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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.

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.

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.

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.

Rising traffic congestion and fuel costs pose significant challenges for supply chains with numerous retailers. This paper addresses these challenges by optimizing transportation routes for processed tomatoes within a long-haul and intercity distribution network. We use the heterogeneous capacitated vehicle routing problem framework to create a new quadratically constrained mixed-integer non-linear programming model that aims to meet demand at multiple destinations while minimizing transportation costs. Our model incorporates real-time data and route optimization strategies that consider traffic conditions based on freight time and route diversions for expedited deliveries. It aims to devise an optimal transportation schedule that minimizes fuel, operational, and maintenance costs while ensuring efficient delivery of tomato paste. By applying this model to a real-world case study, we estimate a significant 27.59% reduction in transportation costs, dropping them from GH¢20,270 ($1,638.91) to GH¢14,676 ($1,186.61) on average. This highlights the effectiveness of our strategy in lowering costs while maintaining smooth and efficient deliveries.

Effective waste management is essential for maintaining a clean and sustainable urban environment. This paper addresses the waste collection challenges in Torreón, Coahuila, Mexico, by integrating data mining techniques with the vehicle routing problem (VRP). The goal is to optimize waste collection routes and schedules to minimize costs, reduce fuel consumption, and enhance operational efficiency. The study leverages historical waste collection data, demographic information, and geographic data to comprehensively understand waste generation patterns, population density, and infrastructure layout. The data mining process involves exploratory analysis, clustering, and classification techniques to identify critical variables and patterns that influence waste generation and collection. This information is used to design efficient collection routes, considering factors such as distance, capacity constraints, traffic patterns, and time windows. The VRP model is then applied to allocate waste collection vehicles optimally, ensuring that each route is serviced within the designated timeframe. The model aims to minimize the number of vehicles used, optimize capacity utilization, and reduce travel distances. Additionally, real-time data on vehicle status, traffic conditions, and waste generation rates are integrated to adjust routes and schedules to improve operational efficiency dynamically. This approach provides waste management authorities in Torreón with valuable insights and tools to enhance waste collection operations. By leveraging data mining and VRP techniques, the study aims to improve waste management practices, reduce environmental impact, and promote a cleaner, healthier environment for residents of Torreón, Coahuila, Mexico.

The vehicle routing problem (VRP) is a combinatorial optimization problem that determines optimal routes to enhance distribution efficiency. One of the most popular strategies in freight distribution is multi-echelon distribution. Multi-echelon distribution networks often apply to supply chain management, land transportation, the maritime industry, aviation, etc., and rely on VRP. This comprehensive review systematically analyses 382 papers retrieved through the Scopus database. We use a bibliometric and network analysis tool to complete a systematic literature mapping identifying key interrelationships and research clusters. The analysis depicts five main research clusters: green logistics and decision analysis, scheduling and inventory optimization, VRP for city logistics, mathematical modeling and optimization, and outbound logistics and customer service, identified based on author keywords of the systematically derived paper pool. Each cluster is provided with foundational knowledge, concepts, theories, and employed techniques. Finally, future studies are suggested to explore more comprehensive investigation in highly discussed domains like city logistics problems in e-commerce, vehicle routing problems for sustainable logistics, and technological advancement-based applications.

Nowadays, supply chain and road networks are full of complexity. Companies can differentiate themselves by offering superior customer service. Therefore, pharmaceutical distributors need to optimize route distribution for efficient and effective delivery to pharmacies, enhancing their competitiveness. In the field of operations research (OR), efficient route optimization is a significant function of the Vehicle Routing Problem (VRP) where the goal is to find the optimal distance travelled. The VRP can be solved using a range of algorithms, comprising exact methods, heuristics and meta-heuristics. This paper gives the basic concepts of some algorithms and these algorithms are compared based on the results. This study also extends its focus to the variation known as the Vehicle Routing Problem with Time Windows (VRPTW), that closely mirrors real-world scenarios, allowing for a more practical assessment of pharmaceutical distribution challenges and optimization solutions.

Evde Sağlık Hizmetleri (ESH), yaşlanan nüfus ve kronik hastalıkların yükselmesiyle birlikte giderek daha fazla önem kazanmaktadır. Ancak, bu hizmetlerin etkin ve verimli bir şekilde planlanması ve yönetilmesi, stokastik hasta talepleri, değişken yol koşulları ve kaynakların kapasitesi gibi birçok kısıtla karşı karşıyadır. Özellikle, hasta taleplerinin stokastik doğası, planlamada önemli bir belirsizlik faktörü oluşturmakta ve planların çoğu zaman yeniden düzenlenmesini gerektirmektedir. Ayrıca, ESH'nin çok periyotlu bir yapısı vardır, yani her hasta için farklı zaman dilimlerinde farklı türden hizmetler gerekebilmektedir. Bu çalışmanın ana amacı, stokastik hasta talepleri ve çok periyotlu planlama ihtiyaçlarını dikkate alarak, ESH hizmetlerinin sunumunu daha etkin ve verimli bir şekilde yapabilecek bir matematiksel model önermektir. Önerilen model, kaynakların daha etkin bir şekilde ayrılmasına, servis kalitesinin artırılmasına ve acil durumlarla daha etkin bir şekilde başa çıkılmasına da katkı sağlayacaktır. Bu, hem hastalara daha iyi hizmet sunumu hem de sağlık sistemi için daha düşük maliyetler anlamına gelmektedir.

