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Traditional vehicular edge computing research usually ignores the mobility of vehicles, the dynamic variability of the vehicular edge environment, the large amount of real‐time data required for vehicular edge computing, the limited resources of edge servers, and collaboration issues. In response to these challenges, this article proposes a vehicular edge computing optimization scheme based on the Lyapunov function and Deep Reinforcement Learning. In this solution, this article uses Digital Twin technology (DT) to simulate the vehicular edge environment. The edge server DT is used to simulate the vehicular edge environment under the edge server, and the base station DT is used to simulate the entire vehicular edge system environment. Based on the real‐time data obtained from DT simulation, this paper defines the Lyapunov function to simplify the migration cost of vehicle tasks between servers into a multi‐objective dynamic optimization problem. It solves the problem by applying the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm. Experimental results show that compared with other algorithms, this scheme can effectively optimize the allocation and collaboration of vehicular edge computing resources and reduce the delay and energy consumption caused by vehicle task processing. [ABSTRACT FROM AUTHOR]

The emergence of electric vehicles in distribution and logistics activities has brought significant benefits due to their unique characteristics, such as energy-efficient and lower carbon emissions. In the perspective of vehicle routing problem, electric vehicles pose challenging constraints regarding the limited battery capacity, and thus their traveling ranges, and the availability of charging stations. In this paper, we propose a model of the fleet electric vehicle routing problem (EVRP) with soft time windows, where a mixed integer linear programming framework is implemented in model formulation. The objective of mathematical programming is to minimize the total operational cost, which consists of a fixed cost, a traveling cost, a battery charging cost, and probably a penalty cost due to time window violation. We implement our model in two simple cases, namely homogeneous and heterogeneous fleets EVRPs, characterized by loading and battery capacities. Each case consists of one depot, five customers, two electric vehicles, and two charging stations. Optimal routes are obtained using the well-known branch-and-bound method under Lingo 17.0. It is found that the existence of charging stations may affect the routes selection and the implementation of soft time windows rather than hard time windows has been proven to increase the feasibility of routing problem. [ABSTRACT FROM AUTHOR]

In the realm of supply chain logistics, the Multi-Depot Multi-Supplier Vehicle Routing Problem (MDMSVRP) poses a significant challenge in optimizing the transportation process to minimize costs and enhance operational efficiency. This problem involves determining the most cost-effective routes for a fleet of vehicles to deliver goods from multiple suppliers to multiple depots, considering various constraints and non-linear relationships. The routing problem (RP) is a critical element of many logistics systems that involve the routing and scheduling of vehicles from a depot to a set of customer nodes. One of the most studied versions of the RP is the Vehicle Routing Problem with Time Windows (VRPTW), in which each customer must be visited at certain time intervals, called time windows. In this paper, it is considered that there are multiple depots (supply centers) and multiple suppliers, along with a fleet of vehicles. The goal is to efficiently plan routes for these vehicles to deliver goods from the suppliers to various customers while considering relaxed time windows. This research is intended to establish a new relaxation scheme that relaxes the time window constraints in order to lead to feasible and good solutions. In addition, this study develops a discrete optimization model as an alternative model for the time-dependent VRPTW involving multi-suppliers. This research also develops a metaheuristic algorithm with an initial solution that is determined through time window relaxation. [ABSTRACT FROM AUTHOR]

Researchers have been investigating solutions to the Vehicle Routing Problem (VRP) as a practical means of tackling the rising transportation costs in businesses. The goal is to develop innovative methods that minimize shipping expenses and maximize profits. The transportation of Hazardous Materials (HazMat) is particularly complex and has attracted significant attention from scholars. When designing logistics networks for HazMat, factors such as time window constraints, uncertainties, vehicle capacity, and mileage capacity in sub-tours need to be considered to minimize overall transportation and pollution costs. This study presents a mathematical model for vehicle routing of HazMat from economic, route sensitivity, and uncertainty perspectives. An optimization approach using a hybrid Genetic and Simulated Annealing (SA) algorithm is then applied to solve the problem. The study includes numerous numerical examples and sensitivity analyses to demonstrate the model's efficacy. The results indicate that an increase in the route sensitivity coefficient leads to an increase in the objective function. Additionally, the effect of demand on the objective function generally increases, although there are instances where it decreases. [ABSTRACT FROM AUTHOR]

Providing first aid and other supplies (e.g., epi‐pens, medical supplies, dry food, water) during and after a disaster is always challenging. The complexity of these operations increases when the transportation, power, and communications networks fail, leaving people stranded and unable to communicate their locations and needs. The advent of emerging technologies like uncrewed autonomous vehicles can help humanitarian logistics providers reach otherwise stranded populations after transportation network failures. However, due to the failures in telecommunication infrastructure, demand for emergency aid can become uncertain. To address the challenges of delivering emergency aid to trapped populations with failing infrastructure networks, we propose a novel robust computational framework for a two‐echelon vehicle routing problem that uses uncrewed autonomous vehicles (UAVs), or drones, for the deliveries. We formulate the problem as a two‐stage robust optimization model to handle demand uncertainty. Then, we propose a column‐and‐constraint generation approach for worst‐case demand scenario generation for a given set of truck and UAV routes. Moreover, we develop a decomposition scheme inspired by the column generation approach to generate UAV routes for a set of demand scenarios heuristically. Finally, we combine the decomposition scheme within the column‐and‐constraint generation approach to determine robust routes for both trucks (first echelon vehicles) and UAVs (second echelon vehicles), the time that affected communities are served, and the quantities of aid materials delivered. To validate our proposed algorithms, we use a simulated dataset that aims to recreate emergency aid requests in different areas of Puerto Rico after Hurricane Maria in 2017. [ABSTRACT FROM AUTHOR]

