Showing papers on "Vehicle routing problem published in 2002"

Theory and Practice of Uncertain Programming

Abstract: From the Publisher: This book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory. It includes numerous modeling ideas, hybrid intelligent algorithms, and various applications in transportation problem inventory system, facility location & allocation, capital budgeting, topological optimization, vehicle routing problem, redundancy optimization, and scheduling. Researchers, practitioners and students in operations research, management science, information science, system science, and engineering will find this work a stimulating and useful reference.

A guide to vehicle routing heuristics

Abstract: Several of the most important classical and modern heuristics for the vehicle routing problem are summarized and compared using four criteria: accuracy, speed, simplicity and flexibility. Computational results are reported.

An Integer L-Shaped Algorithm for the Capacitated Vehicle Routing Problem with Stochastic Demands

Abstract: The classical Vehicle Routing Problem consists ofdetermining optimal routes form identical vehicles, starting and leaving at the depot, such that every customer is visited exactly once. In the capacitated version (CVRP) the total demand collected along a route cannot exceed the vehicle capacity. This article considers the situation where some ofthe demands are stochastic. This implies that the level of demand at each customer is not known before arriving at the customer. In some cases, the vehicle may thus be unable to load the customer's demand, even ifthe expected demand along the route does not exceed the vehicle capacity. Such a situation is referred to as a failure. The capacitated vehicle routing problem with stochastic demands (SVRP) then consists ofminimizing the total cost ofthe planned routes and of expected failures. Here, penalties for failures correspond to return trips to the depot. The vehicle first returns to the depot to unload, then resumes its trip as originally planned. This article studies an implementation of the IntegerL-shaped method for the exact solution of the SVRP. It develops new lower bounds on the expected penalty for failures. In addition, it provides variants of the optimality cuts for the SVRP that also hold at fractional solutions. Numerical experiments indicate that some instances involving up to 100 customers and few vehicles can be solved to optimality within a relatively short computing time.

Fleet scheduling and dispatching for demand-responsive passenger services

Abstract: This paper describes a software system designed to manage the deployment of a fleet of demand-responsive passenger vehicles such as taxis or variably routed buses. Multiple modes of operation are supported both for the fleet and for individual vehicles. Booking requests can be immediate (i.e. with zero notice) or in advance of travel. An initial implementation is chosen for each incoming request, subject to time-window and other constraints, and with an objective of minimising additional travel time or maximising a surrogate for future fleet capacity. This incremental insertion scheme is supplemented by post-insert improvement procedures, a periodically executed steepest-descent improvement procedure applied to the fleet as a whole, and a “rank-homing” heuristic incorporating information about future patterns of demand. A simple objective for trip-insertion and other scheduling operations is based on localised minimisation of travel time, while an alternative incorporating occupancy ratios has a more strategic orientation. Apart from its scheduling functions, the system includes automated vehicle dispatching procedures designed to achieve a favourable combination of customer service and efficiency of vehicle deployment. Provision is made for a variety of contingencies, including travel slower or faster than expected, unexpected vehicle locations, vehicle breakdowns and trip cancellations. Simulation tests indicate that the improvement procedures yield substantial efficiencies over more naive scheduling methods and that the system will be effective in real-time applications.

Parallel simulated annealing for the vehicle routing problem with time windows

Abstract: A parallel simulated annealing algorithm to solve the vehicle routing problem with time windows is presented. The objective is to find the best possible solutions to some well-known instances of the problem by using parallelism. The empirical evidence indicate that parallel simulated annealing can be applied with success to bicriterion optimization problems.

Using Constraint-Based Operators to Solve the Vehicle Routing Problem with Time Windows

Abstract: This paper presents operators searching large neighborhoods in order to solve the vehicle routing problem. They make use of the pruning and propagation techniques of constraint programming which allow an efficient search of such neighborhoods. The advantages of using a large neighborhood are not only the increased probability of finding a better solution at each iteration but also the reduction of the need to invoke specially-designed methods to avoid local minima. These operators are combined in a variable neighborhood descent in order to take advantage of the different neighborhood structures they generate.

Partially dynamic vehicle routing—models and algorithms

Abstract: In this paper we propose a framework for dynamic routing systems based on their degree of dynamism. Next, we consider its impact on solution methodology and quality. Specifically, we introduce the Partially Dynamic Travelling Repairman Problem and describe several dynamic policies to minimize routing costs. The results of our computational study indicate that increasing the dynamic level results in a linear increase in route length for all policies studied. Furthermore, a Nearest Neighbour policy performed, on the average, uniformly better than the other dispatching rules studied. Among these, a Partitioning policy produced only slightly higher average route lengths.