The study first proposes a heterogeneous fleet, multi-compartment electric vehicle routing problem for perishable products (MCEVRP-PP). We capture a lot of practical demands and constraints of the MCEVRP-PP, such as multiple temperature zones, the hard time window, charging more than once during delivery, various power consumption per unit of refrigeration, etc. We model the MCEVRP-PP as a mixed integer program and aim to optimize the total cost including vehicle fixed cost, power cost, and cooling cost. A hybrid ant colony optimization (HACO) is developed to solve the problem. In the transfer rule, the time window is introduced to improve flexibility in route construction. According to the features of multi-compartment electric vehicles, the capacity constraint judgment algorithm is developed in route construction. Six local search strategies are designed with time windows, recharging stations, etc. Experiments based on various instances validate that HACO solves MCEVRP-PP more effectively than the ant colony optimization (ACO). Compared with fuel vehicles and single-compartment vehicles, electric vehicles and multi-compartment electric vehicles can save the total cost and mileage, and increase utilization of vehicles.

Time-dependent vehicle routing problem with time windows (TDVRPTW) is a pivotal problem in logistics domain. In this study, a special case of TDVRPTW with temporal-spatial distance (TDVRPTW-TSD) is investigated, which objectives are to minimize the total travel time and maximize customer satisfaction while satisfying the vehicle capacity. To address it, an improved multiobjective evolutionary algorithm (IMOEA) is developed. In the proposed algorithm, a hybrid initialization strategy with two efficient heuristics considering temporal-spatial distance is designed to generate high-quality and diverse initial solutions. Then, two crossover operators are devised to broaden the exploration space. Moreover, an efficient local search heuristic combing the adaptive large neighborhood search (ALNS) and the variable neighborhood descent (VND) is developed to improve the exploration capability. Finally, detailed comparisons with several state-of-the-art algorithms are tested on a set of instances, which verify the efficiency and effectiveness of the proposed IMOEA.

The Vehicle Routing Problem (VRP) model optimizes the routing of a fleet of vehicles to serve customers and has evolved over time. VRP studies have experienced an 11% growth over the past 5 years. In recent years, researchers have been working on a stable VRP model that optimizes routes based on environmental requirements and clean energy needs. Accordingly, we outline the VRP growth trend and present a systematic classification of features based on economic, social, and environmental issues to achieve a sustainable VRP model. The proposed model integrates issues related to passenger and goods transport, Private Vehicles, and Electric Vehicles.

Vehicle Routing Problem with Uncertain Demands (VRPUD) is one of the research hotspots in the field of logistics scheduling. In this paper, a Discrete Jaya (DJaya) algorithm is presented for the VRPUD to minimize the total cost. A novel dividing-point-based coding scheme is designed to represent solutions with higher robustness. In addition, an efficient repair strategy is embedded into the decoding process to avoid the failure of producing feasible solutions. The best and worst solutions are employed to generate offspring solutions in DJaya. Several efficient local search methods are also presented to enhance the exploitation ability and increase the diversity of solutions. Based on the benchmark data sets of the VRPUD, numerical simulations are carried out for the proposed DJaya algorithm with uncertain demands. Computational results and comparisons with the state-of-the-art algorithms demonstrate the superiority of the proposed algorithm in solving VRPUD.

Production and distribution are critical components of the furniture supply chain, and achieving optimal performance through their integration has become a vital focus for both the academic and business communities. Moreover, as economic globalization progresses, distributed manufacturing has become a pioneering production technique. Via leveraging a distributed flexible manufacturing system, mass flexible production at lower costs can be achieved. To this end, this study presents an integrated distributed flexible job shop and distribution problem to minimize makespan and total tardiness. In our research, a set of custom furniture orders from different customers are processed among flexible job shops and then delivered by vehicles to customers as the due date. To distinctly show the presented problem, a mixed integer mathematical programming model is created, and a multi-objective brain storm optimization method is introduced considering the problem's features. In comparison to the other three advanced methods, the superiority of the algorithm created is showcased. The findings of the experiments demonstrate that the constructed model and the introduced algorithm have remarkable competitiveness in addressing the problem being examined.

The green vehicle routing problem (GVRP) has been a prominent topic in the literature on logistics and transportation, leading to extensive research and previous review studies covering various aspects. Operations research has seen the development of various exact and approximation approaches for different extensions of the GVRP. This paper presents an up-to-date and thorough review of GVRP literature spanning from 2016 to 2023, encompassing 458 papers. significant contribution lies in the updated solution approaches and algorithms applied to both single-objective and multi-objective GVRP. Notably, 92.58 % of the papers introduced a mathematical model for GVRP, with many researchers adopting mixed integer linear programming as the preferred modeling approach. The findings indicate that both metaheuristics and hybrid are the most employed solution approaches for addressing single-objective GVRP. Among hybrid approaches, the combination of metaheuristics-metaheuristics is particularly favored by GVRP researchers. Furthermore, large neighborhood search (LNS) and its variants (especially adaptive large neighborhood search) emerges as the most widely adopted algorithm in single-objective GVRP. These algorithms are proposed within both metaheuristic and hybrid approaches, where A-/LNS is often combined with other algorithms. Conversely, metaheuristics are predominant in addressing multi-objective GVRP, with NSGA-II being the most frequently proposed algorithm. Researchers frequently utilize GAMS and CPLEX as optimization modeling software and solvers. Furthermore, MATLAB is a commonly employed programming language for implementing proposed algorithms.

