Solution Of Vehicle Routing Problem Research Articles

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

Graph Transformer with Reinforcement Learning for Vehicle Routing Problem

Vehicle routing problem (VRP) is one of the classic combinatorial optimization problems where an optimal tour to visit customers is required with a minimum total cost in the presence of some constraints. Recently, VRP is being solved with the use of deep reinforcement learning (DRL), with node sets considered (represented) as a graph structure. Existing Transformer based DRL solutions for VRP rely only on node information ignoring the role of information on the edges between nodes in the graph structure. In this paper, we proposed an attention‐based end‐to‐end DRL model to solve VRP which embeds edge information between nodes for rich graph representation learning. We used Transformer based encoder‐decoder framework with an edge information embedded multi‐head attention (EEMHA) layer in the encoder. The EEMHA‐based encoder learns underlying structure of the graph and generates an expressive graph topology representation by merging node and edge information. We trained our model using proximal policy optimization (PPO) with some code‐level optimization techniques. We conducted an experiment on randomly generated instances and on a real‐world data generated from road networks to verify the performance of our proposed model. The result from all experiments show that our model performs better than the existing DRL methods and most of the conventional heuristics with good generalizability from random instance training to real‐world instance testing of different problem size. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Approximate solution of the shortest path problem with resource constraints and applications to vehicle routing problems

<abstract><p>Vehicle routing problem (VRP) is a fundamental combinatorial optimization and integer programming problem with several important applications. The VRP is usually solved by using branch-and-bound techniques requiring solving a shortest path problem with resource constraints (SPPRC) and the determination of a lower bound, which can be computed by using column generation. The SPPRC entails finding the minimum cost elementary path in a valuated graph that is subject to constraints on resource consumption. The proposed exact solutions to this hard NP-hard problem require an excessive computation time which increases with the number of resources. In this paper, we propose a new approximate resolution of the SPPRC for acyclic and cyclic graphs. Our method is based on a Lagrangian relaxation of a subset of the constraints and using dominance only on a subset of the resources. This reduces the search space and allows users to efficiently compute solutions used to improve the column generation procedure. Extensive evaluation and comparison to the classical exact method show that the proposed algorithm achieves a good compromise between efficiency and quality of the SPPRC and the VRP solutions. Thus, our method can be used for practical large-scale VRP applications.</p></abstract>

Bacterial Memetic Algorithm for Asymmetric Capacitated Vehicle-Routing Problem

The vehicle-routing problem (VRP) has many variants, including the most accurate models of real-life transportation tasks, making it one of the most important mathematical problems in the field of logistics. Our goal was to design an algorithm that can race against the most recent solutions for VRP and capacitated VRP (CVRP), while also being applicable to real-life models with simulations of real transports. Our algorithm is a variant of the bacterial memetic algorithm (BMA), which we improve upon with novel operators and better methods for manual parameter optimization. The key to our performance is a balanced mixture of the global search of evolutionary algorithms, local search of 2-OPT variants, and the pseudo-global search of probabilistic construction algorithms. Our algorithm benefits from the advantages of all three methods resulting in fast convergence and avoidance of global minima. This is the first time BMA is applied for VRP, meaning that we had to adapt the method for the new problem. We compare our method with some of the most-used methods for VRP on the ABEFMP 1995 dataset. We provide comparison results with the coronavirus herd immunity optimizer, genetic algorithm, hybridization of genetic algorithm with neighborhood search, firefly algorithm, enhanced firefly algorithm, ant colony optimization, and variable neighborhood search. Our algorithm performed better on all data instances, yielding at least a 30% improvement. We present our best result on the Belgium 2017 dataset for future reference. Finally, we show that our algorithm is capable of handling real-life models. Here we are also illustrating the significance of the different parameters.

Approximating the Length of Vehicle Routing Problem Solutions Using Complementary Spatial Information

Accurately estimating the length of Vehicle Routing Problem (VRP) distances can inform transportation planning in a wide variety of delivery and service provision contexts. This study extends the work of previous research where multiple linear regression models were used to estimate the average distance of VRP solutions with various customer demands and capacity constraints. This research expands on that approach in two ways: first, the point patterns used in estimation have a wider range of customer clustering or dispersion values as measured by the Average Nearest Neighbor Index (ANNI) as opposed to just using a Poisson or random point process; second, the tour coefficient adjusted by this complementary spatial information is shown to exhibit statistically more accurate estimations. To generate a full range of ANNI values, point patterns were simulated using a Poisson process, a Matern clustering process, and a simple sequential inhibition process to obtain random, clustered, and dispersed point patterns, respectively. The coefficients of independent variables in the models were used to explain how the spatial distributions of customers influence the VRP distances. These results demonstrate that complementary spatial data can be used to improve operational results, a concept that could be applied more broadly.

