Introduction

What is the Traveling Salesman Problem?

Finding the shortest path to visit n points only once and return to the original point

Roundtrip by specified cities

Use cases

And more...

Bus routes

Distribution of Goods

Motherboards layout

Formulation

El papel del procesador en un S.O en tiempo real

Subject to

Objective function

(1)

(2)

(3)

(4)

(5)

Solving Traveling Salesman

Solving the traveling salesman problem

Traveling Salesman is an NP-Hard problem

The Traveling Salesman Algorithm belongs to the NP-Hard problems which means that there is no an exact algorithm to solve it 

Meta Heuristics

In this case we are going to use a Heuristic in the category of evolutionary algorithms, e.g: Ant colony optimization, Genetic algorithms, ...

Ant Colony Optimization

Using an ant colony to understand and solve the Traveling Salesman problem 

Transition

Moving ants depends on the amount of pheromone on the graph edges. 

The probability pik, of transition of an ant from node i to node k is given by the formula

Reverse

The ant follows the same path but in reverse order, also, they left pheromones in the way 

Evaporation of Pheromones

At the end the pheromones on the edges start to evaporate, this helps ants finding the shortest path to food

Computational Experiment

Simulating the problems using computers

32 cities in Slovakia

Using Gams and ACO to find the best solution

Gams

ACO

Simulation m=100

k: 1713

Distance to optimal: 17%

Simulation m=5000

k: 1621

Distance to optimal: 11.56%