meanderingmoose

Crossposted from mybrainsthoughts.com Metals are a unique form of matter, especially with regards to their behavior under heating and cooling. While metals are described by the material they’re made of (e.g. copper or iron), their properties are determined by their arrangement of atoms, and this arrangement can vary significantly. The arrangement is semi-permanent, but can be manipulated through certain heating and cooling techniques. One especially interesting technique is “annealing” (if you’re interested in this technique or the many others, this video provides a great introduction), where the metal is first heated and then slowly cooled over time. Through this process, the metal becomes less hard and more ductile, as the heating provides the necessary energy for the form to shift, and the slow cooling provides the time and energy levels needed to form larger grains (see below). Computer programmers have taken note of these particular properties and ported them into the field, resulting in an algorithm known as “simulated annealing”. The algorithm is used to find an approximate global optimum for a specified problem, and works, like metallurgic annealing, by gradually reducing the “temperature” (for the algorithm, “temperature” determines the likelihood of moving in the direction of a worse solution). We can better understand how the algorithm works by graphically representing the solution space for a problem (the below picture represents a 1-dimensional space, but we can extend the idea to arbitrarily complex N-dimensional spaces). The algorithm starts from a random input value (a random place on the above line), then at each iteration selects a random nearby point (the definition of “nearby” changes with the temperature; at higher temperatures, further points can be chosen). If the randomly selected point is higher than the current point, the algorithm “moves” to that point; if it is lower, the algorithm may or may not “move”, depending on the temperature