Search results for "Travelling salesman problem"
showing 10 items of 32 documents
The probabilistic pickup-and-delivery travelling salesman problem
2019
Abstract Transportation problems are essential in commercial logistics and have been widely studied in the literature during the last decades. Many of them consist in designing routes for vehicles to move commodities between locations. This article approaches a pickup-and-delivery single-vehicle routing problem where there is susceptibility to uncertainty in customer requests. The probability distributions of the requests are assumed to be known, and the objective is to design an a priori route with minimum expected length. The problem has already been approached in the literature, but through a heuristic method. This article proposes the first exact approach to the problem. Two mathematica…
A New Branch-and-Cut Algorithm for the Generalized Directed Rural Postman Problem
2016
The generalized directed rural postman problem, also known as the close-enough arc routing problem, is an arc routing problem with some interesting real-life applications, such as routing for meter reading. In this article we introduce two new formulations for this problem as well as various families of new valid inequalities that are used to design and implement a branch-and-cut algorithm. The computational results obtained on test bed instances from the literature show that this algorithm outperforms the existing exact methods
Branch-price-and-cut algorithms for the pickup and delivery problem with time windows and multiple stacks
2016
Abstract This paper proposes models and algorithms for the pickup and delivery vehicle routing problem with time windows and multiple stacks. Each stack is rear-loaded and is operated in a last-in-first-out (LIFO) fashion, meaning that when an item is picked up, it is positioned at the rear of a stack. An item can only be delivered if it is in that position. This problem arises in the transportation of heavy or dangerous material where unnecessary handling should be avoided, such as in the transportation of cars between car dealers and the transportation of livestock from farms to slaughterhouses. To solve this problem, we propose two different branch-price-and-cut algorithms. The first sol…
Branch-Price-and-Cut for the Soft-Clustered Capacitated Arc-Routing Problem
2021
The soft-clustered capacitated arc-routing problem (SoftCluCARP) is a variant of the classical capacitated arc-routing problem. The only additional constraint is that the set of required edges, that is, the streets to be serviced, is partitioned into clusters, and feasible routes must respect the soft-cluster constraint, that is, all required edges of the same cluster must be served by the same vehicle. In this article, we design an effective branch-price-and-cut algorithm for the exact solution of the SoftCluCARP. Its new components are a metaheuristic and branch-and-cut-based solvers for the solution of the column-generation subproblem, which is a profitable rural clustered postman tour …
Time-dependent asymmetric traveling salesman problem with time windows: Properties and an exact algorithm
2019
Abstract In this paper, we deal with the Time-Dependent Asymmetric Traveling Salesman Problem with Time Windows. First, we prove that under special conditions the problem can be solved as an Asymmetric Traveling Salesman Problem with Time Windows, with suitable-defined time windows and (constant) travel times. Second, we show that, if the special conditions do not hold, the time-independent optimal solution provides both a lower bound and (eventually) an upper bound with a worst-case guarantee for the Time-Dependent Asymmetric Traveling Salesman Problem with Time Windows. Finally, a branch-and-bound algorithm is presented and tested on a set of 4800 instances. The results have been compared…
Das Traveling Salesman Problem
1970
Unter den Reihenfolgeproblemen hat das Traveling Salesman Problem eine besondere Bedeutung. Aus diesem Grund ist ihm der meiste Platz dieses Buches gewidmet. Haufig werden sogar die Begriffe Reihenfolgeproblem und Traveling Salesman Problem synonym verwendet.
An algorithm for the Rural Postman problem on a directed graph
1986
The Directed Rural Postman Problem (DRPP) is a general case of the Chinese Postman Problem where a subset of the set of arcs of a given directed graph is ‘required’ to be traversed at minimum cost. If this subset does not form a weakly connected graph but forms a number of disconnected components the problem is NP-Complete, and is also a generalization of the asymmetric Travelling Salesman Problem. In this paper we present a branch and bound algorithm for the exact solution of the DRPP based on bounds computed from Lagrangean Relaxation (with shortest spanning arborescence sub-problems) and on the fathoming of some of the tree nodes by the solution of minimum cost flow problems. Computation…
An optimization approach for communal home meal delivery service
2009
Abstract: This paper is the first to discuss the communal home meal delivery problem. The problem can be modelled as a multiple travelling salesman problem with time windows, that is closely related to the well-studied vehicle routing problem with time windows. Experimental results are reported for a real-life case study from Central Finland over several alternative scenarios using the SPIDER commercial solver. The comparison with current practice reveals that a significant savings potential can be obtained using off-the-shelf optimization tools. As such, the potential for supporting real-life communal routing problems can be considered to be important for VRP practitioners.
The Steiner Traveling Salesman Problem and its extensions
2019
Abstract This paper considers the Steiner Traveling Salesman Problem, an extension of the classical Traveling Salesman Problem on an incomplete graph where not all vertices have demand. Some extensions including several depots or location decisions are introduced, modeled and solved. A compact integer linear programming formulation is proposed for each problem, where the routes are represented with two-index decision variables, and parity conditions are modeled using cocircuit inequalities. Exact branch-and-cut algorithms are developed for all formulations. Computational results obtained confirm the good performance of the algorithms. Instances with up to 500 vertices are solved optimally.
NP-completeness of the hamming salesman problem
1985
It is shown that the traveling salesman problem, where cities are bit strings with Hamming distances, is NP-complete.