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,...

In the uncapacitated asymmetric traveling salesman with multiple stacks, we perform a hamiltonian circuit to pick up n items, storing them in a vehicle with k stacks satisfying last-in-first-out constraints, and then we deliver every item by performing a hamiltonian circuit. We are interested in the convex hull of the (arc-)incidence vectors of such couples of hamiltonian circuits. For the gene...

Consider a truck running along a road. It picks up a load Li at point βi and delivers it at αi, carrying at most one load at a time. The speed on the various parts of the road in one direction is given by f(x) and that in the other direction is given by g(x). Minimizing the total time spent to deliver loads L1, . . . , Ln is equivalent to solving the Traveling Salesman Problem (TSP) where the c...

The Traveling Salesman Problem(TSP) is one of the most intensively studied problem in computational mathematics. To solve this problem a number of algorithms have been developed using genetic algorithms. But these algorithms are not so suitable for solving large-scale TSP. This paper proposes a new solution for TSP using hierarchical clustering and genetic algorithm. Keywords— Traveling Salesma...

Given a set S of n points in the unit square $[ 0,1 ]^d $, an optimal traveling salesman tour of S is a tour of S that is of minimum length. A worst-case point set for the traveling salesman problem in the unit square is a point set $S^{( n )} $ whose optimal traveling salesman tour achieves the maximum possible length among all point sets $S \subset [ 0,1 ]^d $, where $| S | = n$. An open prob...

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...