Of course, optimization problems present themselves in a number of areas. One is of course model fitting but other applications are in areas like planning and logistics – an example being the ever-popular traveling salesman problem. One of the more recent and interesting techniques in solving optimization problems is through a technique called Ant Colony Optimization (ACO). The optimization is a part of series of more generic AI/ machine learning tools called swarm intelligence. Wikipedia defines swarm intelligence as follows
Swarm intelligence (SI) is the collective behaviour of decentralized, self-organized systems, natural or artificial…. SI systems are typically made up of a population of simple agents or bodies interacting locally with one another and with their environment. The agents follow very simple rules, and although there is no centralized control structure dictating how individual agents should behave, local, and to a certain degree random, interactions between such agents lead to the emergence of "intelligent" global behavior, unknown to the individual agents.
The ACO algorithm tries to mimic the behaviour of ants in search of food. When ants forage for food, every ant involved in the foraging process moves out of the colony in random ways to search for food. When a food source is located, the ant uses the scent trail of its own pheromones to bring the food back to the colony. Other ants begin to then use the trail left behind by the first ant to make further excursions to the food source and bring back food. Also, by the very nature of the pheromone trail (which is a volatile chemical and therefore evaporates after a certain point in time), the tendency of later ants is to follow more recent and fresher trails, which should also be the shortest ones logically speaking.
One of the more interesting business applications has been indeed in the area of material movement, i.e. logistics. The Italian pasta maker Barilla as well as Migros, the Swiss supermarket chain have been using these techniques to optimize their distribution networks and routes. A paper about this technique is available here. It is more technical. A more layman-friendly treatment of the technique appeared recently in the Economist and was also an interesting read.