Genetic Algorithm for Solving a Dynamic Vehicle Routing Problem with Time Windows

This paper presents an overview of recent advances in the field of the vehicle routing problem (VRP), based on papers published in high-quality journals during the period from January 2015 to July 2017. A distinctive feature of the presented survey is its focus on new versions of the VRP, which have recently emerged or gained momentum, and the corresponding new solution methods, with particular emphasis on computational intelligence (CI) approaches. The list of newly proposed or currently popular VRP formulations include last mile and same day delivery, crowdshipping, bike sharing systems, post-disaster response plans, local routing in large production or cargo plants, customer-centric VRP, autonomous delivery, unnamed aerial vehicle delivery, green VRP, waste collection VRP, rich VRP, or VRP with backhauls. Simultaneously, an adequate increase of interest in the application of traditional CI methods (e.g., genetic, memetic, ant colony or particle swarm optimization, simulated annealing, or their various hybrid versions) can be observed in the VRP domain. At the same time, approaches proven efficient in other optimization areas (e.g., hyperheuristics, methods based on Monte Carlo simulations, algorithms rooted in game theory and bi-level optimization-Stackelberg games, or cognitively motivated methods) have lately entered the VRP field and become a viable alternative to more traditional techniques. Since VRP is one of the fastest growing fields in the operations research area, we believe that an analysis of the recently published VRP papers from the perspective of their novelty in problem formulation and/or applied solution method can provide a true value for the CI community, especially young researchers entering the field and seeking challenges in this interesting and fast developing research area.

A vehicle routing problem involves finding a set of optimal route for a fleet of capacitated vehicles which are available at a location to service the demands of a set of customers. In its simplest form, a customer is required to be visited once and the capacity of a vehicle must not be exceeded. In this paper, a review of four common and applicable variants of the vehicle routing problem, namely, capacitated vehicle routing problem, vehicle routing problem with time windows, periodic vehicle routing problem and the dynamic vehicle routing problem, are considered based on formulation techniques, methods of solution and areas of application. A summary table is presented for each variant to emphasis some key features that represent direction of current research.

SYNOPTIC ABSTRACTBranch exchange techniques, such as the well-known 2-opt and 3-opt procedures, are among the most powerful heuristics available for the solution of the classic vehicle routing problem. The imposition of time window constraints on customer delivery time within the vehicle routing problem, however, introduces several complexities that can reduce the power of these techniques. In this paper, two test data sets for the vehicle routing and scheduling problem with time window constraints are studied. Initial solutions are obtained using a variety of heuristics. These solutions are then improved using branch exchange procedures modified to incorporate the time window constraints.

Dynamic vehicle routing problem (DVRP) with single depot has received increasing interest from engineers and scientists. Dynamic multi-depot vehicle routing problem (DMDVRP), an extension of DVRP, however, has not received much attention. In our paper, a distance-based clustering approach is introduced to simplify the DMDVRP by allocating each customer to its nearest depot. Thus, DMDVRP is decomposed to a sequence of DVRPs. An improved ant colony optimisation (IACO) with ant-weight strategy and mutation operation is presented to optimise vehicle routing problem (VRP) in this paper. Moreover, to satisfy the real-time feature of DMDVRP, the nearest addition approach is used to handle the new orders occurring during a time slice on the basis of VRP solution. Finally, the computational results for 17 benchmark problems are reported to validate that IACO with the distance-based clustering approach is more suitable for solving DMDVRP.

The Vehicle Routing Problem (VRP) is a complex and high-level set of routing problems. Two of its important variants are the Dynamic Vehicle Routing Problem (DVRP) and the Green Vehicle Routing Problem (GVRP). The first one has become a challenging research topic in the last two decades, in which not all informations are known in advance, but are revealed as the system progresses. The second one is seen as a new application and solution in new logistics patterns, more specifically, for finding routes of vehicles to serve a set of customers while minimizing the total amount of CO 2 emissions, by increasing the loading rate and reducing the number of empty trips could reduce from 10% to 40% km traveled and therefore CO 2 emissions [1]. In this paper, we combine these two variants (DVRP and GVRP), where we try to minimize, in the dynamic environment, the greenhouse gas especially the carbon dioxide CO 2 , which is the immediate consequence of the depletion of the ozone layer and time duration. We will call this combination the Dynamic Green Vehicle Routing Problem (DGVRP). To study this new problem, we present the technique employed to estimate the amount of CO 2 emissions, the emission matrix and integrate them into the DGVRP model, then we propose the hybridization based on Ant Colony Optimization (ACO) algorithm with a Large Neighborhood Search (LNS) algorithm to solve our problem. The effectiveness of this approach is tested on a set of the dynamic green problems instances, which are adopted in this work from the static GVRP benchmark datasets.

This study considers the distribution network of a well-known perishable food manufacturer and its franchises in Turkey. As the countrywide number of stores is increasing fast, the company is facing problems due to its central distribution of products from a single factory. The objective is to decrease the cost of transportation while maintaining a high level of customer satisfaction. Hence, the focus is on the vehicle routing problem (VRP) of this large franchise chain within each city. The problem is defined as a rich VRP with heterogeneous fleet, site-dependent and compartmentalized vehicles, and soft/hard time windows. This NP-hard problem is modelled and tried with real data on a commercial solver. A basic heuristic procedure which can be used easily by the decision makers is also employed for obtaining quick and high-quality solutions for large instances.