This study focuses on the delivery routing problem faced by a transport company located in Phuket, Thailand. The goal of this study is to find a daily optimum route in order to minimize the total transportation cost, which comprises fixed costs associated with vehicle rental and variable costs calculated based on factors of travel distance, fuel prices, and fuel consumption. The complexity of this problem is compounded by the fact that customer demand often exceeds a vehicle capacity, in terms of weight and volume. In addition, delivery must be made within specific time windows. To tackle this issue, the delivery routing problem is classified as a multi-trip capacitated vehicle routing problem with time window (MTCVRPTW). Since the problem is NP-hard, an application of metaheuristic is more practical to determine the delivery routing of the company within a reasonable computing time. In this study, Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithm are applied to solve MTCVRPTW. The numerical results show that DE provides better solution quality compared to those obtained from PSO and company current practices. [ABSTRACT FROM AUTHOR]

Background: Milkrun-based material supply plays an important role in the automotive industry, as it is a material supply concept where high efficiency can be achieved. When implementing milkrun-based material supply, the milkrun supply of the production plant often has to be integrated with an existing warehouse material handling system, which frequently leads to a less efficient solution. Methods: In this paper, the author investigates the impact of a hub-based milkrun supply, where the collection processes in the component's warehouse and the distribution processes in the assembly plant are connected to a hub, which is responsible for the sequencing of component demands. After a systematic literature review, the paper introduces a novel mathematical model, which makes it possible to describe the conventional milkrun-based solutions, the hub-based milkrun solutions, and to compare them in terms of the length of transportation routes, transportation time, total service time, and virtual emission points of view. Results: The scenario analysis demonstrates that the hub-based solution can lead to an efficiency improvement of about 13% in total service time, 23% savings in transportation time, and 45% savings in transportation time in the component's warehouse. Conclusions: The article's findings suggest that implementing a hub-based milkrun system in automotive material supply can significantly enhance efficiency. The described approach could lead to more streamlined operations in production plants by optimizing the integration of milkrun systems. [ABSTRACT FROM AUTHOR]

Background: This research aims to solve a home healthcare vehicle routing problem (HHCVRP) model that considers the social aspect of sustainability and will be implemented in smart cities. In addition to the dynamism and uncertainty caused by variations in the patient's condition, the proposed model considers parameters and variables that enhance its practicability, such as assuming different levels of patient importance (priority). Methods: The model was solved using a metaheuristic algorithm approach via the Ant Colony Optimization algorithm and the Non-Dominated Sorting technique due to the ability of such a combination to work out with dynamic models with uncertainties and multi-objectives. Results: This study proposes a novel mathematical model by integrating body sensors on patients to keep updating their conditions and prioritizing critical conditions in service. The sensitivity analysis demonstrates that using a heart rate sensor improves service quality and patient satisfaction without affecting the energy consumed. In addition, quality costs are increased if the importance levels of patients increase. Conclusions: The suggested model can assist healthcare practitioners in tracking patients' health conditions to improve the quality of service and manage workload effectively. A trade-off between patient satisfaction and service provider satisfaction should be maintained. [ABSTRACT FROM AUTHOR]

Vehicle routing problem (VRP) is a classic NP-hard optimization problem. It is generally accepted that an optimized routing scheme can cause huge difference in the cost in all stages of transportation. Consequently, the VRP has evoked interest among the researchers of the field. Usually, a metaheuristic or an evolutionary algorithm is used for the solution of a VRP variant. In the last years, a number of swarm intelligence algorithms have been used for the solution of the problem. Initially, the two most classic swarm intelligence algorithms, the Ant Colony Optimization and the Particle Swarm Optimization, were used for the solution of this kind of problems. However, in the last years, more and more researchers solved the problem using a different swarm intelligence algorithm. In this paper, we focused in the presentation and analysis of the swarm intelligence algorithms that have been used for the solution of the problem. We give the advantages and disadvantages of each method, we focus in those ones that produced the best results in difficult VRPs and we present directions for the future of this kind of algorithms for the solution of a VRP variant. [ABSTRACT FROM AUTHOR]

Approximation of the optimal tour length in a Euclidean traveling salesman problem (TSP) has been studied by many researchers. In a previous study, we used the standard deviation in random tour lengths to approximate the optimal tour length in both Euclidean and non‐Euclidean TSPs and we obtained good estimates. In this paper, we show that the strong power‐law relationship between the standard deviation in random feasible solution values and the optimal solution value also holds for other Euclidean and near‐Euclidean combinatorial optimization problems like the minimum spanning tree (MST) and maximum weight matching (MWM) problems. We then enhance the estimation ability of the model by considering a second predictor: the mean in random feasible solution values. Experimental results show that by using the mean, standard deviation, and randomization, we can accurately predict the optimal solution values for the TSP, MST, MWM, and the capacitated vehicle routing problem (VRP). [ABSTRACT FROM AUTHOR]

