Vehicle Routing Problem With Time Windows Research Articles

Application of Lexisearch Algorithm to Vehicle Routing Problem with Time Windows

Vehicle Routing Problem with Time Windows (VRPTW) is an NP hard combinatorial scheduling optimization problem in which a minimum number of routes have to be determined so as to serve each of the destinations within their specified time windows. In this paper, the mail delivery of the Nigerian Postal Services (NIPOST) is modelled as a VRPTW in order to address the problem of delay in mail delivery occurring regularly in NIPOST. The Abuja Post Office is used as a case study and the Model of a related literature is applied with modifications to solve the problem. The problem is solved by applying Lexisearch algorithm using data that was obtained from Abuja Post Office and computational results on Solomon’s 100 instances were used to validate the algorithm.

Qubit Efficient Quantum Algorithms for the Vehicle Routing Problem on Noisy Intermediate‐Scale Quantum Processors

AbstractThe vehicle routing problem with time windows (VRPTW) is a common optimization problem faced within the logistics industry. In this work, the use of a previously‐introduced qubit encoding scheme is explored to reduce the number of qubits, to evaluate the effectiveness of Noisy Intermediate‐Scale Quantum (NISQ) devices when applied to industry relevant optimization problems. A quantum variational approach is applied to a testbed of multiple VRPTW instances ranging from 11 to 3964 routes. These intances are formulated as quadratic unconstrained binary optimization (QUBO) problems based on realistic shipping scenarios. The results are compared with standard binary‐to‐qubit mappings after executing on simulators as well as various quantum hardware platforms, including IBMQ, AWS (Rigetti), and IonQ. These results are benchmarked against the classical solver, Gurobi. The approach can find approximate solutions to the VRPTW comparable to those obtained from quantum algorithms using the full encoding, despite the reduction in qubits required. These results suggest that using the encoding scheme to fit larger problem sizes into fewer qubits is a promising step in using NISQ devices to find approximate solutions for industry‐based optimization problems, although additional resources are still required to eke out the performance from larger problem sizes.

Vehicle Routing Optimization Algorithms for Pharmaceutical Supply Chain: A Systematic Comparison

Abstract 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.

Reinforcement Learning for Solving Multiple Vehicle Routing Problem with Time Window

Vehicle routing problem with time window (VRPTW) is of great importance for a wide spectrum of services and real-life applications, such as online take-out and car-hailing platforms. A promising method should generate high-qualified solutions within limited inference time, and there are three major challenges: (a) directly optimizing the goal with several practical constraints; (b) efficiently handling individual time-window limits; and (c) modeling the cooperation among the vehicle fleet. In this article, we present an end-to-end reinforcement learning framework to solve VRPTW. First, we propose an agent model that encodes constraints into features as the input and conducts harsh policy on the output when generating deterministic results. Second, we design a time penalty augmented reward to model the time-window limits during gradient propagation. Third, we design a task handler to enable the cooperation among different vehicles. We perform extensive experiments on two real-world datasets and one public benchmark dataset. Results demonstrate that our solution improves the performance by up to 11.7% compared to other RL baselines and could generate solutions for instances within seconds, while existing heuristic baselines take for minutes as well as maintain the quality of solutions. Moreover, our solution is thoroughly analyzed with meaningful implications due to the real-time response ability.

Three-stage multi-modal multi-objective differential evolution algorithm for vehicle routing problem with time windows

In this paper, the mathematical model of Vehicle Routing Problem with Time Windows (VRPTW) is established based on the directed graph, and a 3-stage multi-modal multi-objective differential evolution algorithm (3S-MMDEA) is proposed. In the first stage, in order to expand the range of individuals to be selected, a generalized opposition-based learning (GOBL) strategy is used to generate a reverse population. In the second stage, a search strategy of reachable distribution area is proposed, which divides the population with the selected individual as the center point to improve the convergence of the solution set. In the third stage, an improved individual variation strategy is proposed to legalize the mutant individuals, so that the individual after variation still falls within the range of the population, further improving the diversity of individuals to ensure the diversity of the solution set. Based on the synergy of the above three stages of strategies, the diversity of individuals is ensured, so as to improve the diversity of solution sets, and multiple equivalent optimal paths are obtained to meet the planning needs of different decision-makers. Finally, the performance of the proposed method is evaluated on the standard benchmark datasets of the problem. The experimental results show that the proposed 3S-MMDEA can improve the efficiency of logistics distribution and obtain multiple equivalent optimal paths. The method achieves good performance, superior to the most advanced VRPTW solution methods, and has great potential in practical projects.