A new algorithm for a Dynamic Vehicle Routing Problem based on Ant Colony System

Abstract: An aboundant literature on vehicle routing problems is available. However, almost all the work deals with static problems where all data are known in advance, i.e. before the optimization has started. The technological advances of the last few years give rise to a new class of problems, namely the dynamic vehicle routing problems, where new orders are received as time progresses and must be dynamically incorporated into an evolving schedule. In this paper a dynamic vehicle routing problem is examined and a solving strategy, based on the Ant Colony System paradigm, is proposed. The method has been tested on a set of benchmarks we have defined starting from a set of widely available problems. Computational results confirm the effectiveness and the efficiency of the strategy we

A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows

Abstract: This paper addresses the problem of finding the minimum number of vehicles required to visit a set of nodes subject to time window and capacity constraints. The fleet is homogeneous and is located at a common depot. Each node requires the same type of service. An exact method is introduced based on branch and cut. In the computations, ever increasing lower bounds on the optimal solution are obtained by solving a series of relaxed problems that incorporate newly found valid inequalities. Feasible solutions or upper bounds are obtained with the help of greedy randomized adaptive search procedure (GRASP). A wide variety of cuts is introduced to tighten the linear programming (LP) relaxation of the original mixed-integer program. To find violated cuts, it is necessary to solve a separation problem. A substantial portion of the paper is aimed at describing the heuristics developed for this purpose. A new approach for obtaining feasible solutions from the LP relaxation is also discussed. Numerical results for standard 50- and 100-node benchmark problems are reported.

BoneRoute: An Adaptive Memory-Based Method for Effective Fleet Management

Abstract: This paper presents an adaptive memory-based method for solving the Capacitated Vehicle Routing Problem (CVRP), called BoneRoute. The CVRP deals with the problem of finding the optimal sequence of deliveries conducted by a fleet of homogeneous vehicles, based at one depot, to serve a set of customers. The computational performance of the BoneRoute was found to be very efficient, producing high quality solutions over two sets of well known case studies examined.

Solution of a Min-Max Vehicle Routing Problem

Abstract: We use a branch-and-cut search to solve the Whizzkids'96 vehicle routing problem, demonstrating that the winning solution in the 1996 competition is in fact optimal. Our algorithmic framework combines the LP-based traveling salesman code of Applegate, Bixby, ChvAital, and Cook, with specialized cutting planes and a distributed search algorithm, permitting the use of a computing network located across Rice, Princeton, AT&T, and Bonn. The 1996 problem instance wasdeveloped by E. Aartsand J. K. Lenstra, and the competition was sponsored by the information technology firm CMG and the newspaper De Telegraaf.

The school bus routing problem: a case study

Abstract: This paper describes a case study of the school bus routing problem. It is formulated as a multi-objective combinatorial optimisation problem. The objectives considered include minimising the total number of buses required, the total travel time spent by pupils at all pick-up points, which is what the school and parents are concerned with most, and the total bus travel time. It also aims at balancing the loads and travel times between buses. A heuristic algorithm for its solution is proposed. The algorithm has been programmed and run efficiently on a PC. Numerical results are reported using test data from a kindergarten in Hong Kong. It has shown to be effective with a saving of 29% in total travelling times when comparing to current practice.

Parallelization of a Two-Phase Metaheuristic for Routing Problems with Time Windows

Abstract: This paper describes the parallelization of a two-phase metaheuristic for the vehicle routing problem with time windows and a central depot (VRPTW). The underlying objective function combines the minimization of the number of vehicles in the first search phase of the metaheuristic with the minimization of the total travel distance in the second search phase. The parallelization of the metaheuristic follows a type 3 parallelization strategy (cf. Crainic and Toulouse (2001). In F. Glover and G. Kochenberger (eds.). State-of-the-Art Handbook in Metaheuristics. Norwell, MA: Kluwer Academic Publishers), i.e. several concurrent searches of the solution space are carried out with a differently configured metaheuristic. The concurrently executed processes cooperate through the exchange of solutions. The parallelized two-phase metaheuristic was subjected to a comparative test on the basis of 358 problems from the literature with sizes varying from 100 to 1000 customers. The derived results seem to justify the proposed parallelization concept.

A reactive tabu search meta-heuristic for the vehicle routing problem with back-hauls

Abstract: The vehicle routing problem with back-hauls involves the design of a set of minimum cost routes, originating and terminating at a central depot, for a set of vehicles to service a set of customers with known quantities to be either delivered or collected. This paper describes two route-construction heuristics that generate initial solutions quickly. These heuristics are based on the saving-insertion and saving-assignment procedures, respectively. The initial solutions are then improved by a reactive tabu search meta-heuristic. The reactive concept is used in a new way to trigger the switch between different neighbourhood structures for the intensification and diversification phases of the search. Special data structures are also used to manage efficiently the search of the neighbourhood space. Computational results are reported for a number of benchmarks. The results show that the proposed meta-heuristic is robust and competitive to the best approaches in the literature. Copyright © 2002 John Wiley & Sons, Ltd.

Accelerating Strategies in Column Generation Methods for Vehicle Routing and Crew Scheduling Problems

Abstract: This paper focuses on accelerating strategies used in conjunction with column generation to solve vehicle routing and crew scheduling problems. We describe techniques directed at speeding up each of the five phases of the solution process: pre-processor, subproblem, master problem, branch-and-bound, and post-optimizer. In practical applications, these methods often were key elements for the viability of this optimization approach. The research cited here shows their use led to computational gains, and notably to solutions that could not have been obtained otherwise due to practical problem complexity and size. In particular, we present recent methods directed at the integer programming aspect of the approach that were instrumental in substantially reducing the integrality gap found in certain applications, thereby helping to efficiently produce excellent quality solutions.