Quality Analysis of Multi-Agent Multi-Item Pickup and Delivery Solutions Using a Decoupled Approach

In this article, we study the Multi-agent Multi-item Pickup and Delivery (MAMPD), which stands for a problem of finding collision-free trajectories for a fleet of mobile agents transporting a set of items from their initial positions to the specified goal locations. Each agent can carry multiple items up to a given capacity at the same moment. This requires solving two orthogonal problems concurrently: assigning a sequence of items to pick for every agent and finding a set of collision-free trajectories under this assignment. We decouple the problem into two subproblems: the task assignment (TA) and Multi-Agent Pathfinding (MAPF), to determine the lower and upper bounds of the MAMPD. First, a lower bound is estimated by formulating and solving the TA as a Vehicle Routing Problem (VRP). The collisions, which are not considered during the TA, are consequently resolved using a MAPF solver on the VRP solution. The cost of the MAPF solution forms an upper bound of the MAMPD. We show that on a large class of setups, the gap between the lower and upper bounds is small. This signifies that the decoupled MAMPD solver obtained near-optimal solutions. However, we show that on certain setups, intentionally designed to be difficult, the decoupled solver is unable to find a solution with a small gap even when using a bounded suboptimal MAPF solver. By computing the gap, we can determine whether the solution obtained by the decoupled approach is near-optimal or whether it is beneficial to use a more advanced MAMPD solver.

Getting Beyond the First Result of Solving a Vehicle Routing Problem

The simple vehicle routing problem (VRP) is a common topic of discussion in introductory operations research/management science courses. The VRP can be framed in a variety of ways, and it can be difficult to solve to optimality. For solution purposes, introductory textbooks demonstrate how Excel’s Evolutionary Solver (ES) add-in produces a routing. The ES utilizes a genetic algorithm with a heuristic stopping rule to produce a routing that is not guaranteed to be optimal. Beyond pointing out that search controls, such as maximum execution time, may be extended and followed by restart(s) of ES, textbook treatments do not offer alternative ways to continue the search for a possibly better routing. In this paper, a suite of ways is presented in which students may investigate beyond what ES produces or any other optimality-uncertain VRP solution method. The suite includes perturbation methods and other ways that function within an Excel spreadsheet environment that is popular with students and textbook writers. Because there is no demonstrable feature that confirms optimality, the student problem Solver must settle for a ‘best found’ result as unsettling as it may be. The incertitude is addressed.

Tourist group itinerary design: When the firefly algorithm meets the n-person Battle of Sexes

The presented research focuses on generating tourist trip itineraries for a group with different individual preferences on various points of interest. A set of walking routes among selected points of interest is provided by the Prize-Collecting Vehicle Routing Problem solution, considering several imposed constraints. However, the members of a tourist group request to stay together during their trip, despite their different preferences. Thus, to accommodate preferential heterogeneity in group itinerary design, the n-person Prize-Collecting Vehicle Routing Problem is proposed in this research, along with a novel, combined game theory and metaheuristic approach to solve it. Notably, the n-person Battle of Sexes game is utilized to configure a priori the set of locations to be visited, which results in three distinctive sets, depending on whether their visit is prohibited, mandatory, or optional. Consecutively, the metaheuristic firefly algorithm is employed to determine the tourist routes, enhanced with the coordinates-related encoding/decoding process. This process enables the original algorithm to solve discrete optimization problems without altering or hybridizing the original algorithmic framework. Compared with other metaheuristic algorithms, the proposed approach generates efficient and satisfactory tourist trip itineraries for heterogeneous groups.

Modeling and Solution of Vehicle Routing Problem with Grey Time Windows and Multiobjective Constraints

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.

Hybrid Cuckoo Search for the Capacitated Vehicle Routing Problem

Having the best solution for Vehicle Routing Problem (VRP) is still in demand. Beside, Cuckoo Search (CS) is a popular metaheuristic based on the reproductive strategy of the Cuckoo species and has been successfully applied in various optimizations, including Capacitated Vehicle Routing Problem (CVRP). Although CS and hybrid CS have been proposed for CVRP, the performance of CS is far from the state-of-art. Therefore, this study proposes a hybrid CS with Simulated Annealing (SA) algorithm for the CVRP, consisting of three improvements—the investigation of 12 neighborhood structures, three selections strategy and hybrid it with SA. The experiment was conducted using 16 instances of the Augerat benchmark dataset. The results show that 6 out of 12 neighborhood structures were the best and the disruptive selection strategy is the best strategy. The experiments’ results showed that the proposed method could find optimal and near-optimal solutions compared with state-of-the-art algorithms.

