Wednesday, February 22, 2017

Non Traditional Computing, Complex Problems, and Approximation

Illustration for Death of a Salesman by Brian Stauffer for the Soulpepper Theater Company, Toronto

It may seem like a stretch to write about combinatorial optimization problems (aka the traveling salesman problem) on a blog about the ‘language of smell,’ but Limbic Signal isn’t just about smells, or language, but the connections between olfaction and computation. Our olfactory system is a champion at dealing with very large, very complex datasets.

Olfaction uses our brain in ways the other senses don’t. Some of the ways olfaction diverges from the other senses are akin to novel solutions to very complex problems in computation, such as big-data-sifting, pattern recognition, or the aforementioned traveling salesman problem.

 Also note that, in addition to the magnet network described below, another unconventional solution to the traveling salesman problem is to use mold. In fact, slime mold was used to design Spain's motorways and the Tokyo rail system.

So this article below does a good job of explaining the traveling salesman problem; I straight copied it from the writers at And in the second section is an explanation of an interesting solution to the problem.

Researchers create a new type of computer that can solve problems that are a challenge for traditional computers

The traveling salesman problem
There is a special type of problem - called a combinatorial optimization problem - that traditional computers find difficult to solve, even approximately. An example is what's known as the "traveling salesman" problem, wherein a salesman has to visit a specific set of cities, each only once, and return to the first city, and the salesman wants to take the most efficient route possible. This problem may seem simple but the number of possible routes increases extremely rapidly as cities are added, and this underlies why the problem is difficult to solve.

It may be tempting to simply give up on the traveling salesman, but solving such hard optimization problems could have enormous impact in a wide range of areas. Examples include finding the optimal path for delivery trucks, minimizing interference in wireless networks, and determining how proteins fold. Even small improvements in some of these areas could result in massive monetary savings, which is why some scientists have spent their careers creating algorithms that produce very good approximate solutions to this type of problem.

An Ising machine
The Stanford team has built what's called an Ising machine, named for a mathematical model of magnetism. The machine acts like a reprogrammable network of artificial magnets where each magnet only points up or down and, like a real magnetic system, it is expected to tend toward operating at low energy.

The theory is that, if the connections among a network of magnets can be programmed to represent the problem at hand, once they settle on the optimal, low-energy directions they should face, the solution can be derived from their final state. In the case of the traveling salesman, each artificial magnet in the Ising machine represents the position of a city in a particular path.

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