approaches

The growing field of humanitarian operations is driven by frequent events of disasters seen in the world today. Within this field, Operations Research (OR) plays a critical role in alleviating the suffering of victims that are impacted by disasters. This paper focuses on the branch of a well-known OR problem, known as the Vehicle Routing Problem (VRP), within the selected scope of humanitarian operations. A total of 123 papers of the last decade are reviewed and classified under the humanitarian operations of supply and delivery, evacuation as well as rescue operations. Besides specific disaster management phases and disaster types, various modelling challenges are highlighted, hinting towards a richer and more complex VRP seen under selected model characteristic classifications. Furthermore, established solution approaches, including hybrid solutions, are highlighted and classified, discussing how they are applied in the context of these humanitarian operations. The inclusion of a machine learning solution approach under the same classification is proposed. Finally, the trend and future outlook of VRP for the suggested humanitarian operations are discussed and highlighted.

Fitness Landscape Analysis and Edge Weighting-Based Optimization of Vehicle Routing Problems

Vehicle routing problem (VRP) is a highly investigated discrete optimization problem. The first paper was published in 1959, and later, many vehicle routing problem variants appeared to simulate real logistical systems. Since vehicle routing problem is an NP-difficult task, the problem can be solved by approximation algorithms. Metaheuristics give a “good” result within an “acceptable” time. When developing a new metaheuristic algorithm, researchers usually use only their intuition and test results to verify the efficiency of the algorithm, comparing it to the efficiency of other algorithms. However, it may also be necessary to analyze the search operators of the algorithms for deeper investigation. The fitness landscape is a tool for that purpose, describing the possible states of the search space, the neighborhood operator, and the fitness function. The goal of fitness landscape analysis is to measure the complexity and efficiency of the applicable operators. The paper aims to investigate the fitness landscape of a complex vehicle routing problem. The efficiency of the following operators is investigated: 2-opt, order crossover, partially matched crossover, cycle crossover. The results show that the most efficient one is the 2-opt operator. Based on the results of fitness landscape analysis, we propose a novel traveling salesman problem genetic algorithm optimization variant where the edges are the elementary units having a fitness value. The optimal route is constructed from the edges having good fitness value. The fitness value of an edge depends on the quality of the container routes. Based on the performed comparison tests, the proposed method significantly dominates many other optimization approaches.

An efficient parallel genetic algorithm solution for vehicle routing problem in cloud implementation of the intelligent transportation systems

A novel parallelization method of genetic algorithm (GA) solution of the Traveling Salesman Problem (TSP) is presented. The proposed method can considerably accelerate the solution of the equivalent TSP of many complex vehicle routing problems (VRPs) in the cloud implementation of intelligent transportation systems. The solution provides routing information besides all the services required by the autonomous vehicles in vehicular clouds. GA is considered as an important class of evolutionary algorithms that can solve optimization problems in growing intelligent transport systems. But, to meet time criteria in time-constrained problems of intelligent transportation systems like routing and controlling the autonomous vehicles, a highly parallelizable GA is needed. The proposed method parallelizes the GA by designing three concurrent kernels, each of which running some dependent effective operators of GA. It can be straightforwardly adapted to run on many-core and multi-core processors. To best use the valuable resources of such processors in parallel execution of the GA, threads that run any of the triple kernels are synchronized by a low-cost switching mechanism. The proposed method was experimented for parallelizing a GA-based solution of TSP over multi-core and many-core systems. The results confirm the efficiency of the proposed method for parallelizing GAs on many-core as well as on multi-core systems.

A Generic Spatiotemporal Scheduling for Autonomous UAVs: A Reinforcement Learning-Based Approach

Considerable attention has been given to leverage a variety of smart city applications using unmanned aerial vehicles (UAVs). The rapid advances in artificial intelligence can empower UAVs with autonomous capabilities allowing them to learn from their surrounding environment and act accordingly without human intervention. In this paper, we propose a spatiotemporal scheduling framework for autonomous UAVs using reinforcement learning. The framework enables UAVs to autonomously determine their schedules to cover the maximum of pre-scheduled events spatially and temporally distributed in a given geographical area and over a pre-determined time horizon. The designed framework has the ability to update the planned schedules in case of unexpected emergency events. The UAVs are trained using the Q-learning (QL) algorithm to find effective scheduling plan. A customized reward function is developed to consider several constraints especially the limited battery capacity of the flying units, the time windows of events, and the delays caused by the UAV navigation between events. Numerical simulations show the behavior of the autonomous UAVs for various scenarios and corroborate the ability of QL to handle complex vehicle routing problems with several constraints. A comparison with an optimal deterministic solution is also provided to validate the performance of the learning-based solution.

VeRoViz: A Vehicle Routing Visualization Toolkit

VeRoViz is an open-source vehicle routing visualization package, consisting of both Python and web-based components. It was developed to streamline the workflow for vehicle routing researchers by simplifying and automating many of the tedious tasks associated with generating realistic test problems. VeRoViz also provides new functionality to produce customizable visualizations of complex vehicle routing problems. These visualization tools -- including Gantt charts, static maps, and dynamic 3D videos -- assist researchers in validating models and communicating results. Additionally, a comprehensive collection of utility functions within VeRoViz provide researchers with useful tools to assess features of their problems. This paper provides an overview of VeRoViz and highlights the flexibility and ease-of-use of the toolkit.