Optimal routing in VANET using improved meta‐heuristic approach: a variant of Jaya

VANETs are so-called vehicular ad hoc networks, they enable cost-effective, scalable solutions, and hence, they can be applicable in entertainment and transportation platforms with the assistance of multi-hop wireless communications from vehicle-to-vehicle. Conversely, in VANET circumstance, the multi-hop communication development is still a challenging one because of the quick change in topology and regular disconnection of a network. This directs to inefficiency or routing failure in existing mobile ad hoc routing protocols. To resolve routing issues, the number of research studies is going on to attain the multi-constrained Quality of Service (QoS) metrics in VANET. This study intends to propose a cost model as the solution for vehicle routing problem by considering the network quality metrics, including congestion, travel, collision, and QoS awareness cost. Fuzzification of the QoS factor is also included in this entire routing cost. Further, the primary objective of this work focuses on the minimisation of the routing cost model by finding the optimal route. To find an optimal route, this study introduces a new algorithm, namely Mean Computing Jaya Algorithm. At last, the performance of the proposed model is compared with existing work in the literature in terms of cost analysis and convergence analysis, and proves the betterment of the proposed model with reduced routing cost.

A generic exact solver for vehicle routing and related problems

Major advances were recently obtained in the exact solution of vehicle routing problems (VRPs). Sophisticated branch-cut-and-price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best existing VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, path enumeration, and rounded capacity cuts; all generalized through the new concepts of “packing set” and “elementarity set”. The concepts are also used to derive a branching rule based on accumulated resource consumption and to generalize the Ryan and Foster branching rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved.

On the exact solution of vehicle routing problems with backhauls

In this paper, we are interested in the exact solution of the vehicle routing problem with backhauls (VRPB), a classical vehicle routing variant with two types of customers: linehaul (delivery) and backhaul (pickup) ones. We propose two branch-cut-and-price (BCP) algorithms for the VRPB. The first one follows the traditional approach with one pricing subproblem, whereas the second one exploits the linehaul/backhaul customer partitioning and defines two pricing subproblems. The methods incorporate elements of state-of-the-art BCP algorithms, such as rounded capacity cuts, limited-memory rank-1 cuts, strong branching, route enumeration, arc elimination using reduced costs and dual stabilization. Computational experiments show that the proposed algorithms are capable of obtaining optimal solutions for all existing instances with up to 200 customers, many of them for the first time. The approach involving two pricing subproblems appears to be more efficient than the traditional one. We introduce new large instances and find tight bounds for them. We finally evaluate the performance of the algorithms on benchmark instances of the heterogeneous fixed fleet VRPB and the VRPB with time windows.

Optimal Solution of Vehicle Routing Problems with Fractional Objective Function

In this paper, we consider the vehicle routing problem (VRP) with fractional objective function. We investigate how the principal techniques used either in the context of fractional programming or in the context of vehicle routing problems interact. We present new dual and primal bounding procedures that have been incorporated in an exact method. The method proposed allows extending specific variants of the VRP to their counterpart with a fractional objective function. Extensive numerical experiments prove the validity of our approach.

An efficient parallel genetic algorithm solution for vehicle routing problem in cloud implementation of the intelligent transportation systems

A novel parallelization method of genetic algorithm (GA) solution of the Traveling Salesman Problem (TSP) is presented. The proposed method can considerably accelerate the solution of the equivalent TSP of many complex vehicle routing problems (VRPs) in the cloud implementation of intelligent transportation systems. The solution provides routing information besides all the services required by the autonomous vehicles in vehicular clouds. GA is considered as an important class of evolutionary algorithms that can solve optimization problems in growing intelligent transport systems. But, to meet time criteria in time-constrained problems of intelligent transportation systems like routing and controlling the autonomous vehicles, a highly parallelizable GA is needed. The proposed method parallelizes the GA by designing three concurrent kernels, each of which running some dependent effective operators of GA. It can be straightforwardly adapted to run on many-core and multi-core processors. To best use the valuable resources of such processors in parallel execution of the GA, threads that run any of the triple kernels are synchronized by a low-cost switching mechanism. The proposed method was experimented for parallelizing a GA-based solution of TSP over multi-core and many-core systems. The results confirm the efficiency of the proposed method for parallelizing GAs on many-core as well as on multi-core systems.

