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...

An instance of the curve reconstruction problem is a finite sample set V of an unknown collection of curves γ. The task is to connect the points in V in the order in which they lie on γ. Giesen [Proceedings of the 15th Annual ACM Symposium on Computational Geometry (SCG ’99), 1999, pp. 207–216] showed recently that the traveling salesman tour of V solves the reconstruction problem for single cl...

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...

Given a set S of n points in the unit square [0, 1], 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 whose optimal traveling salesman tour achieves the maximum possible length among all point sets S ⊂ [0, 1], where |S| = n. An open problem is to determine the structure...

In the recently published book on the Traveling Salesman Problem, half of Chapter 6 [18] is devoted to domination analysis (DA) of heuristics for the Traveling Salesman Problem. Another chapter [16] is a detailed overview of the whole area of DA. Both chapters are of considerable length. The purpose of this paper is to give a short introduction to results and applications of DA. While we do not...

Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions; however, they give good approximation usually in time. The genetic algorithms are useful for NP-hard problems, especially the traveling salesman problem. The genetic algorithm depends on selection criteria, crossover, and mutatio...

This paper proposes the methods for solving the traveling salesman problems using clustering techniques and evolutionary methods. Gaussian mixer model and K-means clustering are two clustering techniques that are considered in this paper. The traveling salesman problems are clustered in order to group the nearest nodes in the problems. Then, the evolutionary methods are applied to each cluster....