In this paper, an integrated approach is proposed that incorporates the road network design problem and the vehicle routing problem, which are very often studied separately. This approach can be adopted when the routes to follow in a transport system have to be designed (e.g., for public transit with fixed and variable routes, or for freight distribution) jointly with the network topology and capacity. The goal is to minimise congestion and the impacts on the network from passengers and freight vehicles. The design (control) variables consist of the optimal vehicle routes and optimised road network; they are both discrete (link topology for passenger and freight, routes for passengers and freight vehicles, etc.) and continuous (link capacity in terms of reserved lanes, signal settings, etc.). The problem is modelled in congested transportation networks (e.g., in an urban centre). A heuristic algorithm is adopted to find the best network configuration and the best vehicle routes. The proposed model and the adopted algorithm are applied in a test system to analyse the limits of the methodology, to verify the advantage obtained from the joint method and its applicability. In the test system, the joint procedure gives good results in terms of cost decreases. The reported methods can help public and private stakeholders in making decisions regarding transportation policy, especially in the urban environment.

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

This paper deals with the vehicle routing problem involving simultaneous loading and unloading of goods with different temperature regimes. Existing modifications of the problem as well as current software products do not focus on the transport of goods with different temperature regimes. In this paper, restrictive conditions for the joint transportation of goods with multiple temperature regimes are determined, which can be used within various types of optimization algorithms that address vehicle routing problems. Considering the proposed conditions in these algorithms will increase the utilization of the vehicle payload, and load space while complying with the established mandatory rules for the transport of foodstuffs. This will reduce the number of journeys required to carry out the transport, thus resulting in savings in operating costs.

This paper addresses the capacitated vehicle routing problem with pickup and delivery (CVRPPD) in robotic mobile fulfillment systems (RMFSs), focusing on planning routes for robots to transport goods. The CVRPPD in RMFSs has two unique features compared to the classic vehicle routing problem: robots have open starting and ending points, meaning they do not need to start or return to a depot, and there may already be goods on the robots. Based on these features, a mixed integer programming model is formulated for the CVRPPD in RMFSs, aiming to minimize transportation costs. An adaptive large neighborhood search (ALNS) heuristic, combined with adaptive local search, is proposed to solve the problem. The performance of the ALNS heuristic is evaluated through computational experiments. In small-scale instances, the average percentage deviation in objective values compared to the CPLEX solver is 22.04%. In large-scale instances from a real project, the average percentage deviation compared to the greedy algorithm (GA) is -5.8%. Extensive computational results indicate that the proposed heuristic algorithm performs well in terms of solution quality and solving time.

To enable safe and efficient use of multi-robot systems in everyday life, a robust and fast method for coordinating their actions must be developed. In this paper, we present a distributed task allocation and scheduling algorithm for missions where the tasks of different robots are tightly coupled with temporal and precedence constraints. The approach is based on representing the problem as a variant of the vehicle routing problem, and the solution is found using a distributed metaheuristic algorithm based on evolutionary computation (CBM-pop). Such an approach allows a fast and near-optimal allocation and can therefore be used for online applications. Simulation results show that the approach has better computational speed and scalability without loss of optimality compared to the state-of-the-art distributed methods. An application of the planning procedure to a practical use case of a greenhouse maintained by a multi-robot system is given.

This paper examines the challenge of integrated production and distribution, aiming to deliver products to customers precisely on time. Customers, situated within the transportation network, have predefined requirements regarding demand volume and time frames. In the first phase (F1), the problem of planning and allocation of resources is presented as FJSP, while the second phase (F2) addresses the vehicle routing problem as CVRPTW. The first phase, F1, aims to optimize manufacturing processes by appropriately scheduling production tasks to maximize productivity and minimize the time of task execution on machines. Phase 2, F2, encompasses the process of distribution to customers, seeking to minimize the number of vehicles, delivery time, and overall distance travelled. As both problems are among the most challenging in combinatorial optimization, integrating these phases into a single supply chain system poses a significant challenge in problem-solving. A mathematical formulation has been developed to include planning and task allocation in production, as well as vehicle routing, to obtain an optimal solution to the integrated problem. The input data used in the observed case study represent real data in both the first and second phases, forming one integrated supply chain system. Experimental results support the applied methodology.

The increasing interest in environmental protection has propelled reverse logistics as a challenging field in supply chain optimization. This paper addresses the vehicle routing problem with simultaneous pick-up and delivery (VRPSDP) while considering fuzzy payloads, with the primary objective of minimizing fuzzy fuel consumption. The VRPSDP with fuzzy payloads poses a computationally intractable challenge, as it involves a fleet of vehicles departing from a central depot to both deliver and collect goods from a dispersed group of customers. To effectively tackle this problem, a genetic algorithm is applied that incorporates the concept of fuzziness. This problem diverges from the traditional VRPSDP by explicitly considering fuel consumption reduction towards environmental sustainability. To validate and assess the feasibility of the proposed approach, a series of test instances are utilized. The numerical results exhibit the efficiency of the proposed method and place emphasis on the influence of uncertainty in the quantities of goods collected and delivered by customers on the resulting solution.

