Vehicle Routing Optimization Research Articles

Optimal Vehicle Routing in Consumer Goods Distribution: A GNU Linear Programming Kit-Based Analysis

Optimal Vehicle Routing in Consumer Goods Distribution: A GNU Linear Programming Kit-Based Analysis

Integrated Optimization of Vehicle Routing of Automotive Parts Inbound Logistics

Integrated Optimization of Vehicle Routing of Automotive Parts Inbound Logistics

Accelerating Two-Phase Multiobjective Evolutionary Algorithm for Electric Location-Routing Problems

Electric location-routing problem is a challenging problem consisting of the optimization of electric vehicle routing and charging facility location, simultaneously. Existing algorithms generally adopt the two-phase search strategy to alternately optimize the routing and the location. However, they are usually criticized for the inefficiency as the problem scale increases. In order to improve the search efficiency in each phase, we propose an accelerating two-phase multiobjective evolutionary algorithm, where the learning method is used to mine the useful information from the historical search process to generate the high-quality routing and location offspring. To be specific, in the routing optimization phase, an interpolation method is developed to extract the frequent visiting orders existing in the historical best solutions. These frequent visiting orders are used to create potential routing offspring that can accelerate the convergence toward the optimal solutions. In the location optimization phase, a surrogate model is used to approximatively represent the relationship from routing to location, which can directly output a promising location scheme for a given routing offspring and thus reduce the optimization time. Experimental results on different scales of test instances demonstrate the competitiveness of the proposed algorithm in comparison with several state of-the-art algorithms, including four widely used heuristic algorithms and two multiobjective evolutionary algorithms.

An innovative medical waste management system in a smart city using XAI and vehicle routing optimization.

The management of medical waste is a complex task that necessitates effective strategies to mitigate health risks, comply with regulations, and minimize environmental impact. In this study, a novel approach based on collaboration and technological advancements is proposed. By utilizing colored bags with identification tags, smart containers with sensors, object recognition sensors, air and soil control sensors, vehicles with Global Positioning System (GPS) and temperature humidity sensors, and outsourced waste treatment, the system optimizes waste sorting, storage, and treatment operations. Additionally, the incorporation of explainable artificial intelligence (XAI) technology, leveraging scikit-learn, xgboost, catboost, lightgbm, and skorch, provides real-time insights and data analytics, facilitating informed decision-making and process optimization. The integration of these cutting-edge technologies forms the foundation of an efficient and intelligent medical waste management system. Furthermore, the article highlights the use of genetic algorithms (GA) to solve vehicle routing models, optimizing waste collection routes and minimizing transportation time to treatment centers. Overall, the combination of advanced technologies, optimization algorithms, and XAI contributes to improved waste management practices, ultimately benefiting both public health and the environment.

Discovering Lin-Kernighan-Helsgaun heuristic for routing optimization using self-supervised reinforcement learning

Vehicle routing optimization is a crucial responsibility of transportation service providers, which can significantly reduce operating expenses and improve client satisfaction. Learning to tackle routing optimization problems automatically can be the next significant step forward in optimization technology. Despite recent advancements in automatically learned heuristics for routing optimization problems, state-of-the-art traditional methods such as Lin-Kernighan-Helsgaun (LKH) still outperform machine learning-based approaches. To narrow this gap, we propose a novel technique called self-supervised reinforcement learning (SSRL), which combines self-supervised learning with the LKH heuristic. We provide a node decoder and an edge decoder corresponding to reinforcement learning and self-supervised learning for learning node penalties and edge scores, respectively. The self-supervised part with cross-entropy loss offers strong gradient signals for parameter updates. At the same time, the reinforcement learning component functions as a regularizer to drive the supervised part, which focuses on particular rewards. SSRL learns and replicates all of the LKH’s significant components, improving the original LKH’s generalization and performance. Through experiments on multiple vehicle routing problems, SSRL has demonstrated superior accuracy and efficiency compared to existing methods. Our results provide empirical evidence of SSRL’s effectiveness and potential as a promising solution for optimizing complex routing problems.

