The Traveling Salesman Problem (TSP) is perhaps the most studied discrete optimization problem. Its popularity is due to the facts that TSP is easy to formulate, difficult to solve, and has a large number of applications. It appears that K. Menger [31] was the first researcher to consider the Traveling Salesman Problem (TSP). He observed that the problem can be solved by examining all permutati...

We describe how to use the traveling salesman problem (TSP) to create continuous line drawings of target pictures.

The expanded Invasive Weed Optimization algorithm (exIWO) is an optimization metaheuristic modelled on the original IWO version created by the researchers from the University of Tehran. The authors of the present paper have extended the exIWO algorithm introducing a set of both deterministic and nondeterministic strategies of individuals’ selection. The goal of the project was to evaluate the e...

The traveling salesman problem (TSP) has attracted many researchers’ attention in the past few decades, and amounts of algorithms based on heuristic algorithms, genetic algorithms, particle swarm optimization, tabu search and memetic algorithms have been presented to solve it, respectively. Unfortunately, their results have not been satisfied at all yet. This paper is devoted to the presentatio...

This paper presents a Multi-MetaHeuristic combined Ant Colony System (ACS)-Travelling Salesman Problem(TSP) algorithm for solving the TSP. We introduce genetic algorithm in ACS-TSP to search solutions space for dealing with the early stagnation problem of the traveling salesman problem. Moreover, we present a new strategy of Minimum Spanning Tree (MST) coupled with Nearest Neighbor(NN) to const...

Let P be a set of points in R, and let α > 1 be a real number. We define the distance between two points p, q ∈ P as |pq|, where |pq| denotes the standard Euclidean distance between p and q. We denote the traveling salesman problem under this distance function by Tsp(d,α). We design a 5-approximation algorithm for Tsp(2,2) and generalize this result to obtain an approximation factor of 3 + √ 6 ...

Many recent approximation algorithms for different variants of the traveling salesman problem (asymmetric TSP, graph TSP, s-t-path TSP) exploit the well-known fact that a solution of the natural linear programming relaxation can be written as convex combination of spanning trees. The main argument then is that randomly sampling a tree from such a distribution and then completing the tree to a t...

We investigate the diameter of the polytope arising in the n-city symmetric traveling salesman problem (TSP) and perfect matching polytopes. Grötschel and Padberg [The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Wiley-Intersci. Ser. Discrete Math., E. Lawler et al., eds., John Wiley, Chichester, 1985, pp. 251–305] conjectured that the diameter of the symmetric TSP p...

A novel particle swarm optimization (PSO)-based algorithm for the traveling salesman problem (TSP) is presented. An uncertain searching strategy and a crossover eliminated technique are used to accelerate the convergence speed. Compared with the existing algorithms for solving TSP using swarm intelligence, it has been shown that the size of the solved problems could be increased by using the pr...

The Generalized Traveling Salesman Problem (GTSP) is an extension of the well-known Traveling Salesman Problem (TSP), where the node set is partitioned into clusters, and the objective is to find the shortest cycle visiting each cluster exactly once. In this paper, we present a new hybrid Ant Colony System (ACS) algorithm for the symmetric GTSP. The proposed algorithm is a modification of a sim...