Electric Vehicle Fleet Management Using Ant Colony Optimisation

This research is focused on implementation of the ant colony optimisation (ACO) technique to solve an advanced version of the vehicle routing problem (VRP), called the fleet management system (FMS). An optimum solution of VRP can bring benefits for the fleet operators as well as contributing to the environment. Nowadays, particular considerations and modifications are needed to be applied in the existing FMS algorithms in response to the rapid growth of electric vehicles (EVs). For example, current FMS algorithms do not consider the limited range of EVs, their charging time or battery degradation. In this study, a new ACO-based FMS algorithm is developed for a fleet of EVs. A simulation platform is built in order to evaluate performance of the proposed FMS algorithm under different simulation case-studies. The simulation results are validated against a well-established method in the literature called nearest-neighbour technique. In each case-study, the overall mileage of the fleet is considered as an index to measure the performance of the FMS algorithm.

Capacitated vehicle routing problem using genetic algorithm: a case of cement distribution

Vehicle routing problem is a multi-objective problem. The problem involves optimising a fleet of vehicles that are to serve a number of customers from a central depot. Each vehicle has limited capacity and each customer has a certain demand. A procedure is introduced for the optimisation of a customer order service management system with a structured distribution network of a cement company of Bangladesh. The goal of the research is to find a solution of vehicle routing problem using genetic algorithm. It generates feasible clusters of resellers or distributors and determines delivery sequence and an optimal distribution network to meet demands by travelling minimum distance. The results of the study show that genetic algorithm provides a search technique used in computing to find true or approximate solution of search problems. The technique is able to determine the optimum route for the vehicles, while maintaining their constraints to get an optimal distribution network that minimises the total travelling distance.

Autonomous vehicle routing problem solution based on artificial potential field with parallel ant colony optimization (ACO) algorithm

An autonomous vehicle routing problem solution (VRPS) algorithm with parallel ant colony optimization (ACO) considering pilot satisfaction is proposed in this paper to solve the problem in traditional autonomous vehicle routing, such as the service quality is affected by longer flying time of pilot due to too much emphasis on cost factors and ignoring of delivery time. First, the flying time of pilot is considered to improve traditional autonomous flight model so as to comprehensively consider autonomous cost and pilot satisfaction. Then, for NP problems in autonomous flight, a parallel ACO algorithm is used for global optimization and design Mapreduce improvement method of parallel ACO, to improve optimization performance of the algorithm and to obtain optimal global solution. At last, a contrast experiment is conducted and the results show that, the algorithm proposed herein can effectively reduce the flying time of pilot and help to improve the service quality.

Investigation of the robustness of solutions of the problem of transport routing

The article deals with the problem which is of relevance nowadays: vehicle routing problem. This problem is considered in order to reduce delivery costs of the distributor. The solution of this problem allows to optimize and reorganize structure of the company and decrease using of recourses. The model of the vehicle routing problem, i. e. the use of different approaches, tools and algorithms to obtain a better result is investigated. Divid-ing this problem on subproblems gives opportunity for using different approaches in solving vehicle routing problem. The algorithm for solving the vehicle routing problem is proposed. The main idea of this algorithm is to use agglomerative clustering, tabu search, and union of the clusters sequentially. The program module for every method is devel-oped. There is an opportunity to make use of parallel computing, as a result of clustering-based approach. The proposed algorithm of the vehicle routing problem is checked with solving a real problem. Problem location is defined in Dnipro city. The visualization of every step of solving is presented as combining Google Maps API and JavaScript in web implementation. The quasi-optimal solution of the considered problem is obtained and its robustness is checked. The critical values which lead to rapid increase in the transporta-tion cost is found. Randomly data perturbation is also tested. Graphical implementation for every test is considered to create applied interpretation of results. Research results can be applied to obtain a solution to the vehicle routing problem and reduce delivery costs of the distributor. The idea of creating an interface for software, the use of other clustering algorithms, introduction of another algorithm of union of the clusters, and the use of dif-ferent approaches for checking the robustness of vehicle routing problem solution is considered as a further research

A new approach for solution of vehicle routing problem with hard time window: an application in a supermarket chain

In this study, a vehicle routing problem with hard time windows (VRPHTW) that appears to meet demands of customers’ service within time intervals in a supermarket chain is solved. In VRPHTW, to reach a solution by an exact method is quite difficult and sometimes impossible if number of constraints is large enough (i.e., NP-hard), and solution time of a VRPHTW grows exponentially. As the size of the problem grows, a near optimal solution can be found using a heuristic method. A hierarchical approach consisting of two stages as “cluster-first route-second” is proposed. In the first stage, customers are assigned to vehicles using three different clustering algorithms (i.e., K-means, K-medoids and DBSCAN). In the second stage, a VRPHTW is solved using a MILP. The main contribution of the article is that the proposed hierarchical approach enables us to deal with a large size real problem and to solve it in a short time using the exact method. Finally, the proposed approach is employed on a supermarket chain. An instance of the algorithm is demonstrated to illustrate the applicability of the proposed approach and the results obtained are highly favourable.