A stochastic formulation of the two-echelon vehicle routing and loading bay reservation problem

This paper studies a goods delivery problem for multiple courier companies in central city areas integrated with a loading bay scheduling problem. The goods delivery problem is formulated as a stochastic two-echelon vehicle routing problem, while the loading bays are managed through a central reservation system, which assigns loading bays to courier vehicles taking into account their delivery demands. A stochastic programming model with chance constraints is formulated to find the optimal vehicle routing and loading bay reservation strategy, and a hybrid genetic algorithm is developed to solve the model. Numerical results suggest that the reservation system can help coordinate deliveries from different courier companies and substantially improve the overall delivery efficiency and loading space utilisation.

Multi-Trip Vehicle Routing Problem with Time Windows and Resource Synchronization on Heterogeneous Facilities

Inspired by long-distance road transport in industrial logistics in China, this paper studies a simultaneous loading scheduling and vehicle routing problem over a multi-workday planning horizon. Industrial cargo often requires specialized facilities, and these facilities vary in performance and quantity and are subject to available time constraints. Consequently, achieving coordinated optimization of vehicle routing and loading scheduling becomes a significant challenge in practice. We describe the studied problem as a multi-trip vehicle routing problem with time windows and resource synchronization on heterogeneous facilities. First, we develop a mixed integer programming model in a multi-workday setting to minimize the total travel distance and the number of vehicles. Moreover, a three-phase heuristic approach is developed. An initial solution is constructed using a sequential strategy in the first phase, and then an adaptive large neighbourhood search and a post-optimization procedure based on ejection chains are, respectively, designed to optimize the two hierarchical objective functions. Finally, extensive computational experiments are conducted to demonstrate the effectiveness of the proposed method. Specifically, the research results indicate that in long-distance road transport in industrial scenarios, expanding the planning horizon from a single workday to a multi-workday period could significantly reduce logistics operational costs and improve service quality.

Retracted: Vehicle Routing Optimization Based on Multimedia Communication and Intelligent Transportation System

Retracted: Vehicle Routing Optimization Based on Multimedia Communication and Intelligent Transportation System

Integrated scheduling problems of open shop and vehicle routing using an ensemble of group teaching optimization and simulated annealing

Production and distribution are two parts of importance in supply chains. Yet, seldom attention is given to an integrated production and distribution in the case of open shop scheduling and vehicle routing problems. This article addresses an integrated scheduling problem of open shop and vehicle routing optimization, in which the jobs are processed in an open shop, and subsequently are delivered to customers at diverse places. First, a mixed integer programming model is developed to define the problem with minimizing maximum completion time. Second, an ensemble of group teaching optimization and simulated annealing methods is devised to optimally handle the considered problem. A heuristic rule is designed to generate a high-quality initial solution, while a simulated annealing method considering key machines is proposed to reinforce exploitation abilities. A nearest insertion method is used to make delivery decisions of vehicles. At last, the sensitivity analysis of user parameters in the developed approach is executed. Via solving a set of benchmark instances, we carry out extensive comparison experiments. The formulated model is verified by a mathematical programming optimizer CPLEX and the devised approach is compared with four meta-heuristics. The results and discussions confirm the strong competitiveness of the developed model and method for solving the concerned problems.

A New Hybrid Algorithm for Vehicle Routing Optimization

To solve the vehicle routing problem with simultaneous pickup–delivery and time windows (VRPSDPTW), a sine cosine and firefly perturbed sparrow search algorithm (SFSSA) is presented. Based on the standard sparrow search algorithm, the initial population uses tent chaotic mapping to change the population diversity; then, the discoverer location is updated using the sine cosine fluctuation range of the random weight factor, and finally the global population location is updated using the firefly perturbation strategy. In this study, SFSSA was compared with a genetic algorithm (GA), parallel simulated annealing algorithm (p-SA), discrete cuckoo search algorithm (DCS), and novel mimetic algorithm with efficient local search and extended neighborhood (MATE) adopting improved Solomon’s benchmark test cases. The computational results showed that the proposed SFSSA was able to achieve the current optimal solutions for 100% of the nine small-to-medium instances. For large-scale instances, SFSSA obtained the current optimal solutions for 25 out of 56 instances. The experimental findings demonstrated that SFSSA was an effective method for solving the VRPSPDTW problem.

