Vehicle Routing Algorithm Research Articles

State-of-the Art Review—Evolutionary Algorithms for Vehicle Routing

This paper is a survey of the literature on applications of evolutionary algorithms for vehicle routing problems. It reports on genetic algorithms, evolution strategies, and particle swarm optimization when applied to the classical capacitated vehicle routing problem and many of its variants. The performance of evolutionary algorithms is also compared with the best alternative problem-solving approaches on benchmark instances.

Efficient Routing Algorithms for Multiple Vehicles With no Explicit Communications

In this paper, we consider a class of dynamic vehicle routing problems, in which a number of mobile agents in the plane must visit target points generated over time by a stochastic process. It is desired to design motion coordination strategies in order to minimize the expected time between the appearance of a target point and the time it is visited by one of the agents. We propose control strategies that, while making minimal or no assumptions on communications between agents, provide the same level of steady-state performance achieved by the best known decentralized strategies. In other words, we demonstrate that inter-agent communication does not improve the efficiency of such systems, but merely affects the rate of convergence to the steady state. Furthermore, the proposed strategies do not rely on the knowledge of the details of the underlying stochastic process. Finally, we show that our proposed strategies yield an efficient, pure Nash equilibrium in a game theoretic formulation of the problem, in which each agent's objective is to maximize the expected value of the ldquotime spent alonerdquo at the next target location. Simulation results are presented and discussed.

An exact algorithm for vehicle routing and scheduling problem of free pickup and delivery service in flight ticket sales companies based on set-partitioning model

This paper addresses a vehicle routing and scheduling problem arising in Flight Ticket Sales Companies for the service of free pickup and delivery of airline passengers to the airport. The problem is formulated under the framework of Vehicle Routing Problem with Time Windows (VRPTW), with the objective of minimizing the total operational costs, i.e. fixed start-up costs and variable traveling costs. A 0---1 mixed integer programming model is presented, in which service quality is factored in constraints by introducing passenger satisfaction degree functions that limit time deviations between actual and desired delivery times. The problem addressed in this paper has two distinctive characteristics--small vehicle capacities and tight delivery time windows. An exact algorithm based on the set-partitioning model, concerning both characteristics, is developed. In the first phase of the algorithm the entire candidate set of best feasible routes is generated, and then the optimal solution is obtained by solving the set-partitioning model in the second phase. Finally, we use four actual instances to illustrate application of the proposed algorithm. Moreover, the proposed algorithm is applied to a random instance containing more orders to verify the general effectiveness of the proposed algorithm even if the number of passengers increases in future.

Adaptive and Distributed Algorithms for Vehicle Routing in a Stochastic and Dynamic Environment

In this paper we present distributed and adaptive algorithms for motion coordination of a group of m autonomous vehicles. The vehicles operate in a convex environment with bounded velocity and must service demands whose time of arrival, location and on-site service are stochastic; the objective is to minimize the expected system time (wait plus service) of the demands. The general problem is known as the m-vehicle Dynamic Traveling Repairman Problem (m-DTRP). The best previously known control algorithms rely on centralized a-priori task assignment and are not robust against changes in the environment, e.g. changes in load conditions; therefore, they are of limited applicability in scenarios involving ad-hoc networks of autonomous vehicles operating in a time-varying environment. First, we present a new class of policies for the 1-DTRP problem that: (i) are provably optimal both in light- and heavy-load condition, and (ii) are adaptive, in particular, they are robust against changes in load conditions. Second, we show that partitioning policies, whereby the environment is partitioned among the vehicles and each vehicle follows a certain set of rules in its own region, are optimal in heavy-load conditions. Finally, by combining the new class of algorithms for the 1-DTRP with suitable partitioning policies, we design distributed algorithms for the m-DTRP problem that (i) are spatially distributed, scalable to large networks, and adaptive to network changes, (ii) are within a constant-factor of optimal in heavy-load conditions and stabilize the system in any load condition. Simulation results are presented and discussed.