In this paper, we present a hybrid heuristic method based on the harmonic search algorithm to solve the vehicle routing problem with time windows. The importance of efficient path planning in logistics and supply chain management is emphasized herein, particularly under complex constraints like time window and vehicle capacity limits. The hybrid heuristic harmony search algorithm combines the global search capability of the harmony search algorithm with the accuracy of the local search heuristic to efficiently explore and harness the solution space. Through rigorous testing on the Solomon dataset, the hybrid heuristic harmony search algorithm performed remarkably in the generation of competitive solutions while maintaining the computational efficiency of the solutions. The results showed that the algorithm achieved competitive solutions even under strict time window constraints. The convergence of the algorithm was examined, and its strong performance in handling complex instances was revealed. This study enhances the operational efficiency of an organization and provides perspectives and solutions for optimization strategies in the domains of logistics and supply chain management.

The incessant consumption of goods and materials underscores the need to address the growing problem of waste generation and its profound impact on environmental sustainability. The problem of waste removal can be approached in different ways, whether it is the routing of vehicles, the work of drivers, the optimal distribution of waste bins, or other matters in the entire waste process. The aim of this study is to investigate the possibilities of optimizing waste collection processes in the region using a slightly modified Clark–Wright method. Optimal waste collection routes are defined with a focus on cost reduction and overall optimization of logistic chain processes. The established mathematical model for the capacitated vehicle routing problem includes the principles of sustainability and environmental friendliness. The results indicate that the largest messenger of all the newly proposed routes are the routes containing the surrounding settlements. Newly designed routes lead to significant reductions in fuel consumption and vehicle maintenance, which has a positive impact on financial and environmental resources. The conclusion indicates that by applying the Clark–Wright method, we have achieved a reduction in the number of routes of twenty fewer routes. This study provides regions with a detailed plan to improve waste management practices, contributing to a future of increased sustainability and environmental awareness.

This study presents a bi-objective optimization model for the Green Vehicle-Routing Problem in cold chain logistics, with a focus on symmetric distance matrices, aiming to minimize total costs, including carbon emissions, while maximizing customer satisfaction. To address this complex challenge, we developed a Stage-Specific Multi-Objective Five-Element Cycle Optimization algorithm (MOFECO-SS), which dynamically adjusts optimization strategies across different stages of the process, thereby enhancing overall efficiency. Extensive comparative analyses with existing algorithms demonstrate that MOFECO-SS consistently outperforms in solving the multi-objective optimization model, particularly in reducing total costs and carbon emissions while maintaining high levels of customer satisfaction. The symmetric nature of the distance matrix further aids in achieving balanced and optimized route planning. The results highlight that MOFECO-SS offers decision-makers flexible route planning options that balance cost efficiency with environmental sustainability, ultimately improving the effectiveness of cold chain logistics operations.

The emerging working mode of coordinated trucks and drones has demonstrated significant practical potential in various fields, including logistics and delivery, intelligence surveillance reconnaissance, area monitoring, and patrol. The seamless collaboration between trucks and drones is garnering widespread attention in academia and has emerged as a key technology for achieving efficient and secure transportation. This paper provides a comprehensive and in-depth review of the research status on the routing problem for coordinated trucks and drones, covering aspects such as application background, cooperative modes, configurations, issues that have been taken into consideration, and solution methodologies.

This article presents methods of planning unmanned aerial vehicle (UAV) missions in which individual platforms work together during the reconnaissance of objects located within a terrain. The planning problem concerns determining the flight routes of a swarm, where each UAV has the ability to recognize an object using a specific type of sensor. The experiments described in this article were carried out for drone formation; one drone works as a swarm information hub and exchanges information with the ground control station (GCS). Numerical models for mission planning are presented, which take into account the important constraints, simplifying the description of the mission without too much risk of losing the platforms. Several types of objective functions were used to optimize swarm flight paths. The mission models are presented in the form of mixed integer linear programming problems (MILPs). The experiments were carried out on a terrain model built on the basis of graph and network theory. The method of building a network on which the route plan of a drone swarm is determined is precisely presented. Particular attention was paid to the description of ways to minimize the size of the network on which the swarm mission is planned. The presented methods for building a terrain model allow for solving the optimization problem using integer programming tasks.

The logistics demands of industries represented by e-commerce have experienced explosive growth in recent years. Vehicle path-planning plays a crucial role in optimization systems for logistics and distribution. A path-planning scheme suitable for an actual scenario is the key to reducing costs and improving service efficiency in logistics industries. In complex application scenarios, however, it is difficult for conventional heuristic algorithms to ensure the quality of solutions for vehicle routing problems. This study proposes a joint approach based on the genetic algorithm and graph convolutional network for solving the capacitated vehicle routing problem with multiple distribution centers. First, we use the heuristic method to modularize the complex environment and encode each module based on the constraint conditions. Next, the graph convolutional network is adopted for feature embedding for the graph representation of the vehicle routing problem, and multiple decoders are used to increase the diversity of the solution space. Meanwhile, the REINFORCE algorithm with a baseline is employed to train the model, ensuring quick returns of high-quality solutions. Moreover, the fitness function is calculated based on the solution to each module, and the genetic algorithm is employed to seek the optimal solution on a global scale. Finally, the effectiveness of the proposed framework is validated through experiments at different scales and comparisons with other algorithms. The experimental results show that, compared to the single decoder GCN-based solving method, the method proposed in this paper improves the solving success rate to 100% across 15 generated instances. The average path length obtained is only 11% of the optimal solution produced by the GCN-based multi-decoder method.

