#### What am I looking at?

You are looking at the visualization of an algorithm to
solve the Traveling Salesman Problem (TSP).

#### What is the Traveling Salesman Problem (TSP)?

Given a collection of cities, the TSP is a problem where
a salesman has to visit each city exactly once - and to
return to its starting point - by traveling the shortest
distance.

The TSP naturally arises as a subproblem in many
transportation and logistics applications. You can even use
it
to catch
all the pokemons in your area as quickly as
possible.

In the image above, the black circles represent the
cities and the empty circles linked by the red edges form
an elastic. The elastic is the visualization of the
Elastic Net algorithm.

#### What is the Elastic Net algorithm?

The Elastic Net algorithm is
a heuristic
to solve the TSP. It finds a tour that has a short
distance, but not necessary the shortest tour.

The Elastic Net algorithm is an iterative method where an
elastic is gradually stretched until it passes
sufficiently near each city to define a tour. During that
process two forces apply: one for minimizing the distance
between the cities and the points on the elastic (alpha)
and the other one for minimizing the length of the elastic
(beta). These forces are gradually adjusted as the
procedure evolves.
(Potvin,
1992)

You can control these two forces (alpha and beta) by
using the corresponding sliders above.

The algorithm is described in
this paper.

#### Is the Elastic Net algorithm the best method to solve
the TSP?

Absolutely not. I chose it because it is simple to code
and easy to
visualize. Concorde
is the best solver.