Hybrid Genetic Algorithm for Vehicle Routing and Scheduling Problem

Hybrid Genetic Algorithm for Vehicle Routing and Scheduling Problem

Immune co-evolutionary algorithm based partition balancing optimization for tobacco distribution system

In China, the tobacco distribution is organized by fixed districts and routes with low efficiency and high distribution cost due to its unbalanced workload. And, though the dynamic method adopting vehicle routing algorithms produces optimal routes, the unstable routes increase the delivery time and managerial cost. So it is urgent and feasible to break the fixed districts to provide periodic balanced partitions for tobacco distribution. In this paper, a multi-criteria balanced partition model is built, whose minimal objectives including total number of tours in all districts, the travel distance and time of all tours, and the balance objectives include number of tours, total demand, traveling distance and time of each district are considered. An immune co-evolutionary algorithm with two stages is designed to search the optimal balanced partitions. In the first stage, the initial balanced partitions are produced. In the second stage, the clonal selection procedure, with partition proliferation, selection and elimination, and cooperative searching among districts, is adopted to achieve balanced partition. The experiments on Lenfen city in China as a practical application reveal the efficiency of the proposed model and algorithm. First, the searching processes are analyzed by exploring the partitions and Pareto partitions. Second, the evolutionary process of the algorithm is shown by the varying of the multiple objectives. Finally, three methods including fixed districts and routes, dynamic VRP scheduling and periodic balanced partition are compared to show the value of the study.

A vehicle routing algorithm for the distribution of fresh vegetables and similar perishable food

An algorithm for the distribution of fresh vegetables in which the perishability represents a critical factor was developed. This particular problem was formulated as a vehicle routing problem with time windows and time-dependent travel-times (VRPTWTD) where the travel-times between two locations depends on both the distance and on the time of the day. The model considers the impact of the perishability as part of the overall distribution costs and a heuristic approach, based on the tabu search is used to solve the problem. The performance of the algorithm was verified using modified Solomon’s problems. Using parameters typical of the Slovenian food market, different schedules were achieved, giving improvements of up to 47% reduction in perished goods.

A Branch and Price Algorithm for the Combined Vehicle Routing and Scheduling Problem With Synchronization Constraints

In this paper we present a branch and price algorithm for the combined vehicle routing and scheduling problem with synchronization constraints. The synchronization constraints are used to model situations when two or more customers need simultaneous service. The synchronization constraints impose a temporal dependency between vehicles, and it follows that a classical decomposition of the vehicle routing and scheduling problem is not directly applicable. With our algorithm, we have solved 44 problems to optimality from the 60 problems used for numerical experiments. The algorithm performs time window branching, and the number of subproblem calls is kept low by adjustment of the columns service times.

Vehicle routing and crew scheduling for metropolitan mail distribution at Australia Post

This paper presents a new multi-depot combined vehicle and crew scheduling algorithm, and uses it, in conjunction with a heuristic vehicle routing algorithm, to solve the intra-city mail distribution problem faced by Australia Post. First we describe the Australia Post mail distribution problem and outline the heuristic vehicle routing algorithm used to find vehicle routes. We present a new multi-depot combined vehicle and crew scheduling algorithm based on set covering with column generation. The paper concludes with a computational investigation examining the affect of different types of vehicle routing solutions on the vehicle and crew scheduling solution, comparing the different levels of integration possible with the new vehicle and crew scheduling algorithm and comparing the results of sequential versus simultaneous vehicle and crew scheduling, using real life data for Australia Post distribution networks.

A hybrid fuzzy-optimization approach to customer grouping-based logistics distribution operations

This paper presents an integrated fuzzy-optimization customer grouping based logistics distribution methodology for quickly responding to a variety of customer demands. The proposed methodology involves three main mechanisms: (1) pre-route customer classification using fuzzy clustering techniques, (2) determination of customer group-based delivery service priority and (3) en-route goods delivery using multi-objective optimization programming methods. In the process of pre-route customer classification, the proposed method groups customers’ orders primarily based on the multiple attributes of customer demands, rather than by static geographic attributes, which are mainly considered in classical vehicle routing algorithms. Numerical studies including a real-world application are conducted to illustrate the applicability of the proposed method and its potential advantages over existing operational strategies. Using the proposed method, it is shown that the overall performance of a logistics distribution system can be improved by more than 20%, according to the numerical results from the case studied.