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The swap-body vehicle routing problem (SBVRP) represents a specialized extension of the traditional vehicle routing problem (VRP), incorporating additional practical complexities. Effective fuel consumption management and the scheduling of multiple vehicle trips are pivotal strategies for reducing costs and ensuring the sustainability of distribution systems. In response to the acceleration of urbanization, the rising demand for logistics, and the deteriorating living environment, we introduce an SBVRP considering fuel consumption and multiple trips to enable greener, cheaper, and more efficient delivery methods. To tackle the SBVRP, we propose a hybrid multi-population genetic algorithm enhanced with local search techniques to explore various areas of the search space. Computational experiments demonstrate the efficiency of the proposed method and the effectiveness of its components. The algorithm developed in this study provides an optimized solution to the VRP, focusing on achieving environmentally friendly, sustainable, and cost-effective transportation by reducing energy consumption and promoting the rational use of resources. [ABSTRACT FROM AUTHOR]

The most common variant of VRP of Iraqi big-scale enterprises is Capacitated Vehicle Routing Problems (CVRP) where such enterprises have several dispersed affiliates. This paper presents an application-database 3-stages customizable framework based on urban asymmetric road network by including Sweep clustering, PostgreSQL Dijkstra and saving heuristics for routing applied on actual dataset considering CVRP for an enterprise composed of a single depot and 91 nodes in Baghdad. The solution was built in a generalizable flexible architecture applicable for other organizations. It also demonstrates utilizing parallel-processing techniques for speed up. Improved versions of Clarke-Wright and Parker-Holmes algorithms were used and achieved improvement of (15.7 and 9.03) times in asymmetric clustering scenario, 1.57 times in case of asymmetric non-clustering scenario, and 1.678 in symmetric implementation of the cost minimization satisfied by their corresponding original bases. The study includes implementation details, results analysis and provides insightful information to operation-researches practitioners especially in Iraq. [ABSTRACT FROM AUTHOR]

Traveling has become an essential need for people to fulfill their psychological needs. Generally, tourists want to visit a new destination for several days. To get route guidance (visiting schedule), tourists usually use the services of a travel agent, but this service cannot be tailored to the tourist's wishes. In previous research, many have concluded that one-day and multi-day tourist routes are analogous to the Traveling Salesman Problem (TSP). However, this study has yet to emphasize daily optimization for multi-day routes because daily routes are only cut based on time constraints. One possible approach to optimize tourist routes per day is the analogy of solving Vehicle Routing Problem (VRP). Therefore, in this research, we propose a new model that combines the Whale Optimization Algorithm (WOA) with a Variable Neighborhood Search (VNS) strategy known as WOA-VNS to recommend multi-day tourist routes, which is analogous to the VRP to overcome deficiencies with the TSP analogy. The number of vehicles corresponds to the number of days tourists visit, thus ensuring optimal daily routes. The system considers user preferences for popularity, ratings, and time using the concept of Multi-Attribute Utility Theory (MAUT). The MAUT value are used as WOA-VNS fitness values. Five metrics (fitness value, number of Point of Interest (POI)s, trip duration, cost, and rating attributes) were tested on five random POIs. Results show the VRP analog is more suitable for multi-day routes, with WOA-VNS-VRP outperforming WOA-VNS-TSP and conventional algorithms such as Ant Colony Optimization (ACO), Genetic Algorithm (GA), and Bat Algorithm (BA), achieving value average fitness of 0.8570, on the tourist location dataset in Yogyakarta. [ABSTRACT FROM AUTHOR]

In the realm of urban logistics, optimizing vehicle routes for varied cargo types—including refrigerated, fragile, and standard cargo—poses significant challenges amid complex urban infrastructures and heterogeneous vehicle capacities. This research paper introduces a novel model for the multi-type capacitated vehicle routing problem (MT-CVRP) that harnesses an advanced ant colony optimization algorithm, dubbed Lévy-EGACO. This algorithm integrates Lévy flights and elitist guiding principles, enhancing search efficacy and pheromone update processes. The primary objective of this study is to minimize overall transportation costs while optimizing the efficiency of intricate route planning for vehicles with diverse load capacities. Through rigorous simulation experiments, we corroborated the validity of the proposed model and the effectiveness of the Lévy-EGACO algorithm in optimizing urban cargo transportation routes. Lévy-EGACO demonstrated a consistent reduction in transportation costs, ranging from 1.8% to 2.5% compared to other algorithms, across different test scenarios following base data modifications. These findings reveal that Lévy-EGACO substantially improves route optimization, presenting a robust solution to the challenges of MT-CVRP within urban logistics frameworks. [ABSTRACT FROM AUTHOR]

The rapid development of electric vehicles (EVs) and unmanned aerial vehicles (UAVs) provides new ways for personnel search and material distribution during emergency periods. This paper proposes an EV-UAV joint rescue system, in which the UAVs use the EVs as charging and maintenance base stations to provide various services for the objects to be rescued, and the EVs can use distributed generations to obtain diversified electricity supply, which improves the adaptability and endurance level of the system in emergencies. The coordinated scheduling model of the EV-UAV system is established in the mixed-integer linear programming (MILP) formulation, which considers factors including electricity consumption, electricity replenishment, loading capacity, distribution route, and distribution time window of the EVs and the UAVs. Case studies verify the validity of the model proposed, compare the EV-UAV and ground vehicle (GV)-UAV rescue systems, and illustrate the technical characteristics and application potential of the EV-UAV system in emergency assistance.