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.

The challenge of optimizing the distribution path for location logistics in the cold chain warehousing of fresh agricultural products presents a significant research avenue in managing the logistics of agricultural products. The goal of this issue is to identify the optimal location and distribution path for warehouse centers to optimize various objectives. When deciding on the optimal location for a warehousing center, various elements like market needs, supply chain infrastructure, transport expenses, and delivery period are typically taken into account. Regarding the routes for delivery, efficient routes aim to address issues like shortening the overall driving distance, shortened travel time, and preventing traffic jams. Targeting the complex issue of optimizing the distribution path for fresh agricultural products in cold chain warehousing locations, a blend of this optimization challenge was formulated, considering factors like the maximum travel distance for new energy trucks, the load capacity of the vehicle, and the timeframe. The Location-Route Problem with Time Windows (LRPTWs) Mathematical Model thoroughly fine-tunes three key goals. These include minimizing the overall cost of distribution, reducing carbon emissions, and mitigating the depletion of fresh agricultural goods. This study introduces a complex swarm intelligence optimization algorithm (MODRL-SIA), rooted in deep reinforcement learning, as a solution to this issue. Acting as the decision-maker, the agent processes environmental conditions and chooses the optimal course of action in the pool to alter the environment and achieve environmental benefits. The MODRL-SIA algorithm merges a trained agent with a swarm intelligence algorithm, substituting the initial algorithm for decision-making processes, thereby enhancing its optimization efficiency and precision. Create a test scenario that mirrors the real situation and perform tests using the comparative algorithm. The experimental findings indicate that the suggested MODRL-SIA algorithm outperforms other algorithms in every computational instance, further confirming its efficacy in lowering overall distribution expenses, carbon emissions, and the depletion of fresh produce in the supply chain of fresh agricultural products.

This case study is based on Ceylon Petroleum Corporation, Sri Lanka, the national oil and gas company and market leader in Sri Lanka. The company’s outbound logistics consists of a centralized distribution method and a redistribution process of its products across the island. However, this study mainly focused on one regional depot and one petroleum product, Kotagala depot and Lanka Auto Diesel. The currently centralized redistribution process has noticed extra routing costs due to the unreasonable consumption of additional distance. This problem is modelled as a variant of the vehicle routing problem with a heterogeneous vehicle fleet. Our objective is to minimize the routing costs (or milk-run) by imposing constraints on the capacity and the volume. The researcher introduces a centralized vehicle routing problem that is presented. The proposed vehicle routing problem has been used to find the optimal path between clusters. The computational investigation highlights the cost savings that this new VRP can accrue. Cost savings can be accrued as large as 32.35% compared to a company's existing method.

In recent times, there has been a notable increase in interest surrounding the integration of Un-manned Aerial Vehicle (UAV) technology and vehicle routing problems (VRP) for package delivery purposes. While existing studies have explored various types of package deliveries utilizing VRP, limited attention has been given to on-demand food delivery. This study aims to develop a VRP model that incorporates practical constraints such as payload capacity and maximum flying range, with the primary objective of minimizing travel distance in food delivery operations. A comparative analysis is conducted among three delivery methods, including UAV delivery, to determine the most effective approach and assess the feasibility of each method. Through a case study analysis focused on a pizza delivery service in Sri Lanka, it was observed that implementing VRP in a motorbike delivery system resulted in reduced travel distance, time, cost, and CO2 emissions compared to the existing delivery system. Furthermore, the utilization of UAVs in conjunction with VRP yielded even greater improvements across all parameters. Based on a comprehensive cost analysis considering long-term operations, the UAV-based delivery system was identified as the most cost-effective method, followed by the VRP-incorporated motorbike delivery method. Although the VRP-incorporated motorbike delivery system exhibited a slightly higher average time per route compared to the existing method, the total travel time required to complete all routes remained lower. Consequently, the study concludes that the VRP-incorporated motorbike delivery system outperforms the existing delivery method for food delivery, with the use of UAVs incorporating VRP identified as the optimal delivery method among the three alternatives. The findings contribute valuable insights to the optimization of food delivery logistics, emphasizing the potential of VRP and exploring the feasibility of UAVs for sustainable and efficient long-term delivery solutions.

The growth of the economy, urban sprawl, and population expansion precipitate a substantial increase in solid waste generation, particularly in vital regions like the capital area and economically significant cities, including renowned tourist destinations. Furthermore, the protracted spread of the COVID-19 virus has led to a notable increase in the quantity of infectious waste. In this regard, the safe and effective management of municipal solid waste (MSW) collection and transportation emerges as a major concern in MSW management. This paper aims to determine routes for waste collection, both infectious and noninfectious, from waste collection points to diverse waste disposal sites in the mountainous Khao Kho district of Phetchabun province, located in northern Thailand, with the objective of minimizing total fuel consumption and service time. Fuel consumption is contingent upon both the distance traveled and the prevailing condition of the road. The road condition exerts an influence on the vehicle's speed, thereby directly impacting fuel efficiency. In the context of service time, priority is assigned to collection points with substantial quantities of infectious waste, given the imperative to promptly dispose of such waste to mitigate the risk of transmission. In this paper, a mixed-integer programming model and three modified differential evolution (MDE) algorithms were developed to solve the problem. The computational results reveal that the MDE outperformed the traditional DE and is effective for the MSW transportation management system.