Advanced vehicle routing algorithms for complex operations management problems

Vehicle routing encompasses a whole class of complex optimization problems that target the derivation of minimum total cost routes for a number of resources (vehicles) located at a central point (depot) in order to service efficiently a number of demand points (customers). Several practical issues in the food industry, involving both production and transportation decisions are modelled as VRP instances and are hard combinatorial problems in the strong sense (NP-hard). For such problems, metaheuristics, i.e., general solution procedures that explore the solution space to identify high quality solutions and often embed some standard route construction and improvement algorithms have been proposed. This paper surveys the recent research efforts on metaheuristic solution methodologies for the standard and most widely studied version of the Vehicle Routing Problem (VRP), i.e., the Capacitated VRP. The computational performance of each metaheuristic is presented for the 14 benchmark instances of Christofides et al. [Christofides, N., Mingozzi, A., & Toth, P. (1979). Combinatorial optimization (p. 315). Chichester: Wiley].

Time-Varying Travel Times in Vehicle Routing

Models and algorithms for vehicle routing are usually based on known constant travel times between all relevant locations, an assumption that is far from reality, particularly for urban areas. But the consideration of travel times that vary with the time of day poses two serious problems: the adaptation of the algorithms and the procurement of reliable data about the behavior of the travel times in the road network. This article describes the derivation of travel time data from modern traffic information systems. It presents a general framework for the implementation of time-varying travel times in various vehicle-routing algorithms. Finally, it reports on computational tests with travel time data obtained from a traffic information system in the city of Berlin.

Tabu Search Algorithm for Dynamic Vehicle Routing Problems Under Real-Time Information

Dynamic vehicle routing strategies have been widely discussed because of advances in information technologies. Dynamic vehicle routing problems are important aspects of commercial vehicle operation applications of intelligent transportation system technologies. One possible operational benefit of real-time information might be the ability to reroute commercial vehicles efficiently according to current traffic conditions. The present effort is aimed at developing a tabu-based dynamic vehicle routing algorithm under real-time information and then evaluating the algorithm in a simulation-assignment framework. Two types of information, historical information and real-time information, are considered in the tabu search algorithms to design temporal as well as spatial tabu lists for route construction and improvement. Numerical experiments conducted with the network of the city of Taichung, Taiwan, are presented to investigate dynamic vehicle dispatching and routing strategies under real-time information supply strategies and to assess the effectiveness of such strategies for traffic incidents.

A fuzzy-based customer classification method for demand-responsive logistical distribution operations

In some cases, customer classification is important for the development of advanced logistical distribution strategies in response to the growing complexity in business logistical markets. This paper presents a new approach that can be employed to cluster customers before executing fleet routing in logistical operations. The proposed approach is developed on the basis of fuzzy clustering techniques, and involves three sequential mechanisms including: (1) binary transformation, (2) generation of a fuzzy correlation matrix, and (3) customer clustering. Such a customer clustering method should be performed prior to vehicle dispatching and routing in the process of goods distribution. The proposed methodology clusters customers on the basis of their demand attributes, rather than the static geographic property which is considered extensively in most published vehicle routing algorithms. In addition to methodology development, a case study was conducted to demonstrate the potential advantages of the proposed fuzzy clustering based method. It is expected that this study can stimulate more research on time-based logistics control and management.

Fast Local Searches For The Vehicle Routing Problem With Time Windows

The purpose of this paper is to present new deterministic local searches for solving the vehicle routing problem with time windows. The proposed algorithms are based on a new three-phase approach. In the first phase an initial solution is created with one ofthe two proposed route construction heuristics. In the second phase a special local search operator based on ejection chains is used to reduce the number of routes. Finally, in the third phase well-known Or-opt exchanges are used to minimize the total distance of the routes. The findings of computational experiments indicate that the proposed methods are competitive with the best approaches proposed earlier in the literature in terms of solution quality, while being much faster. Moreover, the proposed algorithms may easily be used to create initial solutions for a wide variety of vehicle routing algorithms.

Comparing neuro-dynamic programming algorithms for the vehicle routing problem with stochastic demands