Workstation-oriented distribution optimization of shipbuilding materials

The optimization of material distribution is of great importance on shipbuilding project, which determines whether the production capacity of the ship is fully embodied. A workstation-oriented material distribution problem is formulated with reference to the production characteristics of shipyards. This problem can be considered as a complex vehicle routing problem (VRP) with capacity constraints, time windows and multiple distribution centers. In order to minimize the impact of distribution problems on production, a multi-population genetic algorithm (MPGA) that can minimize the sum of earliness and tardiness penalties is proposed in this paper. The proposed algorithm looks for near-optimal solutions for assigning distribution tasks and optimizing vehicle routing. Then, the evaluation of the solutions generated with MPGA is achieved with a priority-based heuristic algorithm. Simulation results of different cases show that the proposed MPGA allows logistics distribution system to operate more efficiently and solutions can be improved by 71% on average compared to those obtained with the traditional priority rule method.

Vehicle routing problems for last mile distribution after major disaster

This study is dedicated to a complex Vehicle Routing Problem (VRP) applied to the response phase after a natural disaster. Raised by the last mile distribution of relief goods after earthquakes, it is modelled as a rich VRP involving a heterogeneous fleet of vehicles, multiple trips, multiple depots, and vehicle-site dependencies. The proposed method is a generic hybrid heuristic that uses a Set Partitioning formulation to add memory to a Multi-Start Iterated Local Search framework. To better fit the requirements of last mile distribution, the algorithm has been developed in partnership with members of the International Charter on Space and Major Disasters and has been evaluated on real scenarios from Port-au-Prince earthquake. The heuristic quickly computes efficient routes while determining the number of required vehicles and the subset of depots to be used. Moreover, the computational results show that the proposed method is also competitive compared to the state of the art heuristics on closely related problems found in industrial distribution.

Finding optimal solutions for vehicle routing problem with pickup and delivery services with time windows: A dynamic programming approach based on state–space–time network representations

Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). This paper first proposes a new time-discretized multi-commodity network flow model for the VRPPDTW based on the integration of vehicles’ carrying states within space–time transportation networks, so as to allow a joint optimization of passenger-to-vehicle assignment and turn-by-turn routing in congested transportation networks. Our three-dimensional state–space–time network construct is able to comprehensively enumerate possible transportation states at any given time along vehicle space–time paths, and further allows a forward dynamic programming solution algorithm to solve the single vehicle VRPPDTW problem. By utilizing a Lagrangian relaxation approach, the primal multi-vehicle routing problem is decomposed to a sequence of single vehicle routing sub-problems, with Lagrangian multipliers for individual passengers’ requests being updated by sub-gradient-based algorithms. We further discuss a number of search space reduction strategies and test our algorithms, implemented through a specialized program in C++, on medium-scale and large-scale transportation networks, namely the Chicago sketch and Phoenix regional networks.

ROUTING PROBLEMS BASED ON HILS SYSTEM PLATFORM

Background: The logistic systems are very complex socio-technic al systems. In this paper the proposal of application of the hierarchical multi-layers sys tem platform HILS approach for the solution of the complex vehicle routing problems is presented. The interactive syst em functional structure was proposed which by intel ligent dedicated inter-layers interactions enables the professional solutions of these practical problems. To illustrat e these capabilities the complex example of the real-time VRP-SPD-TW routing problem was presented in which upper layers offers the context-related real-time updating network specific ations that stimulates the adequate routing paramet ers and specifications updating for problem solution in opt imization layer. At the bottom dispatching control layer the DISCON (Dispatching CONtrol) method from public transport was adopted to logistics applications in which the a ctual routing is treated as obligatory reference schedule to be stab ilized. The intelligence aspects are related among others to HILS based decomposition, context-related trade-offs between r outing modifications and corrective dispatching con trol capabilities e.g. priority or route guidance actions. Methods: Decomposition of the vehicle routing problem for t he HILS layers tasks creating the ILS system hierar chical structure. Dedicated solution method for the VRP-SP D-TW routing problem. The recognition of the control preferences structure by AHP-Entropy methods. DISCON and PIACON multi-criteria interacting control methods. Results: Original formulation and solution of the vehicle r outing problem by system-wide approach with essential practical advantages: consistency, lack of redundan cy, essential reduction of dimension, dedicated for mulation, multi- criteria approach, exploration of the integration a nd intelligence features supported by the intellige nt PIACON-DISCON methods control activities Conclusions: The presented proposal creates the professional ap proach to the solution of the crucial problems in l ogistics systems with the implementation of modern tools and enabling technologies.

A Multi-Objective Model For A Multi-Period Distribution Management Problem
 

The problems arising in commercial distribution are complex and involve several players and decision levels. One important decision is relatedwith the design of the routes to distribute the products, in an efficient and inexpensive way.This article deals with a complex vehicle routing problem that can beseen as a new extension of the basic vehicle routing problem. The proposed model is a multi-objective combinatorial optimization problemthat considers three objectives and multiple periods, which models in a closer way the real distribution problems. The first objective is costminimization, the second is balancing work levels and the third is amarketing objective. An application of the model on a small example, with5 clients and 3 days, is presented. The results of the model show the complexity of solving multi-objective combinatorial optimization problems and the contradiction between the several distribution management objective.

A food distribution model for famine relief

Many of the problems encountered by the urgency of need to deliver food to famine relief area arose further complicated distribution problems because there were neither inventory systems in place nor plans for transporting goods to these regions. This study develops an effective distribution model for determining optimal patterns of food supply and inventory allocation for famine relief area. This research addresses the formulation of those complex vehicle routing problems incorporating inventory allocation and optimal distribution based on minimizing the amount of pains and starving instead of travel distance or time. Also, we have developed computer programs for each step of approaches and have shown the results of sample run for North Korea famine relief problem. It was known that the proposed model was a very acceptable for the inventory allocation and vehicle routing problems.