Capacitated Vehicle Routing Problem Research Articles

A Dynamic and Stochastic Cumulative Capacitated Vehicle Routing Problem

A Dynamic and Stochastic Cumulative Capacitated Vehicle Routing Problem

Hybrid Artificial Bee Colony Algorithm with Variable Neighborhood Search for Capacitated Vehicle Routing Problem

Aiming at the capacitated vehicle routing problem, a hybrid integer programming model with goal of lowest path cost is constructed, and a hybrid artificial bee colony algorithm with variable neighborhood search based on the model and the characteristics of the CVRP problem is proposed to solve the problem. The hybrid algorithm integrates the artificial bee colony algorithm and the variable neighborhood search algorithm, embeds a multi-variable neighborhood operator in the local search link of the artificial bee colony to carry out iteration. And the operator contains targeted transformation operations on path nodes, strings, and sub paths to ensure the diversity of the bee population. In addition, a variable neighborhood perturbation strategy is used to strengthen the algorithm's ability to escape from local optima. The comparative analysis of the literature study set and its algorithm solution shows that the designed hybrid variable neighborhood artificial bee colony algorithm has strong global search ability and high solution accuracy, especially in solution stability. HABC-VNS can obtain 47 optimal solutions in 74 examples. The average minimum deviation of the optimal solution is 0.34%, and the average deviation of the average CVRP set is 0.57%. The overall performance is better than the algorithm in the comparative literature.

Multi-start team orienteering problem for UAS mission re-planning with data-efficient deep reinforcement learning

AbstractIn this paper, we study the Multi-Start Team Orienteering Problem (MSTOP), a mission re-planning problem where vehicles are initially located away from the depot and have different amounts of fuel. We consider/assume the goal of multiple vehicles is to travel to maximize the sum of collected profits under resource (e.g., time, fuel) consumption constraints. Such re-planning problems occur in a wide range of intelligent UAS applications where changes in the mission environment force the operation of multiple vehicles to change from the original plan. To solve this problem with deep reinforcement learning (RL), we develop a policy network with self-attention on each partial tour and encoder-decoder attention between the partial tour and the remaining nodes. We propose a modified REINFORCE algorithm where the greedy rollout baseline is replaced by a local mini-batch baseline based on multiple, possibly non-duplicate sample rollouts. By drawing multiple samples per training instance, we can learn faster and obtain a stable policy gradient estimator with significantly fewer instances. The proposed training algorithm outperforms the conventional greedy rollout baseline, even when combined with the maximum entropy objective. The efficiency of our method is further demonstrated in two classical problems – the Traveling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP). The experimental results show that our method enables models to develop more effective heuristics and performs competitively with the state-of-the-art deep reinforcement learning methods.

Handling dynamic capacitated vehicle routing problems based on adaptive genetic algorithm with elastic strategy

With the development of e-commerce platforms, the logistics industry is also booming. The transportation process is at the core of the logistics industry, which influences the timeliness and rationality of logistics distribution. In the real world, there are many dynamic demands in logistics distribution, so logistics distribution should deal with dynamic demands quickly to realize more effective route planning. This paper proposes an adaptive genetic algorithm (AGA) with elastic strategy (AGA-ES) to solve the dynamic capacitated vehicle routing problems (DCVRPs). Firstly, AGA designs an adaptive local search operator, which can adaptively adjust the quantity of nodes that need local search, according to the fitness value of different individuals. At the same time, AGA develops adaptive crossover and mutation operators, which can automatically adjust the crossover and mutation probability based on the different fitness values. The experimental results verify the better performance of AGA on the traditional capacitated vehicle routing problems (CVRPs). After that, AGA combines elastic strategy (AGA-ES) to solve DCVRPs. This paper mainly concerns three types of actual demand information in DCVRPs: distribution nodes increase, distribution nodes decrease, and distribution road conditions change, according to the actual background. AGA-ES could interact with demand information and judge the types of different demands, and then adaptively plan new and reasonable routes after receiving one or more of the above demand information. The verification of benchmark data sets shows that AGA-ES can effectively deal with DCVRPs. Furthermore, this paper collects the longitude and latitude coordinates of 100 SF express stations in Xi’an, constructs the distribution information of these express stations, and verifies that AGA-ES can solve the DCVRPs under the actual background.