In warehouses, routing decisions for vehicles are highly related to the schedule of docks and loading operations. To mind the gap that most existing studies consider the routing decisions solely, this study investigates the vehicle routing problem with time windows and loading scheduling (VRPTW-LS). In this problem, the loading schedules at the loading docks and the visiting sequences for vehicles are determined to minimise the total travelled distance. To solve this problem, an adaptive large neighbourhood search algorithm, embedded with a tailored solution representation and an efficient feasibility check mechanism, is developed. In addition, the results of extensive computational experiments verify the effectiveness and efficiency of the proposed algorithm, and some analyses are conducted to obtain managerial insights. [ABSTRACT FROM AUTHOR]

In modular integrated construction (MiC), the resource allocation problem (RAP) adopted by construction sites and vehicle routing problem (VRP) adopted by logistics companies are highly interdependent. However, this interdependence has been overlooked in the literature. Thus, the plans determined by each problem cannot be achieved practically. Moreover, there is no existing VRP model suitable for the MiC application. This study aims to propose a VRP model suitable for MiC, investigate the interdependence between the RAP and proposed VRP model, and develop a blockchain system to secure information sharing between the RAP and VRP. The first two objectives are achieved by developing a coordinated system formulated as a leader-follower Stackelberg game model (LFSGM). This model is presented as a bi-level optimisation model and solved using a nested ant colony optimisation-based algorithm. The effectiveness of the LFSGM is validated using a real case study. The results show that using the traditional approach (i.e. a separate RAP and proposed VRP) succeeds in providing a plan for the construction sites but not for the logistics company. In contrast, the LFSGM offers applicable plans for both the construction sites and logistics company. Lastly, some managerial implications are identified and discussed. [ABSTRACT FROM AUTHOR]

This research article presents a low-carbon and environmental protection viewpoint that combines the idea of a cold chain. In this case, the optimisation problem Food distribution system is solved by developing a low-carbon Routing Problem (LRP) model. The researchers seek to identify the minimum costs and carbon emission costs while Carbon tax policies are also presented to examine their effects on carbon emissions. The model is solved by using a hybrid genetic algorithm with heuristic rules, after which the algorithm’s efficiency is tested with a globally recognised Proudhon data set. The Cycle evolutionary algorithm can quickly and effectively seek the optimal solution of the model. We combine two kinds of operators, inversion mutation and insertion mutation, in the genetic algorithm to form the combined operator of a hybrid genetic algorithm. Then, the approximate optimal solution is obtained. Meanwhile, many experiments are carried out by setting different carbon tax values and the critical interval values of carbon emissions and optimal. A case study from a third-party logistics company is used to test the applicability of the model in the real world. Results showed that the model and carbon tax policies will benefit business operations and the environment.

Adaptive iterated local search (AILS) is a recently proposed metaheuristic paradigm that focuses on adapting the diversity control of iterated local search by online learning mechanisms. It has been successfully applied to the capacitated vehicle routing problem (CVRP) and the heterogeneous vehicle routing problem. Hybridizing it with path relinking (PR) has further improved the intensification of the method for the CVRP, providing outstanding results. However, the potential of this metaheuristic has not yet been investigated on other combinatorial optimization problems, such as location problems. In this paper, we develop a version of AILS for the maximal covering location problem (MCLP). This problem consists of locating a number of facilities to maximize the covered customer demand, where a given facility location can meet the demand of customers located within a coverage radius. Experiments on large‐scale instances of the MCLP indicate that AILS hybridized with PR, called AILS‐PR, outperforms the state‐of‐the‐art metaheuristic. [ABSTRACT FROM AUTHOR]

The past few years of the COVID‐19 pandemic outbreak have shown that optimal management of medical specimens is a key aspect of healthcare logistics, both for addressing the delivery of perishable items such as vaccines, and for ensuring the timely analysis of swabs and samples. Accordingly, recent optimization literature described the problem of optimal collection and delivery of medical specimens, modeled as a multitrip vehicle routing problem with time windows and a completion time objective function. Aiming to achieve good‐quality solutions in short computational times, this work describes a hybrid approach, combining a matheuristic construction phase with an adaptive large neighborhood search (ALNS). Our matheuristic relies on a clustering algorithm to yield subsets of the medical specimens that are optimally served by single vehicles of the fleet. The solutions of the matheuristic phase serve as starting points for the ALNS intensification phase. Extensive experimentation on both new and established benchmark problem instances shows that our hybrid method is able to match the optimality of the state of the art on small instances and outperforms the existing exact method by one order of magnitude on larger problems. [ABSTRACT FROM AUTHOR]

Local search (LS) algorithms are efficient metaheuristics to solve combinatorial problems. The performance of LS highly depends on the neighborhood exploration of solutions. Many methods have been developed over the years to improve the efficiency of LS on different problems of operations research. In particular, the exploration strategy of the neighborhood and the exclusion of irrelevant neighboring solutions are design mechanisms that have to be carefully considered when tackling NP‐hard optimization problems. An MOEA/D framework including an LS‐based mutation and knowledge discovery mechanisms is the core algorithm used to solve a bi‐objective vehicle routing problem with time windows (bVRPTW) where the total traveling cost and the total waiting time of drivers have to be minimized. We enhance the classical LS exploration strategy of the neighborhood from the literature of scheduling and propose new metrics based on customer distances and waiting times to reduce the neighborhood size. We conduct a deep analysis of the parameters to give a fine tuning of the MOEA/D framework adapted to the LS variants and to the bVRPTW. Experiments show that the proposed neighborhood strategies lead to better performance on both Solomon's and Gehring and Homberger's benchmarks. [ABSTRACT FROM AUTHOR]