Logistics Optimization Using Hybrid Genetic Algorithm (HGA): A Solution to the Vehicle Routing Problem With Time Windows (VRPTW)

Logistics Optimization Using Hybrid Genetic Algorithm (HGA): A Solution to the Vehicle Routing Problem With Time Windows (VRPTW)

Vehicle Routing Problem with Time Windows to Minimize Total Completion Time in Home Healthcare Systems

We propose a vehicle routing problem with time windows (VRPTW) with compatibility-matching constraints and total completion time as the objective function, with applications in home healthcare routing and scheduling. Mixed integer linear programming is provided with total completion time minimization as the objective function. The solution approach has two objectives, total completion time (primary objective) and total distance (secondary objective). A heuristic is proposed comprising three phases: initializing to find an initial feasible routing (inserting the procedure with a modified K-means algorithm), swapping and moving the procedure to find a local optimal routing, and shooting the procedure to move away from the local optimum. Proof of feasibility for the inserting procedure is provided to prevent unnecessary insertions. Phases 2 and 3 will be repeated as needed to ensure solution quality. Solving our model with the proposed heuristic algorithm increases the total distance by 90.00% but reduces the total completion time by 25.86%. To test our model and heuristic, we examined a system with 400 home-healthcare cases in Chiang Mai. The heuristic quickly solved the problem. When total completion time is minimized, some caretakers serve up to twice as many patients as their coworkers; when total distance is minimized, workload discrepancies can increase up to seven-fold.

A neighborhood comprehensive learning particle swarm optimization for the vehicle routing problem with time windows

Vehicle routing problem with time windows (VRPTW), which is a typical NP-hard combinatorial optimization problem, plays an important role in modern logistics and transportation systems. Recent years, heuristic and meta-heuristic algorithms have attracted many researchers’ attentions to solve the VRPTW problems. As an outstanding meta-heuristic algorithm, particle swarm optimization (PSO) algorithm exhibits very promising performance on continuous problems. However, how to adapt PSO to efficiently deal with VRPTW is still challenging work. In this paper, we propose a neighborhood comprehensive learning particle swarm optimization (N-CLPSO) to solve VRPTW. To improve the exploitation capability of N-CLPSO, we introduce a new remove-reinsert neighborhood search mechanism, which consists of the removed operator and the reinsert operator. When performing the removed operator, the probability of adjacency between two customers is calculated by an information matrix (IM), which is constructed based on the customers’ time-space information and elite individuals’ local information. When executing the reinsert operator, the IM and a cost matrix (CM), which is introduced to record the cost of customer insertion, are used to find an optimal insert position. Moreover, to enhance the exploration of N-CLPSO, a semi-random disturbance strategy is proposed, in which elites’ longest common sequences (LCS) are saved, aiming to prevent population degradation. The N-CLPSO algorithm is tested on 56 Solomon benchmark instances, and it attains the optimal solutions on 29 instances. The simulation results and comparison results illustrate that the proposed algorithm outperforms or can compete with the majority of other 3 PSO variants as well as other 12 state-of-the-art algorithms.

Solving the vehicle routing problem with time windows using modified football game algorithm

The vehicle routing problem with time windows (VRPTW) is a famous problem in logistics and transportation that has many applications in real life. The objective of the problem is to find the minimum distance covered by a set of vehicles that set to start together from the warehouse and visit some prefixed customers within certain timeframes. In this paper, an efficient optimization algorithm, called modified football game algorithm (MFGA), is proposed to solve the VRPTW as an NP-hard problem. MFGA imitates the behavior of football players during a game to find the best positions to score a goal under the supervision of a team coach. In the presented algorithm, a new method is presented to create an initial solution for the VRPTW problem. In addition, a more efficient method has been designed to create a new location for the player, which makes the algorithm more efficient. The performance of the proposed MFGA is validated against Solomon’s VRPTW benchmark instances. Experimental results confirm that MFGA produces competitive results compared to several state-of-the-art algorithms in terms of various solution quality indicators. The proposed algorithm obtains 17 best-known solutions (BKSs) and improves 12 BKSs in the literature.

An Exact Method for a First-Mile Ridesharing Problem

Motivated by the worldwide development of shared mobility, we investigate a vehicle routing problem with time windows and deadlines called the first-mile ridesharing problem (FMRSP). The FMRSP involves routing a fleet of vehicles, each servicing customers within specific time windows. The FMRSP generalizes the well-known vehicle routing problem with time windows (VRPTW), additionally imposing that each vehicle route arrives at the destination before the earliest deadline associated with the set of customers served by the route. The FMRSP is also related to the VRPTW and release dates, where in addition to time window constraints, a release date is associated with each customer defining the earliest time that the order is available to leave the depot for delivery. For the FMRSP, we present an exact method based on a branch-price-and-cut (BPC) algorithm combining state-of-the-art techniques and an innovative pricing algorithm. The pricing algorithm is based on a bidirectional bucket graph-based labeling algorithm, in which the backward extension of a label is computed in a constant time. Effective dominance rules used to speed up the computation are also described. Extensive computational studies demonstrate that our proposed BPC algorithm can solve optimality-modified Solomon benchmark instances involving up to 100 customers and real-world instances involving up to 290 customers. Funding: This research was supported by the National Natural Science Foundation of China [Grants 71831003, 72171043, 71831006, and 71901180]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0139 .