Optimizing combined tours: The truck-and-cargo-bike case

AbstractIn this paper, we introduce a last-mile delivery concept that is well suited for urban areas. By jointly optimizing the tour of a truck and a cargo bike, we ensure that each vehicle is used optimally. Here, we assume that the bike is restocked by meeting up with the truck so that no dedicated mini-hubs have to be constructed. We model different objective functions and analyze the different variants in comparison to the traveling salesperson problem as well as the capacitated vehicle routing problem. In an experimental evaluation, we compare MIP formulations for different problem variants and assess several heuristic approaches to solve large-scale instances. These results show that we can outperform the truck-only delivery in terms of completion time while reducing the distance driven by the truck.

Advanced vehicle routing in cement distribution: a discrete Salp Swarm Algorithm approach

ABSTRACT In this research, the focus is on addressing the capacitated vehicle routing problem (CVRP), a prominent logistical challenge within transportation management. The discrete salp swarm algorithm (DSSA) has been introduced as an innovative adaptation of the traditional salp swarm algorithm (SSA), specifically redesigned to cater to discrete characteristics inherent in problems like the CVRP. This algorithm integrates the core principles of SSA with mutation and crossover techniques, enhancing its applicability for discrete problems. The paper contributes in two main areas: firstly, the development of DSSA, tailored to address the unique requirements of VRP scenarios and ensuring a balanced approach between exploration and exploitation in discrete optimization. Secondly, the effectiveness of DSSA is demonstrated through practical applications, including an 8-customer routing task and a real-world case study involving cement delivery in Vietnam. In these scenarios, DSSA consistently demonstrates superior performance over other meta-heuristic strategies, marking a noteworthy advancement in the domain of optimization and providing a potential tool for complex routing challenges in logistics and distribution systems.

Vehicle routing with stochastic demand, service and waiting times — The case of food bank collection problems

Food banks play an important role both in combating food waste, and in alleviating hunger. However, due to the many uncertainties that food banks face, they often struggle to effectively collect all food items that donors such as supermarkets are willing to provide. To tackle this problem, we introduce the capacitated vehicle routing problem with travel time restrictions and stochastic demand, service and waiting times, in which the uncertainties are dependent of each other. This problem can be generalized to a large variety of routing applications. The goal of the problem is to determine a minimum number of vehicles, and to plan cost-effective routes for these vehicles so that each route violates the vehicle capacity and the travel time limit with only a very small probability. The resulting problem is highly complex and thus solved by means of a matheuristic, which decomposes the problem into its natural decision components. Thus, it first determines the number of districts into which the service area should be partitioned, before allocating each customer to exactly one district and then plans a route for each district. A set of feedback mechanisms is activated whenever no feasible solution has been found through these steps. Extensive numerical experiments, involving both randomly generated and real-life instances, demonstrate the matheuristic’s effectiveness in solving instances with up to 100 customers. When applying our matheuristic to real-life instances from Dutch and Canadian food banks, we furthermore gain managerial insights to assist in optimizing fleet size and route cost.

Tri-Objective Vehicle Routing Problem to Optimize the Distribution Process of Sustainable Local E-Commerce Platforms