For many variants of vehicle routing and scheduling problems solved by a branch-price-and-cut (BPC) algorithm, the pricing subproblem is an elementary shortest-path problem with resource constraints (SPPRC) typically solved by a dynamic-programming labeling algorithm. Solving the SPPRC subproblems consumes most of the total BPC computation time. Critical to the performance of the labeling algorithms and thus the BPC algorithm as a whole is the use of effective dominance rules. Classical dominance rules rely on a pairwise comparison of labels and have been used in many labeling algorithms. In contrast, partial dominance describes situations where several labels together are needed to dominate another label, which can then be safely discarded. In this work, we consider SPPRCs, where a linear tradeoff describes the relationship between two resources. We derive a unified partial dominance rule to be used in ad hoc labeling algorithms for solving such SPPRCs as well as insights into its practical implementation. We introduce partial dominance for two important variants of the vehicle routing problem, namely the electric vehicle routing problem with time windows with a partial recharge policy and the split-delivery vehicle routing problem with time windows (SDVRPTW). Computational experiments show the effectiveness of the approach, in particular for the SDVRPTW, leading to an average reduction of 20% of the total BPC computation time, with savings of 30% for the more difficult instances requiring more than 600 s of computation time. [ABSTRACT FROM AUTHOR]

[Display omitted] • An integration of vehicle routing problem and life cycle assessment was adopted. • Derived leachate treatment contributes significantly to greenhouse gas emissions. • Centralized vehicle management decreases the greenhouse gas emissions. • Waste separation decreases greenhouse gas emissions significantly. • Vehicle electrification holds big potentials for greenhouse gas reduction. This study presents a comprehensive analysis of greenhouse gas (GHG) emissions associated with waste transfer and transport, incorporating derived leachate treatment—a factor often overlooked in existing research. Employing an integration model of life cycle assessment and a vehicle routing problem (VRP) methods, we evaluated the GHG reduction potential of waste transfer and transport system. Two Chinese counties with different topographies and demographics were selected, yielding 80 scenarios that factored in waste source separation as well as vehicle capacity, energy sources, and routes. The functional unit (FU) is transferring and transporting 1 tonne waste and treating derived leachate. The GHG emissions varied from 12 to 39 kg CO 2 equivalent per FU. Waste source separation emerged as the most impactful mitigation strategy, not only for the studied system but for an integrated waste management system. Followings are the use of larger capacity vehicles and electrification of the vehicles. These insights are instrumental for policymakers and stakeholders in optimizing waste management systems to reduce GHG emissions. [ABSTRACT FROM AUTHOR]

In recent years, the application of Neural Combinatorial Optimization (NCO) techniques in Combinatorial Optimization (CO) has emerged as a popular and promising research direction. Currently, there are mainly two types of NCO, namely, the Constructive Neural Combinatorial Optimization (CNCO) and the Perturbative Neural Combinatorial Optimization (PNCO). The CNCO generally trains an encoder-decoder model via supervised learning to construct solutions from scratch. It exhibits high speed in construction process, however, it lacks the ability for sustained optimization due to the one-shot mapping, which bounds its potential for application. Instead, the PNCO generally trains neural network models via deep reinforcement learning (DRL) to intelligently select appropriate human-designed heuristics to improve existing solutions. It can achieve high-quality solutions but at the cost of high computational demand. To leverage the strengths of both approaches, we propose to hybrid the CNCO and PNCO by designing a hybrid framework comprising two stages, in which the CNCO is the first stage and the PNCO is the second. Specifically, in the first stage, we utilize the attention model to generate preliminary solutions for given CO instances. In the second stage, we employ DRL to intelligently select and combine appropriate algorithmic components from improvement pool, perturbation pool, and prediction pool to continuously optimize the obtained solutions. Experimental results on synthetic and real Capacitated Vehicle Routing Problems (CVRPs) and Traveling Salesman Problems(TSPs) demonstrate the effectiveness of the proposed hybrid framework with the assistance of automated algorithm design. [ABSTRACT FROM AUTHOR]

We present machine learning (ML) methods for automatically selecting a "best" performing fast algorithm for the capacitated vehicle routing problem (CVRP) with unit demands. Algorithm selection is to automatically choose among a portfolio of algorithms the one that is predicted to work best for a given problem instance, and algorithm configuration is to automatically select algorithm's parameters that are predicted to work best for a given problem instance. We present a framework incorporating both algorithm selection and configuration for a portfolio that includes the automatically configured "Sweep Algorithm," the first generated feasible solution of the hybrid genetic search algorithm, and the Clarke and Wright algorithm. The automatically selected algorithm is shown here to deliver high‐quality feasible solutions within very small running times making it highly suitable for real‐time applications and for generating initial feasible solutions for global optimization methods for CVRP. These results bode well to the effectiveness of utilizing ML for improving combinatorial optimization methods. [ABSTRACT FROM AUTHOR]

The order scheduling and rack sequencing problem deals with the order picking process in robotic mobile fulfillment systems: automated guided vehicles lift and transport movable storage racks to picking stations to supply items requested by customer orders which are put together in cardboard boxes on a workbench of limited capacity. To efficiently operate the station, the sequence in which racks visit the station one after another and the intervals at which customer orders are scheduled must be coordinated. We present a dynamic programming algorithm for the order scheduling and rack sequencing problem at a single picking station minimizing the number of rack visits. Despite monolithic mixed integer linear programming formulations, our approach appears to be the first combinatorial solution method for the problem in literature. A computational study demonstrates the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

