Hamilton cycle problem and Traveling Salesman Problem

ArXiv, 2018

We present a benchmark set for Traveling salesman problem (TSP) with characteristics that are different from the existing benchmark sets. In particular, we focus on small instances which prove to be challenging for one or more state-of-the-art TSP algorithms. These instances are based on difficult instances of Hamiltonian cycle problem (HCP). This includes instances from literature, specially modified randomly generated instances, and instances arising from the conversion of other difficult problems to HCP. We demonstrate that such benchmark instances are helpful in understanding the weaknesses and strengths of algorithms. In particular, we conduct a benchmarking exercise for this new benchmark set totalling over five years of CPU time, comparing the TSP algorithms Concorde, Chained Lin-Kernighan, and LKH. We also include the HCP heuristic SLH in the benchmarking exercise. A discussion about the benefits of specifically considering outlying instances, and in particular instances whi...

Graph Theory, 2015

2016

The goal of this paper is to optimize delivering of packages at five randomly chosen addresses in the city of Rijeka. This problem is also known as the Travelling Salesman Problem and it is an NP hard problem. To achieve this goal, the concepts of a Hamilton path and cycle, as well as a Hamilton graph are defined. The theoretical basis for the branch and bound method is also given. The use of this method in the process of finding a solution for a problem is provided at the end of this paper.

A heuristic algorithm has been developed to find out the least cost route (minimum weighted Hamiltonian circuit) for a particular type of weighted graph G (3m + 7, 6m + 16) for m ≥ 1, which is planar, non-regular, non-bipartite and Hamiltonian related with traveling salesman problem

2017

Given an undirected graph $G=(V, E)$ with a weight function $c\in R^E$, and a positive integer $K$, the Kth Traveling Salesman Problem (KthTSP) is to find $K$ Hamilton cycles $H_1, H_2, , ..., H_K$ such that, for any Hamilton cycle $H\not \in \{H_1, H_2, , ..., H_K \}$, we have $c(H)\geq c(H_i), i=1, 2, ..., K$. This problem is NP-hard even for $K$ fixed. We prove that KthTSP is pseudopolynomial when TSP is polynomial.

Springer eBooks, 2013

This paper presents a self-contained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances. Extensive computational results are reported on most of the algorithms described. Optimal solutions are reported for instances with sizes up to several thousand nodes as well as heuristic solutions with provably very high quality for larger instances. This is a preliminary version of one of the chapters of the volume "Networks" edited by M.O. Ball, T.

2002

2001