The dramatic growth of online shopping worldwide in the last few years generated negative consequences for local small retailers who do not adopt information technologies. Furthermore, the e-commerce sector is considered a good opportunity to develop sustainable logistic processes. To reach this goal, the proposed paper presents a mathematical model and a metaheuristic algorithm to solve a multi-objective capacitated vehicle routing problem (CVRP) distinguished by economic, green, and ethical objective functions. The proposed algorithm is a multi-objective simulated annealing (MOSA) that is implemented in a software architecture and validated with real-world instances that differ for the product type delivered and the geographic distribution of customers. The main result of each test is a tri-dimensional Pareto front, i.e., a decision-support system for practitioners in selecting the best solution according to their needs. From these fronts, it can be observed that if the economic and environmental performances slightly deteriorate by 1.6% and 4.5%, respectively, the social one improves by 19.4%. Furthermore, the developed MOSA shows that the environmental and social objective functions depend on the product dimensions and the geographic distribution of customers. Regarding the former aspect, this paper reports that, counter-intuitively, the metabolic energy consumption per driver decreases with bigger products because the number of necessary vehicles (and drivers) increases, and, thus, the workload is divided among more employees. Regarding the geographic distribution, this manuscript illustrates that, despite similar traveled distances, highly variable altitudes cause more carbon emissions compared to flat distributions. Finally, this contribution shows that delivering small goods decreases the distance that vehicles travel empty by 59%, with a consequent cost reduction of 16%.

An exact algorithm for unpaired pickup and delivery vehicle routing problem with multiple commodities and multiple visits

This paper addresses a new multi-commodity unpaired pickup and delivery vehicle routing problem in which each vehicle is allowed to visit each customer more than once for both pickup and delivery of each commodity. It is a complex variant of the classical capacitated vehicle routing problem and comes from resource transfer among different plants in a distributed manufacturing environment. Notably, the pairing decisions of pickup and delivery for each commodity and the routing decisions among customers are interdependent, and they need to be made simultaneously and collaboratively. Firstly, a mixed integer programming model is developed, and then new valid inequalities are derived to improve the linear programming relaxation. Afterwards, a branch-and-cut algorithm is proposed by exploring different branching strategies and tailored separation algorithms. Computational results based on real-case instances from an automobile manufacturing company demonstrate that the costs are considerably reduced by considering the multiple visits compared to the single visit of each customer. In addition, our proposed branch-and-cut algorithm outperforms a manual solution method adopted by the company in practice and two solution methods in the literature. Furthermore, two adaptations of our branch-and-cut algorithm also perform better than two state-of-the-art algorithms in solving two closely-related problems in terms of solution quality and computation time. Sensitivity analyses with respect to vehicle capacity, vehicle duration, and vehicle speed are conducted to derive several valuable managerial insights.

An improved hybrid genetic search with data mining for the CVRP

AbstractThe hybrid genetic search (HGS) metaheuristic has produced outstanding results for several variants of the vehicle routing problem. A recent implementation of HGS specialized to the capacitated vehicle routing problem (CVRP) is a state‐of‐the‐art method for this variant. This paper proposes an improved HGS for the CVRP obtained by incorporating a new solution generation method into its (re‐)initialization process to guide the search more efficiently and effectively. The solution generation method introduced in this work combines an approach based on frequent patterns extracted from good solutions by a data mining process and a randomized version of the Clarke and Wright savings heuristic. As observed in our experimental comparison, the proposed method significantly outperforms the original algorithm regarding the final gap to the best known solutions and the primal integral.

Strategic Optimization in Distribution Centers: Leveraging Relocation, P-Median, and GIS-Based Routing for Enhanced Efficiency

In the realm of B2C (Business to Customer) company marketing, it is imperative to focus on sales and customer satisfaction. To uphold customer contentment, B2C enterprises must strategically position their delivery facilities to optimize efficiency and minimize both time and operational expenditures. PT ABC, a B2C entity specializing in the distribution of packaged goods, currently faces challenges in handling a substantial volume of requests, some of which are situated far from their distribution centers. This predicament leads to elevated fulfillment costs and an inefficient operational process. Consequently, the relocation of distribution center facilities becomes a necessity. The relocation process will be executed employing the P-Median method, facilitated by LINGO software. The P-Median analysis yielded three potential new locations: Cikupa, Jombang Wetan, and Bencongan Indah. Subsequently, further assessment through the resolution of the MTCVRP (Multitrip Capacitated Vehicle Routing Problem) with the aid of ArcGIS software was conducted. As a result, Jombang Wetan emerged as the optimal candidate, exhibiting a remarkable reduction of 165.7 kilometers or a 31.33% decrease in average mileage. This choice promises a more efficient and effective product distribution operation.