A Systematic Literature Review of Vehicle Routing Problems with Time Windows

Vehicle routing problems with time windows (VRPTW) have gained a lot of attention due to their important role in real-life logistics and transport. As a result of the complexity of real-life situations, most problems are multi-constrained and multi-objective, which increases their difficulty. The aim of this paper is to contribute to the effective solution of VRPTW-related problems. Therefore, research questions and objectives are set in accordance with PRISMA guidelines, and data extraction and analysis of the relevant literature within the last five years (2018–2022) are compared to answer the set research questions. The results show that approximately 86% of the algorithms involved in the literature are approximate methods, with more meta-heuristics than heuristics, and nearly 40% of the literature uses hybrid methods combining two or more algorithms.

Distribution Management Problem: Heuristic Solution for Vehicle Routing Problem with Time Windows (VRPTW) in the Moroccan Petroleum Sector

Distribution Management Problem: Heuristic Solution for Vehicle Routing Problem with Time Windows (VRPTW) in the Moroccan Petroleum Sector

Multi-objective Logistics Distribution Path Optimization Based on Annealing Evolution Algorithm

Logistics distribution is a collection of interrelated organizations and facilities. There is a waste of cost and time in many links. Therefore, it is particularly important to use information technology to improve distribution efficiency. Under the constraints of delivery vehicle cost and time, this paper proposes an improved genetic simulated annealing algorithm (SAGA), which combines the global search ability of the genetic algorithm (GA) and the simulated annealing algorithm (SA) with strong local search ability to solve the vehicle routing problem with time windows (VRPTW). The perturbation factor is introduced to improve the local search, and the crossover method is optimized to obtain more efficient genetic operators by using population information. In this paper, combined with the actual application case, the simulation experiment is carried out in MATLAB. The experimental results show that, compared with the traditional genetic algorithm and simulated annealing algorithm, the total cost of the improved genetic simulated annealing algorithm is reduced by about 15%, which provides a more suitable vehicle route planning scheme.

Multi-armed bandit-based hyper-heuristics for combinatorial optimization problems

There are significant research opportunities in the integration of Machine Learning (ML) methods and Combinatorial Optimization Problems (COPs). In this work, we focus on metaheuristics to solve COPs that have an important learning component. These algorithms must explore a solution space and learn from the information they obtain in order to find high-quality solutions. Among the metaheuristics, we study Hyper-Heuristics (HHs), algorithms that, given a number of low-level heuristics, iteratively select and apply heuristics to a solution. The HH we consider has a Markov model to produce sequences of low-level heuristics, which we combine with a Multi-Armed Bandit Problem (MAB)-based method to learn its parameters. This work proposes several improvements to the HH metaheuristic that yields a better learning for solving problem instances. Specifically, this is the first work in HHs to present Exponential Weights for Exploration and Exploitation (EXP3) as a learning method, an algorithm that is able to deal with adversarial settings. We also present a case study for the Vehicle Routing Problem with Time Windows (VRPTW), for which we include a list of low-level heuristics that have been proposed in the literature. We show that our algorithms can handle a large and diverse list of heuristics, illustrating that they can be easily configured to solve COPs of different nature. The computational results indicate that our algorithms are competitive methods for the VRPTW (2.16% gap on average with respect to the best known solutions), demonstrating the potential of these algorithms to solve COPs. Finally, we show how algorithms can even detect low-level heuristics that do not contribute to finding better solutions to the problem.

An improved artificial bee colony with perturbation operators in scout bees’ phase for solving vehicle routing problem with time windows

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>An example of a combinatorial problem is the vehicle routing problem with time windows (VRPTW), which focuses on choosing routes for a limited number of vehicles to serve a group of customers in a restricted period. Meta-heuristics algorithms are successful techniques for VRPTW, and in this study, existing modified artificial bee colony (MABC) algorithm is revised to provide an improved solution. One of the drawbacks of the MABC algorithm is its inability to execute wide exploration. A new solution that is produced randomly and being swapped with best solution when the previous solution can no longer be improved is prone to be trapped in local optima. Hence, this study proposes a perturbed MABC known as pertubated (P-MABC) that addresses the problem of local optima. P-MABC deploys five types of perturbation operators where it improvises abandoned solutions by changing customers in the solution. Experimental results show that the proposed P-MABC algorithm requires fewer number of vehicles and least amount of travelled distance compared with MABC. The P-MABC algorithm can be used to improve the search process of other population algorithms and can be applied in solving VRPTW in domain applications such as food distribution.</span></p></div></div></div>

