# Ant Colony Algorithms

### Emergent Behavior

ACOs are a simple example of how simple systems can self-organize or show emergent behavior. Emergent behavior is not a well-defined term, but generally refers to complex and unexpected outcomes arising from the interaction of simple individual entities. Examples include bird flocking, creation of complex nests by colonies of termites, and (more controversially) structure in human societies, particularly economics and financial markets.

In this article, I construct a colony of virtual ants with a set of deliberately simplified abilities. After describing and setting up a simple mechanism by which these ants can communicate, I'll demonstrate how this virtual colony can solve a classic problem from operations research—the infamous Traveling Salesman problem.

### The Traveling Salesman Problem

The Traveling Salesman problem asks: Given a set of towns that a salesman has to visit, and the distances between each, what is the shortest tour that takes him or her to each town just once, ending up at the starting point?

This type of problem is NP-complete, which is mathematical jargon for "hard." With a small number of towns, it's feasible to try every possible route, but when the number increases, an exponential rise in the computations is required. A brute-force approach for any but the smallest tours requires unfeasibly large amounts of computer power and time.

For real problems, it's not always necessary to get the best solution; a good one is just as useful if it can be found in a short time. The ACO described here gives very good solutions to a test problem in a matter of seconds. And this is useful; the TSP is closely related to a number of important real-world problems in scheduling and design, so a solution to one can quickly be applied to others.

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