Tabu search variants for the mix fleet vehicle routing problem

Abstract: The Mix Fleet Vehicle Routing Problem (MFVRP) involves the design of a set of minimum cost routes, originating and terminating at a central depot, for a fleet of heterogeneous vehicles with various capacities, fixed costs and variable costs to service a set of customers with known demands. This paper develops new variants of a tabu search meta-heuristic for the MFVRP. These variants use a mix of different components, including reactive tabu search concepts; variable neighbourhoods, special data memory structures and hashing functions. The reactive concept is used in a new way to trigger the switch between simple moves for intensification and more complex ones for diversification of the search strategies. The special data structures are newly introduced to efficiently search the various neighbourhood spaces. The combination of data structures and strategic balance between intensification and diversification generates an efficient and robust implementation, which is very competitive with other algorithms in the literature on a set of benchmark instances for which some new best-known solutions are provided.

New assignment algorithms for the multi-depot vehicle routing problem

Abstract: This paper considers the design and analysis of algorithms for the multi-depot vehicle routing problem with time windows (MDVRPTW). Given the intrinsic difficulty of this problem class, approximation methods of the type ‘cluster first, route second’ (two-step approaches) seem to offer the most promise for practical size problems. After describing six heuristics for the cluster part (assignment of customers to depots) an initial computational study of their performance is conducted. Finding, as expected, that the heuristics with the best results (in terms of the routing results) are those with the largest computational efforts.

The Vehicle Routing Problem with Time Windows and Simultaneous Pick-up and Delivery

Abstract: In this paper we consider the problem of a single depot distribution/collection system servicing a set of customers by means of a homogeneous fleet of vehicles. Each customer requires the simultaneous delivery and pick-up of products to be carried out by the same vehicle within a given time window. Products to be delivered are loaded at the depot and picked-up products are transported back to the depot. The objective is to minimize the overall distance traveled by the vehicles while servicing all the customers. To the best of our knowledge no exact algorithms have been introduced for this problem. We implement a Branch and Price approach based on a set covering formulation for the master problem. A relaxation of the elementary shortest path problem with time windows and capacity constraints is used as pricing problem. Branch and Bound is applied to obtain integer solutions. Known benchmark instances for the VRP with time windows have been properly modified to be used for the experimental analysis.

Tabu Search heuristics for the Vehicle Routing Problem with Time Windows

Abstract: This paper surveys the research on the Tabu Search heuristics for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes for a fleet of vehicles from one depot to a set of geographically scattered points. The routes must be designed in such a way that each point is visited only once by exactly one vehicle within a given time interval; all routes start and end at the depot, and the total demands of all points on one particular route must not exceed the capacity of the vehicle. In addition to describing basic features of each method, experimental results for Solomon’s benchmark test problems are presented and analyzed.

Efficient Heuristics for the Heterogeneous Fleet Multitrip VRP with Application to a Large-Scale Real Case

Abstract: The basic Vehicle Routing Problem (VRP) consists of computing a set of trips of minimum total cost, to deliver fixed amounts of goods to customers with a fleet of identical vehicles. Few papers address the case with several types of vehicles (heterogeneous fleet). Most of them assume an unlimited number of vehicles of each type, to dimension the fleet from a strategic point of view. This paper tackles the more realistic tactical or operational case, with a fixed number of vehicles of each type, and the optional possibility for each vehicle to perform several trips. It describes several heuristics, including a very efficient one that progressively merges small starting trips, while ensuring that they can be performed by the fleet. This heuristic seeks to minimize the number of required vehicles as a secondary objective. It outperforms classical VRP heuristics, can easily handle various constraints, and gives very good initial solutions for a tabu search method. The real case of a French manufacturer of furniture with 775 destination stores is presented.

Parallel and Hybrid Models for Multi-objective Optimization: Application to the Vehicle Routing Problem

Abstract: Solving a multi-objective problem means to find a set of solutions called the Pareto frontier. Since evolutionary algorithms work on a population of solutions, they are well-adapted to multi-objective problems. When they are designed, two purposes are taken into account: they have to reach the Pareto frontier but they also have to find solutions all along the frontier. It is the intensification task and the diversification task. Mechanisms dealing with these goals exist. But with very hard problems or benchmarks of great size, they may not be effective enough. In this paper, we investigate the utilization of parallel and hybrid models to improve the intensification task and the diversification task. First, a new technique inspired by the elitism is used to improve the diversification task. This new method must be implemented by a parallel model to be useful. Second, in order to amplify the diversification task and the intensification task, the parallel model is extended to a more general island model. To help the intensification task, a hybrid model is also used. In this model, a specially defined parallel tabu search is applied to the Pareto frontier reached by an evolutionary algorithm. Finally, those models are implemented and tested on a bi-objective vehicle routing problem.