The commodity constrained split delivery vehicle routing problem (C‐SDVRP) is a routing problem where customer demands are composed of multiple commodities. A fleet of capacitated vehicles must serve customer demands in a way that minimizes the total routing costs. Vehicles can transport any set of commodities and customers are allowed to be visited multiple times. However, the demand for a single commodity must be delivered by one vehicle only. In this work, we developed a heuristic with a performance guarantee to solve the C‐SDVRP. The proposed heuristic is based on a set covering formulation, where the exponentially‐many variables correspond to routes. First, a subset of the variables is obtained by solving the linear relaxation of the formulation by means of a column generation approach which embeds a new pricing heuristic aimed to reduce the computational time. Solving the linear relaxation gives a valid lower bound used as a performance guarantee for the heuristic. Then, we devise a restricted master heuristic to provide good upper bounds: the formulation is restricted to the subset of variables found so far and solved as an integer program with a commercial solver. A local search based on a mathematical programming operator is applied to improve the solution. We test the heuristic algorithm on benchmark instances from the literature. The comparison with the state‐of‐the‐art heuristics for solving the C‐SDVRP shows that our approach significantly improves the solution time, while keeping a comparable solution quality and improving some best‐known solutions. In addition, our approach is able to solve large instances with 100 customers and six commodities, and also provides very good quality lower bounds. Furthermore, an instance of the C‐SDVRP can be transformed into a CVRP instance by simply duplicating each customer as many times as the requested commodities and by assigning as demand the demand of the single commodity. Hence, we compare heuristics for the C‐SDVRP against the state‐of‐the‐art heuristic for the Capacitated Vehicle Routing Problem (CVRP). The latter approach revealed to have the best performance. However, our approach provides solutions of comparable quality and has the interest of providing a performance guarantee. [ABSTRACT FROM AUTHOR]

Cold chain logistics requires low-temperature transportation, which consumes more energy and has higher distribution costs than ordinary logistics. Moreover, as the scale of cities continues to expand, traffic congestion is becoming more frequent. Therefore, it is particularly important to plan the distribution route reasonably. In this paper, we study the problem of cold chain logistics vehicle path planning based on travel time prediction. First of all, multiple connected routes with real-time changes in traffic conditions between customers in the road network were considered to describe the distribution scene. Second, a genetic algorithm-optimized backpropagation algorithm fused travel time predictions for road segments based on fixed detector technology and floating car technology to improve the accuracy of road segment travel time prediction. Then, based on the prediction of road segment travel time, a method for predicting the travel time of the route is proposed, and the actual road network is transformed into a travel time network for each customer. Finally, the vehicle routing problem in cold chain logistics was investigated using predicted travel time as input. This problem is formulated as a bi-objective model aimed at minimizing costs and carbon emissions. To address this problem, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) was proposed. The study provides support for cold chain logistics distribution companies to develop distribution strategies based on local environmental policies and their own operational conditions. [ABSTRACT FROM AUTHOR]

In recent years, the growing interest in environmental sustainability has led to Electric Vehicle Routing Problems (EVRPs) attracting more and more attention. EVRPs involve the use of electric vehicles, which have additional constraints, such as range and recharging time, compared to conventional Vehicle Routing Problems (VRPs). The complexity and dynamic nature of solving VRPs often lead to the introduction of Routing Policies (RPs), simple heuristics that incrementally build routes. However, manually designing efficient RPs proves to be a challenging and time-consuming task. Therefore, there is a pressing need to explore the application of hyper-heuristics, in particular Genetic Programming (GP), to automatically generate new RPs. Since this method has not yet been investigated in the literature in the context of EVRPs, this study explores the applicability of GP to automatically generate new RPs for EVRP. To this end, three RP variants (serial, semiparallel, and parallel) are introduced in this study, along with a set of domain-specific terminal nodes to optimise three criteria: the number of vehicles, energy consumption, and total tardiness. The experimental analysis shows that the serial variant performs best in terms of energy consumption and number of vehicles, while the parallel variant is most effective in minimising the total tardiness. A comprehensive analysis of the proposed method is conducted to determine its convergence properties and the impact of the proposed terminal nodes on performance and to describe several generated RPs. The results show that the automatically generated RPs perform commendably compared to traditional methods such as metaheuristics and exact methods, which usually require significantly more runtime. More specifically, depending on the scenario in which they are used, the generated RPs achieve results that are about 20%-37% worse compared to the best known results for the number of vehicles in almost negligible time, in just some milliseconds. [ABSTRACT FROM AUTHOR]

This note comments on the study of [Diri Kenger, Zülal, Çağrı Koç, and Eren Özceylan. 2020. "Integrated Disassembly Line Balancing and Routing Problem." International Journal of Production Research 58 (23): 7250–7268.] which studies an integrated disassembly line balancing and routing problem and develops two mixed integer linear programming (MILP) models and three mixed integer nonlinear programming (MINLP) models to handle five different scenarios, respectively. The purpose is twofold. First, we demonstrate that the two MILP models can be separated into two parallel subproblems whose optimal solutions can be combined to obtain the optimal solution of the original models. Second, we show that the three MINLP models can be linearised and propose two different linearisation techniques to reformulate them as equivalent MILP models. Computational results indicate that the linearised model outperforms the original nonlinear model in most cases. [ABSTRACT FROM AUTHOR]