The holistic optimisation of transportation systems is one of the key challenges in transportation science, because it requires the simultaneous consideration of the numerous interactions between the strategic planning level (e.g., the Facility Location Problem [FLP]) and the tactical and operational planning levels (e.g., Vehicle Fleet and Vehicle Routing Problem [VRP]). Traditional methods for solving the Location Routing Problem (LRP) often focus on the fixed constraints and ignore the variable vehicle characteristics, dynamic operations, different modes or underlying infrastructure. This paper proposes an integrated approach for modular and intuitive metaheuristic for LRP. The route planning phase is incorporated by means of agent-based transport simulation, which provides additional flexibility with respect to the vehicle fleet, demand characteristics, or the use of external problem constraints. Therefore, this approach can be easily applied to practical problems and used to optimise transport networks in a flexible and modular manner. Moreover, the algorithm developed here can independently converge to the near-optimal number and location of logistics sites. We also demonstrate the effectiveness and the performance of our approach by performing several simulation experiments in the context of a sensitivity analysis and comparing the results with well-known benchmark solutions. The results indicate that the Binary-Partition LRP heuristic (BinR-LRP) is able to identify better solutions than the benchmark heuristics in most cases. This emphasises its suitability as a scalable and robust optimisation framework, even for oversized LRP instances.

Efficient route management is critical for optimizing maintenance activities in real estate management. This study delves into the intricate task of allocating maintenance duties among building surveyors, a pivotal concern for property management firms. The primary goal of route planning is to enhance operational efficiency by minimizing travel time. To achieve this, the study explores three distinct algorithms: Saving, Nearest Neighbor, and an Evolutionary Algorithm (EA) customized with Dual Response Surface Optimization (DRSO). The integration of DRSO and EA enhances adaptability, allowing for dynamic responses to changes and improved allocation of maintenance tasks. Practical limitations, such as time and capacity, are considered through a case study involving a well-established building management organization. Results indicate that the Nearest Neighbor Algorithm generates 16–18 routes, the Saving Algorithm produces 18 routes, and the DRSO-driven EA also yields 18 routes. Significantly, the DRSO-driven EA consistently outperforms traditional methods, achieving a remarkable 17.7% reduction in route distance and an 18.8% reduction in journey time. In specific scenarios with 50 and 80 locations in Northeast and Central Bangkok, the DRSO-driven EA demonstrates practicality and efficacy. The algorithm's ability to address real-world challenges is underscored by these examples, showcasing its potential for broader implementation in real estate management. This study contributes significantly to the optimization of maintenance routes, presenting a clear roadmap for enhancing operational efficiency and customer satisfaction. Furthermore, it addresses the challenges posed by capitalism's growth constraints, offering insights for the adoption of sustainable economic practices in management, economics, and engineering.

Distribution costs remain consistently high in crowded city road networks, posing challenges for traditional distribution methods in efficiently handling dynamic online customer orders. To address this issue, this paper introduces the Proactive Dynamic Vehicle Routing Problem considering Cooperation Service (PDVRPCS) model. Based on proactive prediction and order-matching strategies, the model aims to develop a cost-effective and responsive distribution system. A novel solution framework is proposed, incorporating a proactive prediction method, a matching algorithm and a hybrid Genetic Algorithm-Simulated Annealing (GA-SA) algorithm. To validate the effectiveness of the proposed model and algorithm, a case study is conducted. The experimental results demonstrate that the dynamic scheme can significantly reduce the number of vehicles required for distribution, leading to cost reduction and increased efficiency.

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.

Machine learning techniques have advanced rapidly, leading to better prediction accuracy within a short computational time. Such advancement encourages various novel applications, including in the field of operations research. This study introduces a novel way to utilize regression machine learning models to predict the objectives of vehicle routing problems that are solved using a genetic algorithm. Previous studies have generally discussed how (1) operations research methods are used independently to generate optimized solutions and (2) machine learning techniques are used independently to predict values from a given dataset. Some studies have discussed the collaborations between operations research and machine learning fields as follows: (1) using machine learning techniques to generate input data for operations research problems, (2) using operations research techniques to optimize the hyper-parameters of machine learning models, and (3) using machine learning to improve the quality of operations research algorithms. This study differs from the types of collaborative studies listed above. This study focuses on the prediction of the objective of the vehicle routing problem directly given the input and output data, without optimizing the problem using operations research algorithms. This study introduces a straightforward framework that captures the input data characteristics for the vehicle routing problem. The proposed framework is applied by generating the input and output data using the genetic algorithm and then using regression machine learning models to predict the obtained objective values. The numerical experiments show that the best models are random forest regression, a generalized linear model with a Poisson distribution, and ridge regression with cross-validation.