A dynamic approach for the multi-compartment vehicle routing problem in waste management

Urban areas worldwide face a significant environmental challenge which is increasing municipal solid waste rate. Addressing its negative consequences necessitates advancements in waste management systems. Although the previous research focused on the static routing approach in the collection phase, this paper adds a dynamic municipal solid waste collection scheme to optimize vehicle routing, accounting for fluctuations in waste generation and changes in transportation systems. This study employs, for the first time, the application of a discrete choice model (DCM) to streamline the process of re-optimization in dynamic vehicle routing problems (DVRP). At each decision epoch, DCM is applied to determine the likelihood of choosing the next geographical zone to visit bins based on current waste generation levels and traveling costs. Moreover, the multi-compartment vehicles are considered to preserve waste segregation during transportation, thereby increasing operational efficiency and regulatory compliance. Another contribution of this paper is to determine visiting priority for each bin by adjusting the time window based on the threshold waste level. Hence, this paper proposes a framework for sustainable, efficient, and effective waste management practices by integrating the benefits of dynamic and multi-compartment routing. Furthermore, a hybrid Genetic and Particle Swarm Optimization algorithm has been designed to find the best solution for the studied problem as well as some of the latest and most proficient metaheuristic algorithms. Finally, the Best Worst Method is applied to find the best-proposed algorithm to solve the presented problem, indicating that the hybrid algorithm has the highest performance in providing high-quality route plans.

Modular vehicle routing for combined passenger and freight transport

The continuous increase in urban deliveries and the ongoing urbanization of large cities require the development of efficient and sustainable transportation solutions. This study investigates the impact of modular vehicle concepts and the consolidation of different demand types in the route planning on the efficiency of the urban freight and passenger transportation system. Modularity is achieved by connecting multiple vehicles together to form a platoon. The consolidation of different demand types is realized by simultaneously consider passenger and freight demand in the optimization algorithm. The considered vehicles are specific for each demand type by can be connected freely, hence it is possible to transport different demand types in the same platoon. The cost terms in the problem formulation are comprised of travel time costs, travel distance costs, fleet size costs, and cost considering unserved requests. The modular vehicle operations are modeled in a novel pickup and delivery problem which is solved using CPLEX and Adaptive Large Neighborhood Search. In an extensive scenario study and case study in Stockholm, the potentials of the new modular vehicle type are explored for different spatial and temporal demand distributions. A parameter study on vehicle capacity, vehicle range and cost saving assumptions is performed to study their influence on the efficiency. The experiments carried out indicate a general cost savings of 48% due to modularity and an additional 9% due to consolidation. The reduction mainly stems from reduced operating costs and reduced trip duration, while the same number of requests can be served in all cases. Empty vehicle kilometers are reduced by more than 60% by consolidation and modularity. The proposed model and optimization framework can be used by companies and policy makers to identify required fleet sizes, optimal vehicle routes and cost savings.

A mat‐heuristics approach for electric vehicle route optimization under multiple recharging options and time‐of‐use energy prices

