A cutting plane algorithm for the General Routing Problem

نویسندگان

  • Ángel Corberán
  • Adam N. Letchford
  • José María Sanchis
چکیده

The General Routing Problem (GRP) is the problem of finding a minimum cost route for a single vehicle, subject to the condition that the vehicle visits certain vertices and edges of a network. It contains the Rural Postman Problem, Chinese Postman Problem and Graphical Travelling Salesman Problem as special cases. We describe a cutting plane algorithm for the GRP based on facet-inducing inequalities and show that it is capable of providing very strong lower bounds and, in most cases, optimal solutions.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Acceleration of Lagrangian Method for the Vehicle Routing Problem with Time Windows

The analytic center cutting plane method (ACCPM) is one of successful methods to solve nondifferentiable optimization problems. In this paper ACCPM is used for the first time in the vehicle routing problem with time windows (VRPTW) to accelerate lagrangian relaxation procedure for the problem. At first the basic cutting plane algorithm and its relationship with column generation method is clari...

متن کامل

A branch & cut algorithm for the windy general routing problem and special cases

In this paper we present an exact algorithm for the Windy General Routing Problem. This problem generalizes many important Arc Routing Problems and also has some interesting real-life applications. The Branch & Cut method presented here is based on a cutting-plane algorithm that identifies violated inequalities of several classes of facet-inducing inequalities for the corresponding polyhedron. ...

متن کامل

General Arc Routing Problems Solved by a Cutting Plane Algorithm and a Genetic Algorithm

Abstract: This paper considers an extended version of the Capacitated Arc Routing Problem (E-CARP), obtained by adding realistic constraints like prohibited turns to the basic CARP. Two integer linear models are presented, a mono-objective version and a biobjective one. A cutting plane method for the first version provides either an optimum or a lower bound that are used to benchmark a genetic ...

متن کامل

The mixed general routing polyhedron

In Arc Routing Problems, ARPs, the aim is to find on a graph a minimum cost traversal satisfying some conditions related to the links of the graph. Due to restrictions to traverse some streets in a specified way, most applications of ARPs must be modeled with a mixed graph. Although several exact algorithms have been proposed, no polyhedral investigations have been done for ARPs on a mixed grap...

متن کامل

Acceleration of Lagrangian Method for the Vehicle Routing Problem with Time Windows

The analytic center cutting plane method (ACCPM) is one of successful methods to solve nondifferentiable optimization problems. In this paper, ACCPM is used to accelerate Lagrangian relaxation procedure for solving a vehicle routing problem with time windows (VRPTW). First, a basic cutting plane algorithm and its relationship with a column generation technique is clarified. Then, the proposed m...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Math. Program.

دوره 90  شماره 

صفحات  -

تاریخ انتشار 2001