A data-driven preference learning approach for multi-objective vehicle routing problems in last-mile delivery

The last-mile delivery problem is one of the most complex and resource-intensive aspects of modern logistics, especially within the growing e-commerce sector. As online shopping continues to expand, companies are under immense pressure to deliver goods more quickly, efficiently, and at lower costs, all while meeting the demands of increasingly time-sensitive customers. This has created a need for innovative solutions that can tackle challenges related to dynamic traffic patterns, fluctuating customer preferences, and operational constraints such as vehicle capacities and delivery windows. In response to these challenges, this paper explores the application of predictive analytics as a tool for optimizing last-mile delivery routes in real-time.The study begins by identifying the core challenges inherent in last-mile logistics, particularly in the U.S. e-commerce landscape, where the cost of last-mile delivery can represent up to 53% of total shipping costs. With traffic congestion, unpredictable customer availability, and delivery time constraints posing significant hurdles, conventional static route planning models often fall short. In this paper, predictive analytics is proposed as a solution to these challenges, utilizing real-time data to inform more efficient routing decisions. By processing vast amounts of real-time traffic data, customer preferences, and delivery constraints, predictive models can offer a more flexible and responsive approach to last-mile delivery.The research then presents a comprehensive literature review of existing route optimization methods, such as the traditional Vehicle Routing Problem (VRP) and its extensions, including VRP with Time Windows (VRPTW), Dynamic VRP (DVRP), and Capacitated VRP (CVRP). While these models have proven useful, their limitations are exposed when faced with real-time operational complexities in the e-commerce sector. Therefore, this study introduces an advanced dynamic routing model that integrates machine learning algorithms—such as decision trees and neural networks—with traditional VRP frameworks. These machine learning models, trained on historical data, are capable of predicting future traffic patterns, customer behavior, and delivery time windows.A case study is conducted using data from U.S.-based e-commerce companies to demonstrate the practical application of predictive analytics in optimizing last-mile delivery. The case study outlines how predictive models are used to dynamically adjust delivery routes based on real-time conditions, leading to significant improvements in efficiency, cost savings, and customer satisfaction. Key performance indicators such as delivery times, fuel consumption, and vehicle utilization are examined before and after the implementation of the predictive models, with the results showing a reduction in delivery time by 20% and fuel costs by 15%, alongside improved on-time delivery rates.The paper concludes by presenting the proposed dynamic route optimization model as a solution that combines the flexibility and responsiveness of predictive analytics with the robust framework of traditional VRP models. Through the integration of machine learning, real-time data processing, and dynamic routing, the model is shown to significantly improve last-mile delivery efficiency. This study's findings highlight the potential for predictive analytics to revolutionize the logistics industry, particularly in the high-demand e-commerce sector, where quick and reliable delivery is paramount. The research suggests that as e-commerce continues to grow, predictive analytics will play an increasingly critical role in ensuring that last-mile delivery is both cost-effective and responsive to the evolving needs of consumers.

‘Route balance’ is the difference between the longest and the shortest among all the route lengths. The route balance is frequently considered in a vehicle routing problem (VRP) for balancing the distance travelled among delivery vehicles. This is a common practice since in VRPs there are no time elements. However, in recent years, some research works have considered route balance in a vehicle routing problem with time windows (VRPTW). As there are more time elements in VRPTW, this paper refutes that route balance is sufficient for VRPTW by simultaneously optimising makespan and workload imbalance using ‘total time balance’ instead of route balance. On the other hand, ‘total time balance’ is the difference between the longest total time taken and the shortest total time taken among delivery vehicles. As such, makespan is the longest total time taken among vehicles. Total time taken for a vehicle is the sum of vehicle run time, waiting time and service time. In order to demonstrate the importance of using total time balance instead of route balance on VRPTW, three different multi-objective VRPTW models, namely, (1) only with general VRPTW objectives (i.e. ‘total distance travelled’ by all vehicles and ‘total number of vehicles’ used), (2) general VRPTW objectives with route balance and (3) general VRPTW objectives with total time balance are developed and solved by fitness aggregated genetic algorithm (FAGA) for 36 Solomon’s benchmark instances. By comparison of the makespan produced by the FAGA between the three cases, the importance of using total time balance instead of route balance on multi-objective VRPTW is demonstrated. Also, the makespan produced by the FAGA for the third case, i.e. general VRPTW objectives with total time balance is compared with the makespan produced by fitness aggregated differential evolution (FADE). By comparing makespan with statistical testing between FAGA and FADE, the outperformance of FAGA over FADE is verified. To check the practicality of the total time balance on multi-objective VRPTW, an instance with real time windows is also solved for the three cases by the FAGA and its makespan are compared and reported.

