Computation of the travelling salesman problem by a shrinking blob

A Survey on Travelling Salesman Problem

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...

The multi-stripe travelling salesman problem

In the classical Travelling Salesman Problem (TSP), the objective function sums the costs for travelling from one city to the next city along the tour. In the q-stripe TSP with [Formula: see text], the objective function sums the costs for travelling from one city to each of the next q cities in the tour. The resulting q-stripe TSP generalizes the TSP and forms a special case of the quadratic a...

Travelling Salesman Problem with a Center

We study a traveling salesman problem where the path is optimized with a cost function that includes its length L as well as a certain measure C of its distance from the geometrical center of the graph. Using simulated annealing (SA) we show that such a problem has a transition point that separates two phases differing in the scaling behavior of L and C, in efficiency of SA, and in the shape of...

Ant colonies for the travelling salesman problem.

We describe an artificial ant colony capable of solving the travelling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer simulations demonstrate that the artificial ant colony is capable of generating good solutions to b...

A replica analysis of the travelling salesman problem