The presence of multiple, often conflicting, objectives is a naturally occurring scenario in real-world decision making. Such problems are characterized by the existence of a set of efficient solutions instead of a single optimum. Evolutionary algorithms (EAs), which employ a population based search mechanism over a bounded decision/solution space, have emerged as popular tools for concurrently obtaining a good approximation to the entire efficient set, instead of finding a single solution at a time. While EAs hardly impose any restrictions on the form of the objective functions to be optimized, their design is generally based on the requirement that the feasible solution space of the problem be fixed. However, a situation contrary to the aforementioned is seen to occur during a bi-level formulation of the vehicle routing problem. Moreover, the problem is general enough to conceivably arise in many real-world situations. In light of this fact, the present paper alleviates the stated requirement by incorporating a bi-level perspective into a multi-objective EA. Thereafter, a preliminary study is carried out on the multi-objective variant of the NP-hard vehicle routing problem with time window constraints (VRPTW), in order to demonstrate the efficacy of the proposed approach.KeywordsBi-level ProgrammingMulti-Objective OptimizationEvolutionary AlgorithmVehicle Routing Problem with Time Windows

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.

Purpose. In order to study the impact of grey delivery time uncertainty on customer satisfaction and delivery costs, a vehicle routing problem with grey delivery time windows and multiobjective constraints is defined. Method. The paper first defines the uncertainty of the delivery vehicle’s arrival time to the customer as grey uncertainty and then whitens the grey time windows; at the same time, the customer’s hard time windows is expanded into a soft time windows to measure customer satisfaction when the vehicle arrives. Experiment. In order to verify the validity of the established model, numerical experiments are carried out in two groups based on the Solomon example, and the solution is solved based on the improved quantum evolution algorithm. Analysis. Distribution cost fluctuations and customer satisfaction fluctuations with grey time windows are relatively small; under different satisfaction threshold conditions, the distribution cost is increased gently with the satisfaction threshold. Conclusion. The grey delivery time windows have certain advantages in solving the random travel time vehicle routing problem.

A dynamic vehicle routing problem with time-dependent travel times

Minimizing fuel consumption and carbon emissions through vehicle routing is a critical objective for logistics companies, especially in light of stringent greenhouse gas emission policies enforced by various countries. To address this challenge, numerous studies have proposed robust vehicle routing problem models. Many of these focus on heterogeneous vehicle routing with time window constraints, aiming to reduce fuel consumption and emission costs. However, most research treats delays in customer time windows merely as penalty costs, giving limited attention to the impact of these delays on CO 2 emissions and their associated costs. Such delays—often caused by traffic congestion and rerouting—are significant contributors to excess CO 2 emissions. This paper addresses this overlooked aspect by proposing a model that accounts for the additional fuel consumption and CO 2 emissions resulting from delayed deliveries. It explores uncertainty in delivery schedules by analyzing three critical traffic scenarios: (1) vehicles idling in standstill traffic, (2) vehicles moving in slow traffic, and (3) vehicles being rerouted because of traffic uncertainties—all of which exacerbate CO 2 emissions from late deliveries. We propose a heterogeneous vehicle routing problem with carbon penalty, which optimizes routing to minimize CO 2 emissions for both on-time and delayed deliveries. A mathematical model and a robust genetic algorithm are developed, with their effectiveness validated through practical scenarios. The results offer valuable insights for logistics providers seeking to enhance both sustainability and operational efficiency.

In this paper vehicle routing problem with heterogeneous vehicle regarding the delivery time windows is examined . In the present case , each customer has a hard time window and a soft time window . Delivery outside the hardware time window is not possible. Delivery outside the soft time window earliness or delay costs imposed on the model . The mathematical model of the problem , innovative genetic algorithm for a given problem is developed . The results obtained from the sample solution by genetic algorithms , the exact solution of the model in the software Lingo is obtained and s uggests that genetic provided acceptable performance and low error gives an answer in a reasonable time .

In this paper, we consider a variant of vehicle routing problem with multiple trip and time windows. In this alternative problem, we think about the scheduling of trucks to a number of customers in the presence of fixed fleet and time windows constraints. This type of problem can be described as determining a number of vehicle trips minimising total travelled distance complying with the time windows and the multiple use of vehicles. We call this problem a multiple trips fixed fleet vehicle routing problems with time windows (MTFFVRPTW). To solve this variant, a new hybrid evolutionary algorithm for transport optimisation problems, called estimation of distribution algorithm with local search is used. The proposed algorithm integrates a double structure of distribution technique, which is used to introduce the variables dependency. To evaluate our approach we provide a number of experimentation to a modified Solomon's instances for the case of multiple trips. The results show that the hybrid proposed algorithm offer a good quality solution in the term of objective functions, also in the running time.

An Australian company is faced with the logistics problem of distributing small quantities of fibre boards to hundreds of customers every day. The resulting Heterogeneous Fleet Vehicle Routing Problem with Time Windows and Three-Dimensional Loading Constraints has to be solved within a single hour, hence the use of a heuristic instead of an exact method. In previous work, the loading was performed after optimising the routes, which in some cases generated infeasible solutions in need of a repair mechanism. In this work, the feasibility of the loading constraints is maintained during the route optimisation. Iterated Local Search has proved very effective at solving vehicle routing problems. Its success is mainly due to its biased sampling of locl optima. However, its performance heavily depends on the perturbation procedure. We trialled different perturbation procedures where the first one perturbs the given solution by moving deliveries that incur the highest cost on the objective function, whilst the second one moves deliveries that have been shifted less frequently by the local search in previous iterations. Our industry partner provided six sets of daily orders which have varied characteristics in terms of the number of customers, customer distribution, number of fibre boards and fibre boards’ sizes. Our investigations show that an instance becomes more constrained when the customer order contains many different board sizes, which makes it harder to find feasible solutions. The results show that the proposed perturbation procedures significantly enhances the performance of iterated local search specifically on such constrained problems.

Vehicle routing problem with fuzzy time windows