The Vehicle Routing Problem with Time Windows involves finding the lowest-cost set of routes to deliver goods to customers, which have service time windows, using a homogeneous fleet of vehicles with limited capacity. In this paper, we propose and analyze the performance of an improved multi-objective evolutionary algorithm, that simultaneously minimizes the number of routes, the total travel distance, and the delivery time. Empirical results indicate that the simultaneous minimization of all three objectives leads the algorithm to find similar or better results than any combination of only two objectives. These results, although not the best in all respects, are better in some aspects than all previously published approaches, and fully multi-objective comparisons show clear improvement over the popular NSGA-II algorithm.KeywordsTime WindowMutation OperatorTravel DistanceDelivery TimeVehicle Route ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Besides its economic purpose, the vehicle routing problem has also garnered attention due to its social and environmental objectives in recent years.In terms of ensuring sustainability, it is beneficial to consider these three objectives together.CO 2 emissions, which is one of the causes of global warming, which we have felt more prominently in the past few years, has also affected the policies of logistics companies.Organizing working hours and ensuring fairness among employees are also one of our motivations in this study.Financial objectives has always taken into account.Simulated annealing algorithm and adaptive large neighborhood search algorithm are developed for the solution of the multi-objective mix integer mathematical model, in which financial, environmental, and social objective functions, which include alternative ways with different properties between nodes and different speed options.Small problems can be solved with exact solution method in literature, but to solve medium and larger samples heuristic algorithms are needed.When comparing algorithms, Simulated Annealing also gives better results than Adaptive Large Neighborhood Search in a shorter time.

Vehicle routing is considered the basic issue in distribution management. In real-world problems, customer demand for some commodities increases on special situations. On the one hand, one of the factors that are very important for customers is the timely delivery of the demanded commodities. In this research, customers had several different kinds of demands. Therefore, a new routing model was introduced in the form of integer linear programming by combining the concepts of time windows and multiple demands and by considering the two contradictory goals of minimizing travel cost and maximizing demand coverage. Moreover, two approaches were designed for the problem-solving model based on the NSGA-II algorithm with diversification of the mutation operator structure. The two criteria of spread and coverage of non-dominated solutions were used to compare algorithms. Study of some typical created problems indicated the validity of the model and the computational efficiency of the proposed algorithm. The proposed algorithm could increase the criterion of solution spread by about 10%, and increased the number of obtained solutions on the Pareto border compared to other algorithms, which indicated its high efficiency.

Optimization of maintenance services of a company working in the gas metering sector is investigated. In particular, daily tasks of operators are optimized by exploiting the paradigm of vehicle routing problems with a set of predefined time windows that overlap one with the others and four competing objectives to take into account. First, an exact integer formulation is presented that can be solved only for a reduced number of customer sites to visit. Then, a heuristic approach is proposed to find approximate solutions with huge savings on the computational effort, also for high‐dimensional instances. Numerical results on both real and synthetic scenarios showcase the effectiveness of the approach.

This paper was targeted at minimizing the expectation of traveling distance maximizing the expectation of customers' degree satisfaction, a multi-objective vehicle routing problem with stochastic demand (VRPSD) model based on soft time window was proposed. In order to solve the problem, a hybrid PSO algorithm based on Pareto optimization method was designed in this paper. The paper made the standard PSO algorithm discrete by re-defining operators and employing swap recon, utilized challenge tournament method to construct Pareto optimal solution set, applied an external archive to keep the diversity of solutions. Ultimately, a standard example is used to verify the validity of the algorithm.

This study proposes a genetic algorithm to solve the biobjective vehicle routing problem with time windows simultaneously considering total distance and distance balance of active vehicle fleet. A new complex chromosome is used to present the active vehicle route. Through tournament selection, one-point crossover, and migrating mutation operator, the solution of the problem is solved. In experiment on Solomon's benchmark problems, considering the total distance and distance balance, the results are improved in all classes of problems. According to the experimental results, the suggested approach is sufficient and the average GA performance is good.

Article history: Received December 10, 2013 Received in revised format 16 March 2014 Accepted April 29 2014 Available online May 14 2014 A crucial issue in humanitarian relief operations is vehicle routing because there are many difficulties in roads that people face when a disaster is occurred. In such circumstances, selecting more reliable routes could help rescue team act more efficacious. Therefore, we propose a mathematical model that maximizes the reliability of selected routes in disaster relief routing process using a multiple attribute decision making (MADM) technique. Furthermore, the proposed model minimizes the total cost that imposed to system. For this reason, the model is a multi-objective vehicle routing problem (VRP). The problem considered here is NP-hard and its objective is to find near optimal solutions, rather than optimal ones, using the nondominated sorting genetic algorithm. © 2014 Growing Science Ltd. All rights reserved.

Understanding the relationships between objectives in a multiobjective optimisation problem is important for developing tailored and efficient solving techniques. In particular, when tackling combinatorial optimisation problems with many objectives that arise in real-world logistic scenarios, better support for the decision maker can be achieved through better understanding of the often complex fitness landscape. This paper makes a contribution in this direction by presenting a technique that allows a visualisation and analysis of the local and global relationships between objectives in optimisation problems with many objectives. The proposed technique uses four steps: first the global pairwise relationships are analysed using the Kendall correlation method; then the ranges of the values found on the given Pareto front are estimated and assessed; next these ranges are used to plot a map using Gray code, similar to Karnaugh maps, that has the ability to highlight the trade-offs between multiple objectives; and finally local relationships are identified using scatter-plots. Experiments are presented for three different combinatorial optimisation problems: multiobjective multidimensional knapsack problem, multiobjective nurse scheduling problem and multiobjective vehicle routing problem with time windows. Results show that the proposed technique helps in the gaining of insights into the problem difficulty arising from the relationships between objectives.