In the realm of supply chain logistics, the Multi-Depot Multi-Supplier Vehicle Routing Problem (MDMSVRP) poses a significant challenge in optimizing the transportation process to minimize costs and enhance operational efficiency. This problem involves determining the most cost-effective routes for a fleet of vehicles to deliver goods from multiple suppliers to multiple depots, considering various constraints and non-linear relationships. The routing problem (RP) is a critical element of many logistics systems that involve the routing and scheduling of vehicles from a depot to a set of customer nodes. One of the most studied versions of the RP is the Vehicle Routing Problem with Time Windows (VRPTW), in which each customer must be visited at certain time intervals, called time windows. In this paper, it is considered that there are multiple depots (supply centers) and multiple suppliers, along with a fleet of vehicles. The goal is to efficiently plan routes for these vehicles to deliver goods from the suppliers to various customers while considering relaxed time windows. This research is intended to establish a new relaxation scheme that relaxes the time window constraints in order to lead to feasible and good solutions. In addition, this study develops a discrete optimization model as an alternative model for the time-dependent VRPTW involving multi-suppliers. This research also develops a metaheuristic algorithm with an initial solution that is determined through time window relaxation.

Abstract To effectively solve the reverse logistics distribution problem caused by the increasing number of scrapped parts in the automotive market, this study constructs a multi-trip green vehicle routing problem model with time windows by comprehensively considering the coordination between carbon dioxide emissions and cost efficiency. A hybrid adaptive genetic algorithm is proposed to solve this problem, featuring innovative improvements in the nearest neighbor rule based on minimum cost, adaptive strategies, bin packing algorithm based on the transfer-of-state equation, and large-scale neighborhood search. Additionally, to efficiently obtain location data for supplier factory sites in the distribution network, a coordinate extraction method based on image recognition technology is proposed. Finally, the scientific validity of this study is verified based on the actual case data, and the robust optimization ability of the algorithm is verified by numerical calculations of different examples. This research not only enriches the study of green vehicle routing problems but also provides valuable insights for the industry to achieve cost reduction, efficiency enhancement, and sustainable development in reverse logistics.

In recent years, the demand of express industry has increased rapidly, and the express industry is under increasing pressure. The unmanned aerial vehicle (UAV) delivery has become an effective supplement to vehicle delivery due to its low human cost, flexibility and convenience. However, UAVs are often limited by factors such as endurance and load capacity, requiring a low-cost and energy self-sustaining scheduling scheme for delivery and charging to support collaborative delivery of multiple UAVs. A two-stage self-sustaining multiple UAV cooperative delivery and charging scheduling scheme was proposed. The first stage aims at finding the delivery routes of UAVs to complete all delivery tasks in the region such that the number of UAVs was minimized under the energy and load capacity constraints of UAVs. The UAV delivery scheduling algorithm (UDSA) was proposed, and the approximation of UDSA was proved theoretically. The second stage aims to schedule the charging of UAVs with different arrival times to minimize the maximum charging completion time of all UAVs. An approximate UAV delivery scheduling algorithm (UCSA) was proposed to solve the problem. The simulation results show that, compared with the benchmark algorithm, UDSA can reduce the number of UAVs by 44.17% at most, and UCSA can reduce the maximum charging completion time by 18.87% at most.

The Vehicle Routing Problem (VRP) is a classic combinatorial optimization problem commonly encountered in the fields of transportation and logistics. This paper focuses on a variant of the VRP, namely the Vehicle Routing Problem with Stochastic Travel Cost (VRP-STC). In VRP-STC, the introduction of stochastic travel costs increases the complexity of the problem, rendering traditional algorithms unsuitable for solving it. In this paper, the GAT-AM model combining Graph Attention Networks (GAT) and multi-head Attention Mechanism (AM) is employed. The GAT-AM model uses an encoder–decoder architecture and employs a deep reinforcement learning algorithm. The GAT in the encoder learns feature representations of nodes in different subspaces, while the decoder uses multi-head AM to construct policies through both greedy and sampling decoding methods. This increases solution diversity, thereby finding high-quality solutions. The REINFORCE with Rollout Baseline algorithm is used to train the learnable parameters within the neural network. Test results show that the advantages of GAT-AM become greater as problem complexity increases, with the optimal solution generally unattainable through traditional algorithms within an acceptable timeframe. [ABSTRACT FROM AUTHOR]

Cost reduction and staff retention are important optimization objectives in home healthcare (HHC) systems. Home healthcare operators need to balance their objectives by optimizing resource use, service delivery and profits. Minimizing total travel distances to control costs is a common routing problem objective while minimizing total finishing time differences is a scheduling objective whose purpose is to enhance staff satisfaction. To optimize routing and scheduling, we propose mixed integer linear programming with a bi-objective function, which is a subset of the vehicle routing problem with time windows (VRPTWs). VRPTWs is a known NP-hard problem, and optimal solutions are very hard to obtain in practice. Metaheuristics offer an alternative solution to this type of problem. Our metaheuristic uses the simulated annealing algorithm and weighted sum approach to convert the problems to single-objective problems and is equipped with operators including swapping, moving, path exchange and ruin and recreate. The results show, firstly, that the algorithm can effectively find the Pareto front, and secondly, that minimizing total finishing time differences to balance the number of jobs per caretaker is an efficient way to tackle HHC scheduling. A statistical test shows that the algorithm can obtain the Pareto front with a lower number of weighted sum problems. [ABSTRACT FROM AUTHOR]