Solving the cumulative capacitated vehicle routing problem with drones

ABSTRACT In this paper, we consider the Cumulative Capacitated Vehicle Routing Problem (CCVRP), which is used to model many real-world applications, especially in the area of supplying humanitarian aid after a natural disaster. Interestingly, in this study, Unmanned Aerial Vehicles (UAVs) so-called drones are used to assist the trucks in delivering parcels to customers. Each of them travels to different locations to perform specified tasks and meet periodically with the vehicle from which it takes off to swap its battery. In this paper, a mathematical model is formulated which is then tested with small-sized problems using CPLEX software. Due to the difficulty of solving large instances to optimality, we propose a heuristic algorithm based on a well-established type of cluster-first, route-second approach. Then, it is enhanced by some proposed properties. Hereafter, we develop a minimum spanning tree based-lower bound. Finally, extensive computational experiments are carried out by using instances from the literature. They show the good performance of the proposed heuristic algorithm to solve large instances in a very competitive running time.

Capacitated Multi Drone Assisted Vehicle Routing Problem

Transportation is developing rapidly with today’s technology. By following different methods in every field, sustainable and low-cost transportation systems are tried to be created. Vehicle routing problems (VRP), which differ according to the fields, have been defined to produce solutions for these purposes. These differences occur according to the vehicles, nodes, and time limitations in the system. In much of the literature on VRPs, transportation varies according to the modes used, and these are referred to as air, land, and water transport. However, transportation modes that can operate as a hybrid, that is, integrated at the same time, have emerged with the development of technology. In this study, new generation vehicle routing problems integrated with emerging technology have been studied and, unlike other studies, a mixed integer programming model has been developed for the Multiple-Drone Assisted Capacitated Vehicle Routing Problem (mDroneCVRP), which minimizes the time of the last vehicle arriving at the warehouse. As the most important contribution, the assumption that drones take off from the same vehicle and land on the same vehicle in other studies has been stretched, thus providing the opportunity to take off and land from different vehicles. A constructive heuristic based on a greedy procedure is also developed and its solutions are compared with the MIP solution to analyze the performance of the algorithm.

Penerapan Algoritma Sweep dan Particle Swarm Optimization (PSO) sebagai Alternatif Menentukan Rute Distribusi

<em><span lang="EN-ID">One aspect of marketing activities is distribution. In the process of distributing goods, it is important to determine the optimal route that minimize mileage and reduce costs. This study aims to provide alternative solutions in determining distribution routes with the shortest distance which has implications for shorter travel times and lower costs. This research adapts the Capacitated Vehicle Routing Problem (CVRP) model with the approach of sweep and Particle Swarm Optimization (PSO) algorithm to determine the route. To generate a comparison route, we use the Nearest Neighbor (NN) algorithm. The result was that 100 agents were divided into 6 clusters and the total distance of the PSO-generated route is 218.115 units or 85.70% of the route distance generated by Nearest Neighbor algorithm</span></em><span lang="EN-ID">.</span>

Learning Feature Embedding Refiner for Solving Vehicle Routing Problems.

While the encoder-decoder structure is widely used in the recent neural construction methods for learning to solve vehicle routing problems (VRPs), they are less effective in searching solutions due to deterministic feature embeddings and deterministic probability distributions. In this article, we propose the feature embedding refiner (FER) with a novel and generic encoder-refiner-decoder structure to boost the existing encoder-decoder structured deep models. It is model-agnostic that the encoder and the decoder can be from any pretrained neural construction method. Regarding the introduced refiner network, we design its architecture by combining the standard gated recurrent units (GRU) cell with two new layers, i.e., an accumulated graph attention (AGA) layer and a gated nonlinear (GNL) layer. The former extracts dynamic graph topological information of historical solutions stored in a diversified solution pool to generate aggregated pool embeddings that are further improved by the GRU, and the latter adaptively refines the feature embeddings from the encoder with the guidance of the improved pool embeddings. To this end, our FER allows current neural construction methods to not only iteratively refine the feature embeddings for boarder search range but also dynamically update the probability distributions for more diverse search. We apply FER to two prevailing neural construction methods including attention model (AM) and policy optimization with multiple optima (POMO) to solve the traveling salesman problem (TSP) and the capacitated VRP (CVRP). Experimental results show that our method achieves lower gaps and better generalization than the original ones and also exhibits competitive performance to the state-of-the-art neural improvement methods.

