Scatter search for the vehicle routing problem with time windows

In this paper we use a scatter search framework to solve the vehicle routing problem with time windows (VRPTW). Our objective is to achieve effective solutions and to investigate the effects of reference set design parameters pertaining to size, quality and diversity. Both a common arc method and an optimization-based set covering model are used to combine vehicle routing solutions. A reactive tabu search metaheuristic and a tabu search with an advanced recovery feature, together with a set covering procedure are used for solution improvement. Our approach led to a robust solution method, generating solution quality that is competitive with the current best metaheuristics.     

The vehicle routing problem with coupled time windows

In this article we introduce the vehicle routing problem with coupled time windows (VRPCTW), which is an extension of the vehicle routing problem with time windows (VRPTW), where additional coupling constraints on the time windows are imposed. VRPCTW is applied to model a real-world planning problem concerning the integrated optimization of school starting times and public bus services. A mixed-integer programming formulation for the VRPCTW within this context is given. It is solved using a new meta-heuristic that combines classical construction aspects with mixed-integer preprocessing techniques, and improving hit-and-run, a randomized search strategy from global optimization. Solutions for several randomly generated and real-world instances are presented.     

The open vehicle routing problem with time windows

In this paper, we consider the open vehicle routing problem with time windows (OVRPTW). The OVRPTW seeks to find a set of non-depot returning vehicle routes, for a fleet of capacitated vehicles, to satisfy customers’ requirements, within fixed time intervals that represent the earliest and latest times during the day that customers’ service can take place. We formulate a comprehensive mathematical model to capture all aspects of the problem, and incorporate in the model all critical practical concerns. The model is solved using a greedy look-ahead route construction heuristic algorithm, which utilizes time windows related information via composite customer selection and route-insertion criteria. These criteria exploit the interrelationships between customers, introduced by time windows, that dictate the sequence in which vehicles must visit customers. Computational results on a set of benchmark problems from the literature provide very good results and indicate the applicability of the methodology in real-life routing applications.     

A route-neighborhood-based metaheuristic for vehicle routing problem with time windows

In this paper, a two-stage metaheuristic based on a new neighborhood structure is proposed to solve the vehicle routing problem with time windows (VRPTW). Our neighborhood construction focuses on the relationship between route(s) and node(s). Unlike the conventional methods for parallel route construction, we construct routes in a nested parallel manner to obtain higher solution quality. Valuable information extracted from the previous parallel construction runs is used to enhance the performance of parallel construction. In addition, when there are only a few unrouted customers left, we design a special procedure for handling them. Computational results for 60 benchmark problems are reported. The results indicate that our approach is highly competitive with all existing heuristics, and in particular very promising for solving problems of large size.     

Simulated annealing metaheuristics for the vehicle routing problem with time windows

This paper develops simulated annealing metaheuristics for the vehicle routing and scheduling problem with time window constraints. Two different neighborhood structures, the λ-interchange mechanism of Osman and thek-node interchange process of Christofides and Beasley, are implemented. The enhancement of the annealing process with a short-term memory function via a tabu list is examined as a basis for improving the metaheuristic approach. Computational results on test problems from the literature as well as large-scale real-world problem are reported. The metaheuristics achieve solutions that compare favorably with previously reported results.     

A bi-criteria heuristic for the vehicle routing problem with time windows

This paper describes a heuristic for the Vehicle Routing and Scheduling Problem with Time Windows (VRSPTW). Unique to this problem are the so-called time windows, i.e. time slots during which the vehicle must arrive at the customer to deliver the goods. The heuristic builds on the well-known Clarke and Wright Savings method with an additional criterion that models an intuitive view of time influence on route building. Experiments show that this added criterion yields significantly better solutions to the VRSPTW than pure routing heuristics, and also compares favorably to other new heuristics, developed specifically for the VRSPTW.     

POPMUSIC for a real-world large-scale vehicle routing problem with time windows

This paper presents a heuristic approach based on the POPMUSIC framework for a large-scale Multi Depot Vehicle Routing Problem with Time Windows derived from real-world data. POPMUSIC is a very powerful tool for tackling large problem instances. A Memetic Algorithm is used as an optimizer in the POPMUSIC framework. It is shown that a population-based search combined with decomposition strategies is a very efficient and flexible tool to tackle real-world problems with regards to solution quality as well as runtime.     