SummaryTraveling has contributed a lot to the evolution of mankind. Today, electric vehicles (EVs) are being preferred due to their greater efficiency, comfort, and environment‐friendly qualities. The EVs' contribution to future mobility is projected to rise exponentially in years to come. To make this innovative technology more successful, there is a dire need to install a sufficient number of charging stations (CSs). As the EVs are limited by their cruising range, they require multiple recharging to cover long distances (especially in the case of logistics delivery services). Thus, there is a great need to develop an efficient and cost‐effective EV route optimization approach considering multiple recharging options and time‐of‐use (ToU) energy prices. In this regard, a novel mat‐heuristic approach named (firefly with ant colony algorithm) has been proposed to solve the problem of EVRPTW (electric vehicle routing problem with time windows) incorporating detailed modeling of multiple charging flexibility (i.e., battery swapping, partial recharge, and different charging levels) and ToU energy prices. Our proposed approach aims to minimize the total cost of traveling, which is highly influenced by the cost of recharging. Ant colony algorithm (ACA) serves as the basic optimization framework in the proposed approach, while the firefly approach explores hitherto unexplored solution space and avoids local optima. The computation performance of the proposed approach is compared with existing state‐of‐the‐art similar domain approaches such as variable neighborhood search (VNS) and ant colony optimization using local search (ACO‐LS) which has average deviation of nearly 20%–25% from with optimal solution achieved by the proposed . The proposed approach yields a near‐optimal solution with a faster convergence rate (approximately 50%) compared to other existing approaches. Moreover, the multiple recharging options modeled in our proposed approach justify their significance in terms of cost‐effectiveness for most scenarios.

Optimization of Simultaneous Pickup and Delivery Vehicle Routing with Three-Dimensional Balanced Loading Constraints

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

PENERAPAN METODE SAVING MATRIX DALAM PENENTUAN RUTE TERPENDEK PENGANGKUTAN SAMPAH DI KABUPATEN KUBU RAYA

The process of transporting waste from the Waste Disposal Site (TPS) to the Final Disposal Site (TPA) is one of the problems in Kubu Raya district that needs attention. This is because the volume of waste in each TPS in Kubu Raya varies, and the number and capacity of transport vehicles provided by the PUPR Office of Kubu Raya is limited. Of course, these problems affect the distance traveled by the transport vehicle, travel time and costs incurred. Therefore, it is necessary to choose the optimal transportation route. The route is said to be optimal when each TPS is transported one way and does not exceed the capacity of the conveyance, so that the total distance obtained is the minimum total distance. The existing problems are then modeled in mathematical form and solved using the Saving Matrix method. This method combines destination points that can be traversed one way by paying attention to the volume of demand for each destination so as not to exceed the vehicle capacity. Based on the research results obtained four optimal vehicle routes with a total distance of 141.6 km. with details for the distance of vehicle route one which is 41.5 km, vehicle route two is 35.95 km, vehicle route three is 35.9 km, and vehicle route four is 28.25 km. This shows that the application of the Saving Matrix method provides more efficient results compared to the previous route of 162 km

Integrated optimization of inventory, replenishment, and vehicle routing for a sustainable supply chain utilizing a novel hybrid algorithm with carbon emission regulation

An integrated approach of making supply chain decisions has been proven to be more cost-effective compared to the strategy of taking supply chain decisions sequentially. It has influenced researchers to break the norm and focus on integrated supply chain decision-making. Considering this an integrated sustainable supply chain network for a single vendor and multiple buyers is formulated along with trade credit policy. The vendor offers a trade credit policy to its buyers. Emissions generated from production, vehicle routing, and storage are taken into account. To minimize carbon emissions, a cap & trade policy is applied. The buyers are served by a fleet of vehicles available at the vendor location. Considering the aforementioned scenario, a mathematical formulation is developed so as to minimize the overall total cost subject to a set of constraints. The integrated decisions regarding production, inventory management, vehicle routing, and carbon emissions are taken. Besides this, a unique metaheuristic technique is also suggested to solve the proposed problem. The solutions obtained through the process of well-known genetic algorithm are further improved during the ruin and recreate phase of the hybridized algorithm named as GA-RR. An in-depth empirical examination of GA-RR algorithm is also done through a quantitative analysis of exploration and exploitation. To better illustrate the proposed mathematical problem, two numerical examples are also demonstrated. It is followed by an extensive sensitivity analysis of the various input parameters so as to highlight important results. It can be concluded that GA-RR outperforms other existing metaheuristic techniques for the proposed mathematical problem.

