This paper surveys the research on the metaheuristics for the Vehicle Routing Problem with Time Windows (VRPTW). The VRPTW can be described as the problem of designing least cost routes 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. Metaheuristics are general solution procedures that explore the solution space to identify good solutions and often embed some of the standard route construction and improvement heuristics described in the first part of this article. In addition to describing basic features of each method, experimental results for Solomon's benchmark test problems are presented and analyzed.

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Vehicle Routing Problem with Time Windows, Part II: Metaheuristics

This paper is the second part of a comprehensive survey on pickup and delivery models. Basically, two problem classes can be distinguished. The first part dealt with the transportation of goods from the depot to linehaul customers and from backhaul customers to the depot. In this class four subtypes were considered, namely the Vehicle Routing Problem with Clustered Backhauls (VRPCB all linehauls before backhauls), the Vehicle Routing Problem with Mixed linehauls and Backhauls (VRPMB any sequence of linehauls and backhauls permitted), the Vehicle Routing Problem with Divisible Delivery and Pickup (VRPDDP customers demanding delivery and pickup service can be visited twice), and the Vehicle Routing Problem with Simultaneous Delivery and Pickup (VRPSDP customers demanding both services have to be visited exactly once). The second part now considers all those problems where goods are transported between pickup and delivery locations, denoted as Vehicle Routing Problems with Pickups and Deliveries (VRPPD). These are the Pickup and Delivery VRP (PDVRP unpaired pickup and delivery points), the classical Pickup and Delivery Problem (PDP paired pickup and delivery points), and the Dial-A-Ride Problem (DARP paired pickup and delivery points and user inconvenience taken into consideration). A single as well as a multi vehicle mathematical problem formulation for all three VRPPD types is given, and the respective exact, heuristic, and metaheuristic solution methods are discussed.

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A survey on pickup and delivery problems: Part II: Transportation between pickup and delivery locations

This paper is the first part of a comprehensive survey on pickup and delivery problems. Basically, two problem classes can be distinguished. The first class, discussed in this paper, deals with the transportation of goods from the depot to linehaul customers and from backhaul customers to the depot. This class is denoted as Vehicle Routing Problems with Backhauls (VRPB). Four subtypes can be considered, namely the Vehicle Routing Problem with Clustered Backhauls (VRPCB – all linehauls before backhauls), the Vehicle Routing Problem with Mixed linehauls and Backhauls (VRPMB – any sequence of linehauls and backhauls permitted), the Vehicle Routing Problem with Divisible Delivery and Pickup (VRPDDP – customers demanding delivery and pickup service can be visited twice), and the Vehicle Routing Problem with Simultaneous Delivery and Pickup (VRPSDP – customers demanding both services have to be visited exactly once). The second class, dealt with in the second part of this survey, refers to all those problems where goods are transported between pickup and delivery locations. These are the Pickup and Delivery Vehicle Routing Problem (PDVRP – unpaired pickup and delivery points), the classical Pickup and Delivery Problem (PDP – paired pickup and delivery points), and the Dial-A-Ride Problem (DARP – passenger transportation between paired pickup and delivery points and user inconvenience taken into consideration). Single as well as multi vehicle versions of the mathematical problem formulations are given for all four VRPB types, the corresponding exact, heuristic, and metaheuristic solution methods are discussed.

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A survey on pickup and delivery problems

In this paper, we propose a metaheuristic to solve the pickup and delivery problem with time windows. Our approach is a tabu-embedded simulated annealing algorithm which restarts a search procedure from the current best solution after several non-improving search iterations. The computational experiments on the six newly-generated different data sets marked our algorithm as the first approach to solve large multiple-vehicle PDPTW problem instances with various distribution properties.

A metaheuristic for the pickup and delivery problem with time windows

Publisher Summary This chapter discusses some of the most important vehicle routing problem types. The vehicle routing problem lies at the heart of distribution management. It is faced each day by thousands of companies and organizations engaged in the delivery and collection of goods or people. Because conditions vary from one setting to the next, the objectives and constraints encountered in practice are highly variable. Most algorithmic research and software development in this area focus on a limited number of prototype problems. By building enough flexibility in optimization systems, these can be adapted to various practical contexts. The classical vehicle routing problem (VRP) is one of the most popular problems in combinatorial optimization, and its study has given rise to several exact and heuristic solution techniques of general applicability. The chapter presents a comprehensive overview of the available exact and heuristic algorithms for the VRP, most of which have been adapted to solve other variants.

Chapter 6 Vehicle Routing

In this paper, we propose a metaheuristic basedon annealing-like restarts to diversify andintensify local searches for solving the vehicle routing problem with time windows (VRPTW). Using the Solomons benchmark instances for the problem, our methodobtainedseven new best results andequaled19 other best results. Extensive comparisons indicate that our methodis comparable to the best in publishedliterature. This approach is flexible andcan be extend edto handle other variants of vehicle routing problems and other combinatorial optimization problems. 2002 Elsevier Science B.V. All rights reserved.

Andrew Lim

Papers

Discrete Optimization Local search with annealing-like restarts to solve the VRPTW