A parallel ant colony algorithm for the Travelling Salesman Problem (TSP) is presented. Some experiments using a MPI based framework are made and analyzed. The achieved results prove that the TSP parallel implementation is efficient. Key-Words: Travelling Salesman Problem, Ant Colony Optimization, Parallel Algorithms, Framework, Message Passing Interface.

Abstract: Mukherjee and Basu (Application of fuzzy ranking method for solving assignment problems with fuzzy costs, International Journal of Computational and Applied Mathematics, 5, 2010, 359-368) proposed a new method for solving fuzzy assignment problems. In this paper, some fuzzy assignment problems and fuzzy travelling salesman problems are chosen which cannot be solved by using the fore-m...

The Travelling Salesman problem is one of the most popular problems from the NP set, it is also one of the hardest too. The solution to this problem enjoys wide applicability in a variety of practical fields. Thus it highly raises the need for an efficient solution for this NP Hard problem. However even the most common deterministic solutions to the problem are known to possess an exponential t...

2014 We study the travelling salesman problem on dilute lattices where the cities are represented by random lattice sites, occupied with concentration p, and the salesman intends to visit a finite fraction f of the total number of cities. The variation of the average optimal travel distance per city L (p, f) against f are investigated here for various values of p. The values of the normalised t...

The Travelling Salesman Problem is a well known problem which has becomea comparison benchmark test for different computational methods. Its solution is computationally difficult, although the problem is easily expressed. TSP is one of the most famous combinatorial optimization (CO) problems and which has wide application background. The aim of our work is to compare existing algorithms that ar...

Earlier research on problem solving suggested that including a diagram in a physics problem brings little, if any, benefit to students’ problem solving success. In 6 AB experiments conducted in our MOOC, we tested the usefulness of problem diagram on 12 different physics problems, collecting over 8000 student responses in total. We found that including a problem diagram that contains no additio...

The travelling salesman problem is to find a shortest path from the travelling salesman’s hometown, make the round of all the towns in the set, and finally go back home. This paper investigates the travelling salesman problem with fuzzy random travelling time. Three concepts are proposed: expected shortest path, (α, β)-path and chance shortest path according to different optimal desire. Corresp...

Travelling salesman problem is a NP complete problem and can be solved using approximation algorithm. It is a minimization problem starting and finishing at a specified vertex after having visited each other vertex exactly once. Often, the model is a complete graph. An algorithm that returns near-optimal solutions is called approximation algorithms. Through analyzing the Metric TSP the performa...

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...

In this paper we introduce a discrete version of the online traveling salesman problem (DOLTSP). We represent the metric space using a weighted graph, where the server is allowed to modify its route only at the vertices. This limitation directly affects the capacity of the server to react and increases the risk related to each decision. We prove lower bounds on the performance of deterministic ...