Showing papers by "Stefan Ropke published in 2009"

Branch and Cut and Price for the Pickup and Delivery Problem with Time Windows

Abstract: In the pickup and delivery problem with time windows vehicle routes must be designed to satisfy a set of transportation requests, each involving a pickup and delivery location, under capacity, time window, and precedence constraints. This paper introduces a new branch-and-cut-and-price algorithm in which lower bounds are computed by solving through column generation the linear programming relaxation of a set partitioning formulation. Two pricing subproblems are considered in the column generation algorithm: an elementary and nonelementary shortest path problem. Valid inequalities are added dynamically to strengthen the relaxations. Some of the previously proposed inequalities for the pickup and delivery problem with time windows are also shown to be implied by the set partitioning formulation. Computational experiments indicate that the proposed algorithm outperforms a recent branch-and-cut algorithm.

The traveling salesman problem with pickup and delivery: polyhedral results and a branch-and-cut algorithm

Abstract: The Traveling Salesman Problem with Pickup and Delivery (TSPPD) is defined on a graph containing pickup and delivery vertices between which there exists a one-to-one relationship. The problem consists of determining a minimum cost tour such that each pickup vertex is visited before its corresponding delivery vertex. In this paper, the TSPPD is modeled as an integer linear program and its polyhedral structure is analyzed. In particular, the dimension of the TSPPD polytope is determined and several valid inequalities, some of which are facet defining, are introduced. Separation procedures and a branch-and-cut algorithm are developed. Computational results show that the algorithm is capable of solving to optimality instances involving up to 35 pickup and delivery requests, thus more than doubling the previous record of 15.

Parallel large neighborhood search - a software framework

Abstract: This paper propose a simple, parallel, portable software framework for the metaheuristic named large neighborhood search (LNS). The aim is to provide a framework where the user has to set up a few data structures and implement a few functions and then the framework provides a metaheuristic where parallelization ”comes for free”. LNS was proposed in [14] and has been gaining popularity in the recent years, but is not as widely used e.g. tabu search, simulated annealing or genetic algorithms. We apply the parallel LNS heuristic to two different problems: the traveling salesman problem with pickup and delivery (TSPPD) and the capacitated vehicle routing problem (CVRP). We explain the TSPPD in Section 2 while we, because of the page-limitation, refer the reader to [17] for a description of the more well-known CVRP. Section 3 describes the large neighborhood search metaheuristic, Section 4 describes how the metaheuristic has been parallelized, 5 and 6 explains how the framework has been applied to the TSPPD and CVRP, respectively. Section 7 presents computational results.

Computer aided discovery of families of valid inequalities

Abstract: Computer aided discovery of families of valid inequalities When designing a branch-and-cut method for a specic problem class it is important to know classes of valid inequalities for the problem. We present a computer program that helps the user discovering new families of valid inequalities. It does so by finnding simple valid inequalities that are violated by a fractional solution supplied by the user. It is up to the user to generalize these examples further. We will present examples of new families of inequalities for the capacitated vehicle routing problem and the traveling salesman problem with pickup and deliveries found using the program.

Intelligent Freigth Transport Systems: Visions for real-time distribution planning

Abstract: The Danish innovation project entitled “Intelligent Freight Transport Systems” aims at developing prototype systems integrating public intelligent transport systems (ITS) with the technology in vehicles and equipment as well as the IT-systems at various transport companies. The objective is to enhance the efficiency and lower the environmental impact in freight transport. In this paper, a pilot project involving real-time waste collection at a Danish waste collection company is described, and a solution approach is proposed. The problem corresponds to the dynamic version of the waste collection problem which can be formulated as a dynamic version of the vehicle routing problem with time windows (VRPTW).

Disjunctive cuts in a branch-and-price algorithm for the capacitated vehicle routing problem

Abstract: This talk presents computational results that show the usefulness of the general-purpose valid inequalities disjunctive cuts when applied to the CVRP. Results indicate that the disjunctive cuts are able to reduce the gap between lower bound and upper bound more than state-of-the-art problem specific inequalities. Results also indicate that introducing the cuts leads to a smaller branch and bound tree and faster solution times overall. 1 Disjunctive cuts for the capacitated vehicle routing problem This talk presents another entry in the quest for proven optimal solutions to the capacitated vehicle routing problem (CVRP). The CVRP can be described as follows. We are given a set of customers {1, . . . , n} that each has a certain demand di. The customers must be served by a fleet of K homogeneous vehicles with capacity C. All vehicles are based in a common depot denoted 0. For each pair (i, j) ∈ {0, 1, . . . , n} we are given a travel cost cij . The objective of the problem is to construct K vehicle routes of minimum total cost. All vehicle routes must start and end at the depot, all customers must be visited exactly once and each route must satisfy the capacity limit of the vehicle. For details see [8]. Exact solution of the CVRP have intrigued researchers for decades and in recent years we have witnessed a substantial improvement of solution methods for the CVRP, see for example [7], [4] and [3]. The aim of our work is to investigate the effect of using disjunctive cuts in a branch-andcut-and-price algorithm for the CVRP. The branch-and-cut-and-price algorithm itself is is based

Intelligent Freight Transport Systems: Visions For Real-Time Distribution Planning

Abstract: The Danish innovation project entitled “Intelligent Freight Transport Systems” aims at developing prototype systems integrating public intelligent transport systems (ITS) with the technology in vehicles and equipment as well as the IT-systems at various transport companies. The objective is to enhance the efficiency and lower the environmental impact in freight transport. In this paper, a pilot project involving real-time waste collection at a Danish waste collection company is described, and a solution approach is proposed. The problem corresponds to the dynamic version of the waste collection problem which can be formulated as a dynamic version of the vehicle routing problem with time windows (VRPTW).