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Stigmergy as an Approach to Metaheuristic Optimization - Computer ...

Stigmergy as an Approach to Metaheuristic Optimization - Computer ...

10 2

10 2 Optimization with ant colonies upon and modify this initial idea or question, eventually constructing an elaborate structure of connected thoughts. Stigmergy can be viewed as a clever strategy used by nature to get populations of beings to self-organize, tell each other where to find resources, create sophisticated messaging systems and build complex architectural structures. The sections in this chapter mainly follow the works of Guntsch and Branke [43], Dorigo and Stüztle [27, 111], and Belal et al. [7]. 2.1 Stigmergy in ant colonies It is known that only 2% of all insect species are eusocial. But these 2% represent more than 50% of the total insect biomass [2]. Insect colonies are capable of solving a number of problems that none of the individual insects would be able to solve by themselves. Examples of this can be seen in finding short paths when foraging for food (see Figure 2.1), task allocation when assigning labor to workers, and clustering when orga- Figure 2.1 Stigmergy is an organizing principle in emergent systems in which the individual parts of the system communicate with one another indirectly by modifying their local environment. Ant colonies are a classic example. The ants communicate indirectly. Information is exchanged through modifications of the environment (local gradients of pheromone).

2.1 Stigmergy in ant colonies 11 nizing brood chambers. All of these tasks have counterparts in real-world optimization problems like routing, scheduling, and clustering. Individuals of a colony usually communicate with each other in a more or less direct way. It all depends on the species in question. Some species, like bees, communicate through the use of a characteristic dance [122]. With this dance one bee “shows” other bees where the food source is located. This is a type of direct communication because it requires visual contact. There are also other forms of direct communication, like stimulation by physical contact or with the exchange of food or liquid. On the other hand, in indirect communication between the individuals of a colony, one has to change the environment in a such way that it will influence the behavior of the individuals later appearing in the modified environment. An example of indirect communication can be seen at ants foraging for food, or at termites constructing a nest [85]. While an ant is foraging for food, it will mark its path by distributing an amount of pheromone on the trail it is taking. When another ant, who is also foraging for food, founds this trail, it will be encouraged, but not forced, to follow the trail. The higher is the amount of pheromone, the greater is the encouragement. As already mentioned, this communication principle is called stigmergy. In many ant colonies stigmergy is the basis for organization. The ants in a colony are self-organized. The term self-organization is used here to describe the complex behavior that emerges from the interaction of comparatively simple agents (ants). Selforganization enables ants to solve the complex problems encountered on a daily basis. Self-organization is used as a basis for problem solving, and it is especially apparent in its distributed and robust form. Effectively, an ant colony can maintain meaningful behavior even if a large number of ants are incapable of contributing for some amount of time. This can be a really useful feature in some real-world problems where these kinds of “interruptions” are very common (e.g., the internet). To better understand the mechanism behind the ability of an ant colony to converge to good solutions when looking for a short path from the nest to a food source, Deneubourg et al. [21] made the following experiment: between a nest of the Argentine ant Linepithema humile and a food source two paths of identical length were put.

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