The paper considers a version of the vehicle routing problem where customers’ demands are uncertain. The focus is on dynamically routing a single vehicle to serve the demands of a known set of geographically dispersed customers during real-time operations. The goal consists of minimizing the expected distance traveled in order to serve all customers’ demands. Since actual demand is revealed upon arrival of the vehicle at the location of each customer, fully exploiting this feature requires a dynamic approach. This work studies the suitability of the emerging field of neuro-dynamic programming (NDP) in providing approximate solutions to this difficult stochastic combinatorial optimization problem. The paper compares the performance of two NDP algorithms: optimistic approximate policy iteration and a rollout policy. While the former improves the performance of a nearest-neighbor policy by 2.3%, the computational results indicate that the rollout policy generates higher quality solutions. The implication for the practitioner is that the rollout policy is a promising candidate for vehicle routing applications where a dynamic approach is required. Scope and purpose Recent years have seen a growing interest in the development of vehicle routing algorithms to cope with the uncertain and dynamic situations found in real-world applications (see the recent survey paper by Powell et al. [1]). As noted by Psaraftis [2], dramatic advances in information and communication technologies provide new possibilities and opportunities for vehicle routing research and applications. The enhanced capability of capturing the information that becomes available during real-time operations opens up new research directions. This informational availability provides the possibility of developing dynamic routing algorithms that take advantage of the information that is dynamically revealed during operations. Exploiting such information presents a significant challenge to the operations research/management science community. The single vehicle routing problem with stochastic demands [3] provides an example of a simple, yet very difficult to solve exactly, dynamic vehicle routing problem [2, p. 157] . The problem can be formulated as a stochastic shortest path problem [4] characterized by an enormous number of states. Neuro-dynamic programming [5,6] is a recent methodology that can be used to approximately solve very large and complex stochastic decision and control problems. In this spirit, this paper is meant to study the applicability of neuro-dynamic programming algorithms to the single-vehicle routing problem with stochastic demands.

Approximating Capacitated Routing and Delivery Problems

We provide approximation algorithms for some capacitated vehicle routing and delivery problems. These problems can all be viewed as instances of the following k-delivery TSP: given n source points and n sink points in a metric space, with exactly one item at each source, find a minimum length tour by a vehicle of finite capacity k to pick up and deliver exactly one item to each sink. The only known approximation algorithm for this family of problems is the 2.5-approximation algorithm of Anily and Hassin [ Networks, 22 (1992), pp. 419--433] for the special case k=1. For this case, we use matroid intersection to obtain a 2-approximation algorithm. Based on this algorithm and some additional lower bound arguments, we devise a factor-approximation for k-delivery TSP with arbitrary finite k. We also present a 2-approximation algorithm for the case $k = \infty$. We then initiate the study of dynamic variants of k-delivery TSP that model problems in industrial robotics and other applications. Specifically, we consider the situation where a robot arm (with finite or infinite capacity) must collect n point-objects moving in the Euclidean plane, and deliver them to the origin. The point-objects are moving in the plane with known, identical velocities---they might, for instance, be on a moving conveyor belt. We derive several useful structural properties that lead to constant-factor approximations for problems of this type that are relevant to the robotics application. Along the way, we show that maximum latency TSP is implicit in the dynamic problems, and that the natural "farthest neighbor" heuristic produces a good approximation for several notions of latency.

Roteamento de veículos com base em sistemas de informação geográfica

Um algoritmo para roteamento de veículos é integrado a um Sistema de Informação Geográfica, de cuja base de dados obtém as informações necessárias para o roteamento e no qual mostra as rotas resultantes. O algoritmo de roteamento utilizado tem como base a metaheurística de simulated annealing, que apresenta neste caso resultados computacionais de boa qualidade. Descrevemos a interface do algoritmo com um SIG específico e a aplicação do sistema resultante a um programa de entregas simulado, no bairro de Copacabana, no Rio de Janeiro.

A tabu search algorithm for the multi-trip vehicle routing and scheduling problem

This paper describes a novel tabu search heuristic for the multi-trip vehicle routing and scheduling problem (MTVRSP). The method was developed to tackle real distribution problems, taking into account most of the constraints that appear in practice. In the MTVRSP, besides the constraints that are common to the basic vehicle routing problem, the following ones are present: during each day a vehicle can make more than one trip; the customers impose delivery time windows; the vehicles have different capacities considered in terms of both volume and weight; the access to some customers is restricted to some vehicles; the drivers' schedules must respect the maximum legal driving time per day and the legal time breaks; the unloading times are considered.

A genetic algorithm for vehicle routing with backhauling

In this paper, a greedy route construction heuristic for a vehicle routing problem with backhauling is described. This heuristic inserts customers one by one into the routes using a fixed a priori ordering of customers. Then, a genetic algorithm is used to identify an ordering that produces good routes. Numerical comparisons are provided with an exact algorithm and with other heuristic approaches.