This is a Java application that demonstrates the Simulated Annealing algorithm with

an attack on the "traveling salesman" problem.


What is simulated annealing?



Simulated annealing is a technique, which was developed to help solve large

combinatorial optimization problems. It is based on probabilistic methods that avoid

being stuck at local (non-global) minima. It has proven to be a simple but

powerful method for large-scale combinatorial optimization.



For practical purposes, simulated annealing has solved the famous traveling

salesman problem: find the shortest of N! paths connecting N cities. Simulated

annealing finds a very good approximation to the shortest path out of the huge

number of all possible paths.



Annealing is nature's trick to find extrema in very complicated situations.

Simulated annealing mimics on a computer the natural process by which crystal lattices

of glass or metal relax when heated. The molecules of hot glass or metal are free

to move about. Temperature is an average of the thermal energy in each molecule

of an object. If the temperature drops quickly, these molecules solidify into a

complex structure. However, if the temperature drops slowly, they form a highly

ordered crystal. The molecules of a crystal solidify into a minimal energy state.



Some real applications simulated annealing:



Determining the sequence of observations for an automated astronomical telescope [2]

Computer Aided Geometric Design

Optimization of Econometric Statistical Functions

Games with random moves determined by the simulated annealing algorithm

Arranging connections on chips and switching devices in telephone networks



The algorithm:



In the simulated annealing algorithm, an objective function to be minimized is

defined. Here it will be the total path length through a set of points.