This document discusses the intersection of sustainability and digitalization in manufacturing companies, highlighting the challenges they face in addressing environmental and social impacts. The concept of Maintenance 4.0 is introduced as a way to enhance and advance maintenance processes using technologies such as the Industrial Internet of Things (IIoT), Augmented Reality (AR), Virtual Reality (VR), Big Data Analytics (BDA), and AI. The document also provides an overview of 13 articles included in a special issue on Maintenance 4.0 and sustainability, covering topics such as predictive maintenance, augmented reality, digital twins, and environmental considerations in maintenance activities. The authors emphasize the importance of Industry 4.0 technologies in transforming maintenance processes and supporting sustainable development goals. [Extracted from the article]

Vehicle routing problems (VRPs) are challenging problems. Many variants of the VRP have been proposed. However, few studies on VRP have combined robustness and just-in-time (JIT) requirements with uncertainty. To solve the problem, this paper proposes the just-in-time-based robust multiobjective vehicle routing problem with time windows (JIT-RMOVRPTW) for the assembly workshop. Based on the conflict between uncertain time and JIT requirements, a JIT strategy was proposed. To measure the robustness of the solution, a metric was designed as the objective. Afterwards, a two-stage nondominated sorting ant colony algorithm with deep reinforcement learning (NSACOWDRL) was proposed. In stage I, ACO combines with NSGA-III to obtain the Pareto frontier. Based on the model, a pheromone update strategy and a transfer probability formula were designed. DDQN was introduced as a local search algorithm which trains networks through Pareto solutions to participate in probabilistic selection and nondominated sorting. In stage II, the Pareto frontier was quantified in feasibility by Monte Carlo simulation, and tested by diversity-robust selection based on uniformly distributed weights in the solution space to select robust Pareto solutions that take diversity into account. The effectiveness of NSACOWDRL was demonstrated through comparative experiments with other algorithms on instances. The impact of JIT strategy is analyzed and the effect of networks on the NSACOWDRL is further discussed. [ABSTRACT FROM AUTHOR]

In the everchanging landscape of human mobility and commerce, efficient route planning has become paramount. This paper addresses the open vehicle routing problem (OVRP), a major logistical challenge in route optimization for a fleet of vehicles serving geographically dispersed customers. Using a heuristic approach, we explore the complexities of OVRP, comparing the results with advanced optimization methods. This study not only highlights the effectiveness of mathematical modeling, but also explores the practicality of heuristic algorithms such as Greedy, Nearest Neighbor and 2-opt to provide quality solutions. The findings highlight the nuanced interplay between solution quality and computational efficiency, providing valuable insights for addressing real-world logistics challenges. Recommendations delve into optimization opportunities and the integration of emerging technologies, ensuring adaptable solutions to the intricate the problem of open vehicle routing. [ABSTRACT FROM AUTHOR]

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that arises in various fields including transportation and logistics. The CVRP extends from the Vehicle Routing Problem (VRP), aiming to determine the most efficient plan for a fleet of vehicles to deliver goods to a set of customers, subject to the limited carrying capacity of each vehicle. As the number of possible solutions increases exponentially with the number of customers, finding high-quality solutions remains a significant challenge. Recently, the Quantum Approximate Optimization Algorithm (QAOA), a quantum–classical hybrid algorithm, has exhibited enhanced performance in certain combinatorial optimization problems, such as the Max-Cut problem, compared to classical heuristics. However, its ability diminishes notably in solving constrained optimization problems including the CVRP. This limitation primarily arises from the typical approach of encoding the given problems as unconstrained binary optimization problems with penalty terms. In this case, the QAOA faces challenges in sampling solutions satisfying all constraints. Addressing this, our work presents a new binary encoding for the CVRP, with an alternative objective function of minimizing the shortest path that bypasses the vehicle capacity constraint of the CVRP. The search space is further restricted by the constraint-preserving mixing operation. We examine and discuss the effectiveness of the proposed encoding under the framework of the variant of the QAOA, Quantum Alternating Operator Ansatz (AOA), through its application to several illustrative examples. Compared to the typical QAOA approach, our proposed method not only preserves the feasibility but also achieves a significant enhancement in the probability of measuring optimal solutions. [ABSTRACT FROM AUTHOR]

Electric vehicles (EVs) have gained considerable popularity, driven in part by an increased concern for the impact of automobile emissions on climate change. Electric vehicles (EVs) cover more than just conventional cars and trucks. They also include electric motorcycles, such as those produced by Gogoro, which serve as the primary mode of transportation for food and package delivery services in Taiwan. Consequently, the Electric Vehicle Routing Problem (EVRP) has emerged as an important variation of the Capacitated Vehicle Routing Problem (CVRP). In addition to the CVRP's constraints, the EVRP requires vehicles to visit a charging station before the battery level is insufficient to continue service. EV battery consumption is linearly correlated to their weight. These additional constraints make the EVRP more challenging than the conventional CVRP. This study proposes an improved Harmony Search Algorithm (HSA), with performance validated by testing 24 available benchmark instances in the EVRP. This study also proposes a novel update mechanism in the improvement stage and a strategy to improve the routes with charging stations. The results show that in small and large instances, the proposed HSA improved the number of trips to the charging stations by 24% and 4.5%, respectively. These results were also verified using the Wilcoxon signed-rank significant test. [ABSTRACT FROM AUTHOR]