Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time O(n2·2n) where n is the number of nodes in the graph. The branch-and-cut algorithm has been applied to solve the problem with a large number of nodes. However,...

Many real-world applications require the successful combination of spatial and temporal reasoning. In this paper, we study the general framework of the Traveling Salesman Problem with Simple Temporal Constraints. Representationally, this framework subsumes the Traveling Salesman Problem, Simple Temporal Problems, as well as many of the frameworks described in the literature. We analyze the theo...

The traveling salesman problem is a classical NP-hard problem, and also hard to approximate at all under the assumption P 6= NP. Definition 1. A vertex tour of a graph G is a path which visits all vertices and returns to its starting vertex. This is another name for a Hamiltonian cycle on G. Traveling salesman problems involve finding a tour of undirected graph G with edge weights d(·), which w...

In this paper we present a fast approach for solving large scale Traveling Salesman Problems (TSPs). The heuristic is based on Delaunay Triangulation and its runtime is therefore bounded by O(n log n). The algorithm starts by construction the convex hull and successively replaces one edge with two new edges of the triangulation, thus inserting a new city. The decision which edge to remove is ba...

The black and white traveling salesman problem (BWTSP) is a new class of NP-hard problem arising from work on airline scheduling and telecommunication fiber networks. The existing Ghiani LP for the undirected BWTSP contains an exponential number of constraints. For a special case of the directed BWTSP whose L = +∞ , the LP with polynomial number of constraints could be obtained by transforming ...

The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of the sales, minimizing the amount of time. In this paper we address the on-line version of the problem, where requests are given over time. We present algorithms for various metric spaces, and analyze their performan...

This paper deals with the pickup and delivery traveling salesman problem. First we show how to adapt some classical traveling salesman heuristics to solve this problem, then we propose a new and e$cient composite heuristic. The proposed heuristic is composed of two phases: a solution construction phase including a local optimization component and a deletion and re-insertion improvement phase. T...