Delivering and picking goods under time window restrictions: an effective evolutionary algorithm

This paper studied the VRPSPDTW (Vehicle Routing Problem with Simultaneous Pickups and Deliveries and Time-Windows). An integer programming model is constructed, its objective is to minimize the delivery time. To further improve the convergence speed and optimization capability of the genetic algorithm, an improved genetic algorithm with local search (IGALS) is proposed, which is based on a hybrid crossover operation with elitist strategy and a local search using the thought of allowed delay time. The paper analyzed the advantages of heuristic algorithm to solve the problem by comparing the computation complexity between exact algorithm and heuristic algorithm. Testing by Solomon Benchmarks instances, the results show the IGALS has better performance than simple GA, which has better global optimization capability and faster convergence speed.

The vehicle routing problem with time windows (VRPTW) which has both capacity and time constraints is an extension of vehicle routing problem (VRP). The problem is solved by optimizing routes for the vehicles so as to meet all given constraints as well as to minimize travelling distance and number of vehicles. This paper proposes to analyze a multi objective evolutionary algorithm (MOEA) that incorporates Various heuristics for local exploitation in the evolutionary search and the concept of pareto’s optimality to solve multi objective optimization in VRPTW. In this paper we model VRPTW as a modified version specialized for a multi objective context, using Evolutionary Algorithm to get a set of pareto optimal solutions considering three objectives, the number of vehicles, the total travel distance and the total delivery time at the same time. This new approach is validated with very good results and the comparison is performed on a standard benchmark problems showing that the algorithm outperforms highly competitive results compared with previously published studies.

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.

Vehicle routing problem with fuzzy time windows

Vehicle routing problems with simultaneous pickup and delivery with time windows are studied in this paper. In a closed-loop logistics network, vehicles visiting customers for pickup and delivery may be only allowed for certain time intervals. A mixed integer programming model of the problem is presented. It has been known that solving vehicle routing problems with time windows is NP-hard. A heuristic solution procedure is developed to solve the problem. The proposed heuristic is tested on a number of numerical examples based on modified benchmark problems in the literature.

An adaptive memory methodology for the vehicle routing problem with simultaneous pick-ups and deliveries

In this paper, a parallel clustering technique and route construction heuristic have been developed for the vehicle routing problem (VRP) with split deliveries and pickups. An MILP formulation for determining the exact solution to the problem has also been included. It has been shown through extensive experimentation that the algorithm proposed in this paper statistically produces better results than the only heuristic existing for this class of problems in literature. We also form a basis of comparison between this class of problems and the VRP with simultaneous deliveries and pickups. We note that while heuristics for simultaneous deliveries and pickups cannot be applied in situations where customers' delivery or pickup demands exceed the vehicle capacity, heuristics allowing split deliveries and pickups can, in fact, be applied in every situation, even producing superior results under the combined objective of minimization of the fixed charge and mileage associated with vehicle routes. A guideline as to which heuristic could be used under what parametric conditions and objective functions, has also been provided.

The Clustered Vehicle Routing Problem with Time Window (CVRPTW) is an extension of the traditional Vehicle Routing Problem (VRP), which aims to find a high efficiency and feasible solution. In actual situation, the distribution of customer is not dispersed, but centralized in several regions. CVRPTW has greater research implications. Compared with Vehicle Routing Problem with Time Window (VRPTW), CVRPTW often has many constraints. The process of finding the optimal solution is more complicated, and the consumption of time resources is relatively large. Therefore, this paper proposes a multiobjective evolutionary algorithm with fast convergence strategy (MOEA-FCS) to solve CVRPTW. The fast convergence strategy divides the population into subpopulations, each of subpopulation evolves in different directions. Experimental results show that MOEA-FCS converges much faster than NSGA-II and SPEA2, the distribution of solutions is better than NSGA-II and SPEA2.

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.

The field of grain logistics transport vehicle route has seen the development of a variety of mathematical techniques, and the practical application of these techniques has depended on the use of spatial information, such as regional allocation information of road network. Vehicle Routing Problem (VRP) is regarded as the key of grain logistics distribution. In this paper, firstly, focus on the grain logistics VRP with time windows, then VRP model is successful constructed. In order to reduce the cost of grain logistics distribution, to combine the VRP model to geographic information system (GIS) by analyzing the VRP model. GIS takes into account for grain logistics, and the Particle Swarm Optimization (PSO) is used for the identification of optimal routes. And the optimal route for grain distribution is urgent since it has been calculated that, of the total cost for transportation. It improves the efficiency of grain logistics distribution and gets a better effect.

In this paper, an optimization algorithm based on lagrangian relaxation is proposed to solve the vehicle routing problem with time windows (VRPTW). The VRPTW is the generalization of the Vehicle Routing Problem, with a service time interval constraint available with every customer node. Here, an approach is used which relaxes the constraint set that justify that each customer should be serviced. The problem consists of introducing optimal lagrangian multipliers and then the subgradient method is used to find the appropriate multipliers. Here the problem focuses on, compared to the problems in the literature, not only the minimization of the transportation cost but also the used number of vehicles. The method has been implemented and tested on a series of well known benchmark test problems. The algorithm results to be very competitive and the results are better than the optimal solution.

This paper addresses the Multi-Vehicle Routing Problem with Time Windows and Simultaneous Pickup and Delivery (MVRPTWSPD), aiming to optimize logistics distribution routes and minimize total costs. A vehicle routing optimization model is developed based on the operational requirements of the KS Logistics Center, focusing on minimizing vehicle dispatch, loading and unloading, operating, and time window penalty costs. The model incorporates constraints such as vehicle capacity, time windows, and travel distance, and is solved using a genetic algorithm to ensure optimal route planning. Through MATLAB simulations, 34 customer points are analyzed, demonstrating that the simultaneous pickup and delivery model reduces total costs by 30.13%, increases vehicle loading rates by 20.04%, and decreases travel distance compared to delivery-only or pickup-only models. The results demonstrate the significant advantages of the simultaneous pickup and delivery mode in reducing logistics costs and improving vehicle utilization, offering valuable insights for enhancing the operational efficiency of the KS Logistics Center.

A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery

Approximative solutions to the bicriterion Vehicle Routing Problem with Time Windows

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