When a flood strikes, the two most critical tasks are evacuation and relief distribution. It is essential to integrate these tasks, particularly before the floodwater reaches the vulnerable area, to minimize loss and damage. This paper presents a mathematical model of vehicle routing problems to optimize an integrated disaster relief operation. The model addresses routing for both the evacuation and relief distribution tasks in the early stages of a flood, aiming to identify a minimal number of vehicles required with their corresponding routes to transport vulnerable individuals and simultaneously distribute emergency relief. The new model incorporates several features, including vehicle reuse, multi-trip and split delivery scenarios for evacuees and emergency relief items, uncertainty in evacuation demands, and closing time windows at evacuation points. Due to the complexity of vehicle routing problems, particularly in large-scale scenarios, the exact approach for obtaining optimal solutions is time-consuming. Therefore, we propose the use of a metaheuristic algorithm, specifically a modified genetic algorithm, to find an approximate solution for the proposed model. We apply the developed model and modified algorithm to various simulated flood scenarios and a real-life case study from Indonesia. The experimental results demonstrate that our approach requires fewer vehicles compared to standard models for similar scenarios. Moreover, while the exact approach fails to find optimal solutions within a reasonable timeframe for large-scale scenarios, our new approach provides near-optimal solutions in a much shorter time. In smaller simulated scenarios, the modified genetic algorithm obtains optimal or near-optimal solutions approximately 92.5% faster than the exact approach.

The split delivery vehicle routing problem (SDVRP) is a classic combinatorial optimization problem, which is usually solved using a heuristic algorithm. The ant colony optimization algorithm is an excellent heuristic algorithm that has been successfully applied to solve various practical problems, and it has achieved good results. However, in the existing ant colony optimization algorithms, there are issues with weak targeting of different customer selection strategies, difficulty in balancing convergence speed and global search ability, and a predisposition to become trapped in local optima. To solve these problems, this paper proposes an improved ant colony algorithm (IACA). First, in terms of customer point selection, the initial customer and noninitial customer selection strategies are proposed for different customers, and the adaptive selection threshold is designed. Second, in terms of pheromone processing, an initial pheromone distribution method based on a greedy strategy, a pheromone backtracking mechanism, and an adaptive pheromone volatile factor are proposed. Finally, based on the 2-opt local search method, vehicle path self-search and intervehicle path search are proposed to further improve the quality of the solution. This paper tests the performance of the IACA on datasets of different scales. The experimental results show that compared with the clustering algorithm, artificial bee colony algorithm, particle swarm optimization algorithm, traditional ant colony algorithm, and other algorithms, the IACA can achieve more competitive results. Specifically, compared to the path length calculated by other algorithms, the path length calculated by IACA decreased by an average of 1.58%, 4.28%, and 3.64% in small, medium, and large-scale tests, respectively.

Optimization algorithms have a wide range of applications in symmetry problems, such as graphs, networks, and pattern recognition. In this paper, a dynamic periodic multi-depot multi-trip vehicle routing model for scheduling test samples is constructed, which considers the differences in testing unit price and testing capacity of various agencies and introduces a cross-depot collaborative transport method. Both the cost and the testing time are minimized by determining the optimal sampling routes and testing agencies, subjecting to the constraints of vehicle capacity, number of vehicles, and delivery time. To solve the model, a knowledge-guided multi-objective shuffled frog leaping algorithm (KMOSFLA) is proposed. KMOSFLA adopts a convertible encoding mechanism to realize the diversified search in different search spaces. Three novel strategies are designed: the population initialization with historical information reuse, the leaping rule based on the greedy crossover and genetic recombination, and the objective-driven enhanced search. Systematic experimental studies are implemented. First, feasibility analyses of the model are carried out, where effectiveness of the cross-depot collaborative transport is validated and sensitivity analyses on two parameters (vehicle capacity and proportion of the third-party testing agencies) are performed. Then, the proposed algorithm KMOSFLA is compared with five state-of-the-art algorithms. Experimental results indicate that KMOSFLA can provide a set of non-dominated schedules with lower cost and shorter testing time in each scheduling period, which provides a reference for the dispatcher to make a final decision.

Given the swift expansion of fresh e-commerce, the front warehouse mode can respond quickly and ensure the quality of fresh products. However, the complexity of the supply chain structure under front warehouse mode poses a challenge in reducing logistics costs and improving distribution efficiency while meeting consumers’ immediate delivery demands. Therefore, this paper studies the vehicle routing problem of two-echelon fresh e-commerce under front warehouse mode. Considering trans-shipment time constraints between the two echelons and the characteristics of terminal distribution, this paper initially models the vehicle routing problem for front warehouses as a two-echelon multi-trip capacitated vehicle routing problem with time windows. A mixed-integer linear programming model is subsequently established. To solve the model, a hybrid genetic algorithm integrated with neighborhood search is developed. Matrix coding is employed to merge vehicle selection and route assignment decisions. Simultaneously, neighborhood search is applied to enhance the search capability of algorithms, thereby improving the quality of solutions. Furthermore, the effectiveness and efficiency of the model and algorithm are verified through experiments of varying scales. Finally, comparative strategies and sensitivity analysis highlight the advantages of multi-trip strategies and provide insights into the optimal vehicle capacity limit.