The p-hub centre routing problem with emissions budget: Formulation and solution procedure

In recent years, the use of fossil fuels has led to a drastic increase in the emissions of CO2 and other greenhouse polluting gases. The transportation sector stands out as one of the main contributors to this pollution. Thus, several network design problems are being revisited to uncover cost and energy-efficient solutions. In this paper, we formulate and solve a p-hub centre routing problem under a CO2 emissions budget. The aim is to locate hub nodes, allocate client nodes in local tours of capacitated vehicles, and decide on vehicle speeds during transportation. The objective is to minimise the maximum time of service subject to a budget constraint on the total CO2 emissions cost of the hub network. To solve the introduced problem, we implement an efficient simulated annealing algorithm with a temperature-dependent penalty cost function, a fixed size prohibited solutions list, and a speed-based reparation heuristic. Additionally, we present a novel clustering-based construction heuristic to generate initial starting solutions for our algorithm, while hub location–allocation, vehicle routing, and speed optimisation operators are considered during the local search step. Extensive computational experiments on adapted AP data set instances show that the proposed solution approach outperforms a state-of-art solver in terms of CPU time and solution quality. Finally, we study the trade-off between the quality of service and the CO2 emission costs and discuss the effect of the CO2 budget on the design of hub networks.

Optimizing the drinking water gallon distribution using vehicle routing problems with pick-up and delivery approach (Case Study of Berkah RO Drinking Water Depot)

Distribution activities play an essential role in the industry nowadays. Every company will design new effective and efficient strategies to improve its distribution systems, such as route selection, scheduling the number of vehicles, and many others. The optimal route selection model is an adequately considered issue in product distribution. The problem model commonly arises in the distribution activity is the vehicle routing problem (VRP). This distribution problem model also occurred in one of the drinking water gallon companies, Berkah RO Drinking Water Depot, where they still subjectively selected the route. In addition, the factor of damaged vehicles causes some demands for water gallons not to be fulfilled. The problem in this company is categorized as a vehicle routing problem (VRP) model with pick-up and delivery. This research uses a saving matrix and nearest-neighbor methods to solve the problem of determining the optimal vehicle route. An application is then developed based on the algorithm for determining the optimal vehicle route with a saving matrix and nearest-neighbor methods. This application aims to acquire faster results than manual calculations if each customer's demand changes. The final result of this research is determining the optimal vehicle routing with the shortest distance considering the arrival and departure time allocation and total distribution cost.

Autonomous Electric Vehicle Route Optimization Considering Regenerative Braking Dynamic Low-Speed Boundary

Finding the optimal speed profile of an autonomous electric vehicle (AEV) for a given route (eco-driving) can lead to a reduction in energy consumption. This energy reduction is even more noticeable when the regenerative braking (RB) capability of AEVs is carefully considered in obtaining the speed profile. In this paper, a new approach for calculating the optimum eco-driving profile of an AEV is formulated using mixed-integer linear programming (MILP) while carefully integrating the RB capability and its limitations in the process of obtaining a driving profile with minimum energy consumption. One of the most important limitations of RB which has been neglected in previous studies is operation below the low-speed boundary (LSB) of electric motors, which impairs the energy extraction capability of RB. The novelty of this work is finding the optimal speed profile given this limitation, leading to a much more realistic eco-driving profile. Python is used to code the MILP problem, and CPLEX is employed as the solver. To verify the results, the eco-driving problem is applied to two scenarios to show the significance of considering a dynamic LSB. It is shown that for the route under study, up to 27% more energy can be harvested by employing the proposed approach.

Evolutionary Carrier Selection for Shared Truck Delivery Services

With multiple carriers in a logistics market, customers can choose the best carrier to deliver their products and packages. In this paper, we present a novel approach of using the stochastic evolutionary game to analyze the decision-making of the customers using the less-than-truckload (LTL) delivery service. We propose inter-related optimization and game models that allow us to analyze the vehicle routing optimization for the LTL carriers and carrier selection for the customers, respectively. The stochastic evolutionary game model incorporates a small perturbation of customers' decision-making which exists due to irrationality. The solution of the stochastic evolutionary game in terms of stochastically stable states is characterized by using the Markov chain model. The numerical results show the impact of carriers' and customers' parameters on the stable states.