A hybrid search method for the vehicle routing problem with time windows

Vehicle Routing Problems have been extensively analyzed to reduce transportation costs. More particularly, the Vehicle Routing Problem with Time Windows (VRPTW) imposes the period of time of customer availability as a constraint, a common characteristic in real world situations. Using minimization of the total distance as the main objective to be fulfilled, this work implements an efficient algorithm which associates non-monotonic Simulated Annealing to Hill-Climbing and Random Restart. The algorithm is compared to the best results published in the literature for the 56 Solomon instances and it is shown how statistical methods can be used to boost the performance of the method.     

A greedy look-ahead heuristic for the vehicle routing problem with time windows

In this paper we consider the problem of physically distributing finished goods from a central facility to geographically dispersed customers, which pose daily demands for items produced in the facility and act as sales points for consumers. The management of the facility is responsible for satisfying all demand, and promises deliveries to the customers within fixed time intervals that represent the earliest and latest times during the day that a delivery can take place. We formulate a comprehensive mathematical model to capture all aspects of the problem, and incorporate in the model all critical practical concerns such as vehicle capacity, delivery time intervals and all relevant costs. The model, which is a case of the vehicle routing problem with time windows, is solved using a new heuristic technique. Our solution method, which is based upon Atkinson's greedy look-ahead heuristic, enhances traditional vehicle routing approaches, and provides surprisingly good performance results with respect to a set of standard test problems from the literature. The approach is used to determine the vehicle fleet size and the daily route of each vehicle in an industrial example from the food industry. This actual problem, with approximately two thousand customers, is presented and solved by our heuristic, using an interface to a Geographical Information System to determine inter-customer and depot–customer distances. The results indicate that the method is well suited for determining the required number of vehicles and the delivery schedules on a daily basis, in real life applications.     

A two-phase hybrid metaheuristic for the vehicle routing problem with time windows

The subject of this paper is a two-phase hybrid metaheuristic for the vehicle routing problem with time windows and a central depot (VRPTW). The objective function of the VRPTW considered here combines the minimization of the number of vehicles (primary criterion) and the total travel distance (secondary criterion). The aim of the first phase is the minimization of the number of vehicles by means of a (μ,λ)-evolution strategy, whereas in the second phase the total distance is minimized using a tabu search algorithm. The two-phase hybrid metaheuristic was subjected to a comparative test on the basis of 356 problems from the literature with sizes varying from 100 to 1000 customers. The derived results show that the proposed two-phase approach is very competitive.     

A vehicle routing problem with multi-trips and time windows for circular items

This article presents a vehicle routing problem with time windows, multiple trips, a limited number of vehicles and loading constraints for circular objects. This is a real problem experienced by a home delivery service company. A linear model is proposed to handle small problems and a two-step heuristic method to solve real size instances: the first step builds an initial solution through the modification of the Solomon I1 sequential insertion heuristic, and the second step improves the initial solution through the Tabu search algorithm proposed; in both steps, the problems related to circle packing with different sizes and bin packing are solved jointly with the use of heuristics. Finally, the computing results for two different sets of instances are presented.     

Heuristic solutions for the vehicle routing problem with time windows and synchronized visits

We present a simulated annealing based algorithm for a variant of the vehicle routing problem (VRP), in which a time window is associated with each client service and some services require simultaneous visits from different vehicles to be accomplished. The problem is called the VRP with time windows and synchronized visits. The algorithm features a set of local improvement methods to deal with various objectives of the problem. Experiments conducted on the benchmark instances from the literature clearly show that our method is fast and outperforms the existing approaches. It produces all known optimal solutions of the benchmark in very short computational times, and improves the best results for the rest of the instances.     

A powerful route minimization heuristic for the vehicle routing problem with time windows

We suggest an efficient route minimization heuristic for the vehicle routing problem with time windows. The heuristic is based on the ejection pool, powerful insertion and guided local search strategies. Experimental results on the Gehring and Homberger’s benchmarks demonstrate that our algorithm outperforms previous approaches and found 18 new best-known solutions.     

A column generation algorithm for the vehicle routing problem with soft time windows

The Vehicle Routing Problem with Time Windows consists of computing a minimum cost set of routes for a fleet of vehicles of limited capacity visiting a given set of customers with known demand, with the additional constraint that each customer must be visited in a specified time window. We consider the case in which time window constraints are relaxed into “soft” constraints, that is penalty terms are added to the solution cost whenever a vehicle serves a customer outside of his time window. We present a branch-and-price algorithm which is the first exact optimization algorithm for this problem.     