A Two-Echelon Capacitated Vehicle Routing Problem With Sharing Satellite Resources

A Two-Echelon Capacitated Vehicle Routing Problem With Sharing Satellite Resources

Techno-economic analysis of natural gas distribution using a small-scale liquefied natural gas carrier

The design of the gas distribution for small-demand power plants located on remote islands is logistically challenging. The use of small-scale liquefied natural gas (LNG) vessels can be an option for these logistic problems. This paper aims to conduct a techno-economic analysis of using small-scale LNG vessels for gas distribution to the power plants that are spread across different islands. Route optimisation has been conducted using the capacitated vehicle routing problem method. The ship’s principal dimensions were determined using the aspect ratio from a linear regression of existing small-scale LNG vessels. As a case study, the gas demands for a gas power plant in eastern Indonesia were analysed into four distribution clusters. The results of the techno-economic analysis showed that the four distribution clusters have different characteristics regarding the LNG requirements, location characteristics and ship specifications. The capacity of small-scale LNG vessels feasible in terms of technical aspects varies from 2500, 5000, to > 10,000 m3 with variations in the ship speed depending on the location of the power plants. The amount of cargo requested and the shipping distance was affected to the cost of LNG transportation. The economic assessment proposes that the feasible investment by considering small-scale LNG cargo distribution, from the case study shows that with a ship capacity of 5000 m3 feasible margin rate is ≥ 3 USD/metric million British thermal units with an internal rate of return of 10% and estimated payback period is less than 15 years.

Learning to repeatedly solve routing problems

In the last years, there has been a great interest in machine‐learning‐based heuristics for solving NP‐hard combinatorial optimization problems. The developed methods have shown potential on many optimization problems. In this paper, we present a learned heuristic for the reoptimization of a problem after a minor change in its data. We focus on the case of the capacited vehicle routing problem with static clients (i.e., same client locations) and changed demands. Given the edges of an original solution, the goal is to predict and fix the ones that have a high chance of remaining in an optimal solution after a change of client demands. This partial prediction of the solution reduces the complexity of the problem and speeds up its resolution, while yielding a good quality solution. The proposed approach resulted in solutions with an optimality gap ranging from 0% to 1.7% on different benchmark instances within a reasonable computing time.

Pallets delivery: Two matheuristics for combined loading and routing

The implementation of novel regulatory and technical requirements for the distribution of vehicle axle weights in road freight transport introduces a new set of constraints on vehicle routing. Until now, axle weight distribution in determining the load plan for freight transport units has been overlooked in the vehicle routing process. Compliance with these axle weight constraints has become paramount for road freight transport companies, since noncompliance with the axle weight distribution legislation translates into heavy fines. This work aims to provide a tool capable of generating cargo loading plans and routing sequences for a palletised cargo distribution problem. The problem addressed integrates the capacitated vehicle routing problem with time window and the two-dimensional loading problem with load balance constraints. Two integrative solution approaches are proposed, one giving greater importance to the routing and the other prioritising the loading. In addition, a novel MILP model is proposed for the 2D pallet loading problem with load-balance constraints that take advantage of the standard dimension of the pallets. Extensive computational experiments were performed with a set of well-known literature benchmark instances, extended to incorporate additional features. The computational results show the effectiveness of the proposed approaches.

Meliorated Crab Mating Optimization Algorithms for Capacitated Vehicle Routing Problem

Meliorated Crab Mating Optimization Algorithms for Capacitated Vehicle Routing Problem