Purpose – This paper proposes an approach to solve the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) in the context of the Physical Internet (PI) supply chain. The main objective is to minimize the total distribution costs (transportation cost and holding cost) to supply retailers from PI hubs. Design/methodology/approach – Mixed integer programming (MIP) is proposed to solve the problem in smaller instances. A random local search (RLS) algorithm and a simulated annealing (SA) metaheuristic are proposed to solve larger instances of the problem. Findings – The results show that SA provides the best solution in terms of total distribution cost and provides a good result regarding holding cost and transportation cost compared to other heuristic methods. Moreover, in terms of total carbon emissions, the PI concept proposed a better solution than the classical supply chain. Research limitations/implications – The sustainability of the route construction applied to the PI is validated through carbon emissions. Practical implications – This approach also relates to the main objectives of transportation in the PI context: reduce empty trips and share transportation resources between PI-hubs and retailers. The proposed approaches are then validated through a case study of agricultural products in Thailand. Social implications – This approach is also relevant with the reduction of driving hours on the road because of share transportation results and shorter distance than the classical route planning. Originality/value – This paper addresses the VRPSPD problem in the PI context, which is based on sharing transportation and storage resources while considering sustainability.

The issues in Vehicle Routing with Time Windows (VR-TW) are addressed in this study using a novel hybrid swarm-intelligent frog jumping optimisation (HSIFJO) algorithm. The method employs a diversity management strategy for developing memeplexes, which assists in preserving diversity and prevents the premature termination of the search. To increase population diversity and improve solution quality, an enhanced clone selection (CS) process is employed. To maximise the algorithm's potential, an enhanced and extended extremal optimisation (EO) strategy is used, coupled with different move operators. A proposed adaptive soft time windows (ASTW) surcharge approach acknowledges the possibility of impractical solutions during the evolution process. When compared to existing state-of-the-art heuristics, the suggested approach performs exceptionally well in performance evaluation.

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

The vehicle routing problem (VRP) is a highly significant and extensively studied issue in post-disaster rescue. In recent years, there has been widespread utilization of helicopters for post-disaster rescue. However, efficiently dispatching helicopters to reach rescue sites in post-disaster rescue is a challenge. To address this issue, this study models the issue of dispatching helicopters as a specific variant of the VRP with time window (VRPTW). Considering that the VRPTW is an NP-hard problem, the genetic algorithm (GA) as one of the prominent evolutionary algorithms with robust optimization capabilities, is a good candidate to deal with this issue. In this study, an improved GA with a local search strategy and global search strategy is proposed. To begin, a cooperative initialization strategy is proposed to generate an initial population with high quality and diversity. Subsequently, a local search strategy is presented to improve the exploitation ability. Additionally, a global search strategy is embedded to enhance the global search performance. Finally, 56 instances extended from Solomon instances are utilized for conducting simulation tests. The simulation results indicate that the average relative percentage increase (RPI) of the distance travelled by helicopters as obtained by the proposed algorithm is 0.178, 0.027, 0.075 and 0.041 times smaller than the average RPIs obtained by the tabu search algorithm, ant colony optimization algorithm, hybrid GA and simulated annealing algorithm, respectively. Simulation results reveal that the proposed algorithm is more efficient and effective for solving the VRPTW to reduce the driving distance of the helicopters in post-disaster rescue.

In order to realize the efficient collection and low-carbon transport of municipal garbage and accelerate the realize the “dual-carbon” goal for urban transport system, based on the modeling and solving method of vehicle routing problem, the municipal solid waste (MSW) collection and transport routing optimization of an Improved Ant Colony-Shuffled Frog Leaping Algorithm (IAC-SFLA) is proposed. In this study, IAC-SFLA routing Optimization model with the goal of optimization collection distance, average loading rate, number of collections, and average number of stations is constructed. Based on the example data of garbage collection and transport in southern Baohe District, the comparative analysis with single-vehicle models, multiple-vehicle models, and basic ant colony algorithms. The multi-vehicle model of collection and transportation is superior to the single-vehicle model and the improved ant colony algorithm yields a total collection distance that is 19.76 km shorter and an average loading rate that rises by 4.15% from 93.95% to 98.1%. Finally, the improved ant colony algorithm solves for the domestic waste collection and transportation path planning problem in the north district of Baohe. Thus, the effectiveness and application of the proposed algorithm is verified. The research result can provide reference for vehicle routing in the actual collection and transport process, improve collection and transport efficiency, and achieve the goal of energy conservation and emission reduction.

In this work, we extend the time-dependent vehicle routing problem with time windows on a road network by considering two types of vehicles, large and small, to serve customers. Motivated from city logistics applications, large vehicles are forbidden from the downtown area. Accordingly, goods must be transferred from large to small vehicles to serve downtown customers. This leads to synchronization issues at transfer points, which are special locations without storage capacity. The problem is not a pure two-echelon vehicle routing problem, since customers outside of the downtown area can be served directly by large vehicles. The problem is further compounded by the presence of time-dependent travel times that are defined on the arcs of the road network and are used to model congestion periods. To solve this difficult problem, we propose an adaptation of the Slack Induction by String Removals metaheuristic, which is state-of-the-art for the classical capacitated vehicle routing problem. Computational results on a set of test instances with different characteristics empirically demonstrate the optimization capabilities of this new metaheuristic on a problem which is much more complicated than the capacitated vehicle routing problem.