Addressing the Algorithm Selection Problem through an Attention-Based Meta-Learner Approach

In the algorithm selection problem, where the task is to identify the most suitable solving technique for a particular situation, most methods used as performance mapping mechanisms have been relatively simple models such as logistic regression or neural networks. In the latter case, most implementations tend to have a shallow and straightforward architecture and, thus, exhibit a limited ability to extract relevant patterns. This research explores the use of attention-based neural networks as meta-learners to improve the performance mapping mechanism in the algorithm selection problem and fully take advantage of the model’s capabilities for pattern extraction. We compare the proposed use of an attention-based meta-learner method as a performance mapping mechanism against five models from the literature: multi-layer perceptron, k-nearest neighbors, softmax regression, support vector machines, and decision trees. We used a meta-data dataset obtained by solving the vehicle routing problem with time window (VRPTW) instances contained in the Solomon benchmark with three different configurations of the simulated annealing meta-heuristic for testing purposes. Overall, the attention-based meta-learner model yields better results when compared to the other benchmark methods in consistently selecting the algorithm that best solves a given VRPTW instance. Moreover, by significantly outperforming the multi-layer perceptron, our findings suggest promising potential in exploring more recent and novel advancements in neural network architectures.

Application of Swarm Intelligence Optimization Algorithm in Logistics Delivery Path Optimization under the Background of Big Data

Traditional logistics delivery route optimization algorithm has some problems such as long time to find the optimal route. Based on this, this paper discusses swarm intelligence optimization algorithm and logistics delivery route optimization. To solve the logistics vehicle routing problem, considering that the basic ACO (ant colony optimization) has the disadvantages of slow convergence speed and easy to fall into local optimum, this paper proposes a new hybrid population optimization algorithm and applies it to VRPTW (vehicle routing problem with time windows). In addition, the concept of crowding degree in AFSA (artificial fish swarm algorithm) is introduced into ACO. In the early stage of the optimization process, a strong crowding degree limit is set to ensure that most ants are not affected by pheromone concentration to conduct random optimization. The simulation results show that the AC (accuracy rate) of this algorithm is 95.08%, which is higher than the traditional PSO (particle swarm optimization) algorithm and general heuristic algorithm. The hybrid algorithm can effectively improve the optimization efficiency of VRPTW, lay a foundation for solving large-scale VRPTW, and provide new research ideas and methods. At the same time, the results fully show that the algorithm in this paper has certain advantages in performance, and it can be applied to logistics delivery route optimization.

Optimization of the COVID-19 Vaccine Distribution Route Using the Vehicle Routing Problem with Time Windows Model and Capacity Constraint

At this time the effectiveness of the COVID-19 vaccines has been proven, and it is crucial to carry out the complete vaccination of the population. Therefore, it is imperative to optimize the vaccine distribution fleets. This paper discusses the optimization of distribution routes for the Pfizer vaccine in Portugal in terms of transportation time, total costs, and CO2 emissions. To this end, the Vehicle Routing Problem with Time Windows (VRPTW) model with a vehicle capacity restriction was used. The VRPTW model was tested for two scenarios. The first scenario allowed the driver to work overtime (585 min). The second scenario considered that the driver works 8 h (480 min). The results are presented to compare and justify the proposed method with large significance placed in terms of safety concerns, economic savings, environmental protection, and energy consumption. This paper aims to contribute to the healthcare system by optimizing the COVID-19 vaccine distribution routes and minimizing this process’s carbon footprint.

Vehicle Routing Optimization for Vaccine Distribution Considering Reducing Energy Consumption

In recent years, the energy consumption of vehicles has gained widespread attention due to the increasing importance of energy and environmental issues. Coupled with the explosive demand for vaccines that has spawned the massive deployment of refrigerated trucks, energy savings and efficiency improvement are the goals pursued by pharmaceutical logistics companies while getting the vaccine distribution task done. In order to evaluate the fuel consumption of refrigerated trucks during vaccine distribution, in this paper, we construct a mathematical model for the vehicle routing problem with time windows (VRPTW) for vaccine distribution with the aim of minimizing the total cost, including fossil fuel cost and penalty cost. Due to the NP-hardness and nonlinearity of the model, a genetic algorithm with a large neighborhood search operator (GA-LNS) and TSP-split encoding method is customized to address the large-scale problem. Numerical experiments show that the algorithm can obtain a near-optimal solution in an acceptable computational time. In addition, the proposed algorithm is implemented to evaluate a case of vaccine distribution in Haidian, Beijing, China. Insights on the effects of seasonal temperature, vehicle speed, driver working hours, and refrigeration efficiency are also presented.

An improved genetic algorithm for solving the helicopter routing problem with time window in post-disaster rescue.

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.