We present a very simple family of traveling salesman instances with n cities where the nearest neighbor rule may produce a tour that is Θ(log n) times longer than an optimum solution. Our family works for the graphic, the euclidean, and the rectilinear traveling salesman problem at the same time. It improves the so far best known lower bound in the euclidean case and proves for the first time ...

In the single objective period traveling salesman problem (SOPTSP), each of given n cities has to be visited by the traveling salesman a fixed number of times according to some allowable day combinations over a given m day planning period with the objective to minimize the total traveling distance over the whole period. The existing solution methods for the SOPTSP always generate a set of unbal...

In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. KeyWords: Linear Programming; Network Optimization; Integer Programming; Traveling Salesman Problem; Combinatorial Optimization; Scheduling; Sequencing.

While it was known for a long time how to transform an asymmetric traveling salesman problem on the complete graph with n vertices into a symmetric traveling salesman problem on an incomplete graph with 2n vertices, no method was available until recently for using this correspondence to derive facets of the symmetric traveling salesman polytope from facets of the asymmetric one. In this paper w...

In this paper, we present a polynomial-sized linear programming formulation of the Traveling Salesman Problem (TSP). The proposed linear program is a network flow-based model. Numerical implementation issues and results are discussed. Key-Words: Linear Programming; Network Optimization; Integer Programming; Traveling Salesman Problem; Combinatorial Optimization; Scheduling; Sequencing. (Forthco...

The k-traveling salesman problem, or k-TSP is: given a graph with edge weights and an integer k, find a simple cycle of minimum weight visiting exactly k nodes. To obtain lower bounds for the traveling salesman problem the 2-matching relaxation and the 1-tree relaxation can be used. We generalize these two relaxations for the k-TSP.

in today’s competitive transportation systems, passengers search to find traveling agencies that are able to serve them efficiently considering both traveling time and transportation costs. in this paper, we present a new model for the traveling salesman problem with multiple transporters (tspmt). in the proposed model, which is more applicable than the traditional versions, each city has diffe...

The travelling salesman problem is to find a shortest path from the travelling salesman’s hometown, make the round of all the towns in the set, and finally go back home. This paper investigates the travelling salesman problem with fuzzy random travelling time. Three concepts are proposed: expected shortest path, (α, β)-path and chance shortest path according to different optimal desire. Corresp...

Weconsider theRailwayTravelingSalesmanProblem (RTSP) in which a salesman using the railway network wishes to visit a certain number of cities to carry out his/her business, starting and ending at the same city, and having as goal to minimize the overall time of the journey. RTSP is an NP-hard problem. Although it is related to the Generalized Asymmetric Traveling Salesman Problem, in this paper...