A sharing logistics platform for less-than-truckloads could increase efficiency in city pickup and last-mile deliveries under time window constraints by pairing (matching) truck bidders and last-mile logistics requesters. The platform will propose new tours based on localization data, travel time and time-window constraints; it operates a matching algorithm to search for stable truck-sharing deals aiming to reduce the number of trucks in use as well as their operational costs. These sharing deals also reduce traveling distances and gas emissions. We simulate a model to understand the effects of fixed costs and variable costs in the operations, we account for reductions, and we provide some managerial insights. Additionally, we perform sensitivity analysis to consider the effect of delivery time windows’ relaxation and additional travel distance constraints to evaluate the proposed solutions under practical conditions.

Fleet management integrates strategies and technologies to solve fleet-related challenges efficiently while balancing the objectives of diverse stakeholders such as customers, fleet owners, service providers, and city governors. This thesis focuses on Vehicle Routing Problems (VRPs), which involve planning routes for capacitated vehicles to fulfill customer demands optimally under various constraints. Traditional methods, including exact and metaheuristic approaches, face inefficiencies and scalability issues with increasing problem complexity. Learning-based methods offer promising alternatives, providing high-quality solutions quickly once trained. However, challenges remain in managing extensive solution spaces in multi-objective settings, developing proactive depot generation strategies, and achieving scale generalization with a single training session. This research addresses these challenges through three studies. The first study introduces a Distance-Based Attention Mechanism (DBAM) that incorporates 2-D spatial positional information to enhance model performance in multi-objective VRPs, demonstrating superior results over traditional and existing learning-based methods. The second study presents a generative DRL framework for proactive depot generation in multi-depot logistics scenarios, showing significant improvements in routing efficiency. The third study proposes a Mix-scale learning framework enabling single-session training for multiple problem scales, achieving comparable or superior performance to scale-specific trained models. Collectively, these studies advance learning-based fleet management by enhancing reliability, efficiency, and scalability, offering practical, scalable solutions for real-world fleet logistics challenges.

The vehicle routing problem with time windows (VRPTW) has previously been investigated as a multi-objective problem. In this paper estimated carbon emissions is added as an objective alongside the number of vehicles required and distance travelled. We term this new problem formulation (E)VRPTW. In order to estimate emissions we require detailed information regarding the nature of the route to be taken. As previous benchmark VRPTW problem instances do not supply such information we generate new problem instances based upon street network data from Open Street Map. Results suggest that by adding emissions as the third objective, in many cases the search may be directed to areas that allow improvement in the distance and vehicles objectives. As emissions and distance are inherently related, we do not search for pareto fronts. Rather we attempt to find solutions that either minimise distance or minimise vehicles used. Adding the third emissions objective is shown to enable a multi-objective EA to find improved solutions in terms of minimal vehicles or minimal distance when compared to the same multi-objective EA using only two objectives.

Capacitated vehicle routing problem with time window (CVRPTW) is a critical issue in forwarding business. In this problem, normal cargoes (excluding freeze and hazardous goods) are normally consolidated before shipping to customer sites. Two objectives of delivery lead-time and total shipping cost are considered subject to vehicle capacity and time windows constraints. The fuzzy-compromise programming approach is utilised to handle the multi-objective model. Then, a so-called adaptive inertia weight particle swarm optimisation (AIWPSO) algorithm is applied to handle the cases of large number of delivered customers. In this work, a real case of a leading forwarding company in Vietnam is investigated to validate the proposed solution.

Vehicle routing problems (VRPs) have usually been studied with a single objective function defined by the distances associated with the routing of vehicles. The central problem is to design a set of routes to meet the demands of customers at minimum cost. However, in real life, it is necessary to take into account other objective functions, such as social functions, which consider, for example, the drivers' workload balance. This has led to growth in both the formulation of multiobjective models and exact and approximate solution techniques. In this article, to verify the quality of the results, first, a mathematical model is proposed that takes into account both economic and work balance objectives simultaneously and is solved using an exact method based on the decomposition approach. This method is used to compare the accuracy of the proposed approximate method in test cases of medium mathematical complexity. Second, an approximate method based on the Iterated Local Search (ILS) metaheuristic and Decomposition (ILS/D) is proposed to solve the biobjective Capacitated VRP (bi-CVRP) using test cases of medium and high mathematical complexity. Finally, the nondominated sorting genetic algorithm (NSGA-II) approximate method is implemented to compare both medium- and high-complexity test cases with a benchmark. The obtained results show that ILS/D is a promising technique for solving VRPs with a multiobjective approach.