The vehicle routing problem with flexible time windows and traveling times

We generalize the standard vehicle routing problem by allowing soft time window and soft traveling time constraints, where both constraints are treated as cost functions. With the proposed generalization, the problem becomes very general. In our algorithm, we use local search to determine the routes of vehicles. After fixing the route of each vehicle, we must determine the optimal start times of services at visited customers. We show that this subproblem is NP-hard when cost functions are general, but can be efficiently solved with dynamic programming when traveling time cost functions are convex even if time window cost functions are non-convex. We deal with the latter situation in the developed iterated local search algorithm. Finally we report computational results on benchmark instances, and confirm the benefits of the proposed generalization.     

A branch-price-and-cut algorithm for the vehicle routing problem with time windows and multiple deliverymen

We address a variant of the vehicle routing problem with time windows that includes the decision of how many deliverymen should be assigned to each vehicle. In this variant, the service time at each customer depends on the size of the respective demand and on the number of deliverymen assigned to visit this customer. In addition, the objective function consists of minimizing a weighted sum of the total number of routes, number of deliverymen and traveled distance. These characteristics make this variant very challenging for exact methods. To date, only heuristic approaches have been proposed for this problem, and even the most efficient optimization solvers cannot find optimal solutions in a reasonable amount of time for instances of moderate size when using the available mathematical formulations. We propose a branch-price-and-cut method based on a new set partitioning formulation of the problem. To accelerate the convergence of the method, we rely on an interior-point column and cut generation process, a strong branching strategy and a mixed-integer programming-based primal heuristic. Additionally, a hierarchical branching strategy is used to take into account the different components of the objective function. The computational results indicate the benefits of using the proposed exact solution approach. We closed several instances of the problem and obtained upper bounds that were previously unknown in the literature.     

Scatter search for the fleet size and mix vehicle routing problem with time windows

This work proposes a scatter search (SS) approach to solve the fleet size and mix vehicle routing problem with time windows (FSMVRPTW). In the FSMVRPTW the customers need to be serviced in their time windows at minimal costs by a heterogeneous fleet. Computational results on 168 benchmark problems are reported. Computational testing revealed that our algorithm presented better results compared to other methods published in the literature.     

An iterated local search algorithm for the time-dependent vehicle routing problem with time windows

We generalize the standard vehicle routing problem with time windows by allowing both traveling times and traveling costs to be time-dependent functions. In our algorithm, we use a local search to determine routes of the vehicles. When we evaluate a neighborhood solution, we must compute an optimal time schedule for each route. We show that this subproblem can be efficiently solved by dynamic programming, which is incorporated in the local search algorithm. The neighborhood of our local search consists of slight modifications of the standard neighborhoods called 2- opt^*, cross exchange and Or-opt. We propose an algorithm that evaluates solutions in these neighborhoods more efficiently than the ones computing the dynamic programming from scratch by utilizing the information from the past dynamic programming recursion used to evaluate the current solution. We further propose a filtering method that restricts the search space in the neighborhoods to avoid many solutions having no prospect of improvement. We then develop an iterated local search algorithm that incorporates all the above ingredients. Finally we report computational results of our iterated local search algorithm compared against existing methods, and confirm the effectiveness of the restriction of the neighborhoods and the benefits of the proposed generalization.     

An incremental tabu search heuristic for the generalized vehicle routing problem with time windows

This paper describes an incremental neighbourhood tabu search heuristic for the generalized vehicle routing problem with time windows. The purpose of this work is to offer a general tool that can be successfully applied to a wide variety of specific problems. The algorithm builds upon a previously developed tabu search heuristic by replacing its neighbourhood structure. The new neighbourhood is exponential in size, but the proposed evaluation procedure has polynomial complexity. Computational results are presented and demonstrate the effectiveness of the approach.     

A hybrid generational genetic algorithm for the periodic vehicle routing problem with time windows

We propose a new population-based hybrid meta-heuristic for the periodic vehicle routing problem with time windows. This meta-heuristic is a generational genetic algorithm that uses two neighborhood-based meta-heuristics to optimize offspring. Local search methods have previously been proposed to enhance the fitness of offspring generated by crossover operators. In the proposed method, neighborhood-based meta-heuristics are used for their capacity to escape local optima, and deliver optimized and diversified solutions to the population of the next generation. Furthermore, the search performed by the neighborhood-based meta-heuristics repairs most of the constraint violations that naturally occur after the application of the crossover operators. The genetic algorithm we propose introduces two new crossover operators addressing the periodic vehicle routing problem with time windows. The two crossover operators are seeking the diversification of the exploration in the solution space from solution recombination, while simultaneously aiming not to destroy information about routes in the population as computing routes is NP-hard. Extensive numerical experiments and comparisons with all methods proposed in the literature show that the proposed methodology is highly competitive, providing new best solutions for a number of large instances.