AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION (TECHNICAL REPORT-TR06, OCTOBER, 2005)
Dervis KARABOGA
karaboga@
Erciyes University, Engineering Faculty
Computer Engineering Department
Kayri/Türkiye
I. INTRODUCTION
Swarm intelligence has become a rearch interest to many rearch scientists of related fields in recent years. Bonabeau has defined the swarm intelligence as “any attempt to design algorithms or distributed problem-solving devices inspired by the collective behaviour of social inct colonies and other animal societies” [1]. Bonabeau et al. focud their viewpoint on social incts alone such as termites, bees, wasps as well as other different ant species. However, the term swarm is ud in a gen
eral manner to refer to any restrained collection of interacting agents or individuals. The classical example of a swarm is bees swarming around their hive; nevertheless the metaphor can easily be extended to other systems with a similar architecture. An ant colony can be thought of as a swarm who individual agents are ants. Similarly a flock of birds is a swarm of birds. An immune system [2] is a swarm of cells and molecules as well as a crowd is a swarm of people [3]. Particle Swarm Optimization (PSO) Algorithm models the social behaviour of bird flocking or fish schooling [4].
Two fundamental concepts, lf-organization and division of labour, are necessary and sufficient properties to obtain swarm intelligent behaviour such as distributed problem-solving systems that lf-organize and adapt to the given environment:
a) Self-organization can be defined as a t of dynamical mechanisms, which result in structures at the global level of a system by means of interactions among its low-level components. The mechanisms establish basic rules for the interactions between the components of the system. The rules ensure that the interactions are executed on the basis of purely local information without any relation to the global pattern. Bonabeau et al. have characterized four basic properties on which lf organization relies: Positive feedback, negative feedback, fluctuations and multiple interactions [1]:
i) Positive feedback is a simple behavioural “rules of thumb” that promotes the creation of convenient structures. Recruitment and reinforcement such as trail laying and following in some ant species or dances in bees can be shown as the examples of positive feedback.
qq名片ii) Negative feedback counterbalances positive feedback and helps to stabilize the collective pattern. In order to avoid the saturation which might occur in terms of available foragers, food source exhaustion, crowding or competition at the food sources, a negative feedback mechanism is needed.春晚点评
iii) Fluctuations such as random walks, errors, random task switching among swarm individuals are vital for creativity and innovation. Randomness is often crucial for emergent structures since it enables the discovery of new solutions.
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iv) In general, lf organization requires a minimal density of mutually tolerant individuals, enabling them to make u of the results from their own activities as well as others.
b) Inside a swarm, there are different tasks, which are performed simultaneously by specialized individuals. This kind of phenomenon is called division of labour. Simultaneous task performance by cooperating specialized individuals is believed to be more efficient than the quential task performance by unspecialized individuals [2,5-7]. Division of labour also enables the swarm to respo
nd to changed conditions in the arch space. Two fundamental concepts for the collective performance of a swarm prented above, lf-organization and division of labour are necessary and sufficient properties to obtain swarm intelligent behaviour such as distributed problem-solving systems that lf-organize and -adapt to the given environment.
II. BEHAVIOUR OF HONEY BEE SWARM
The minimal model of forage lection that leads to the emergence of collective intelligence of honey bee swarms consists of three esntial components: food sources, employed foragers and unemployed foragers and the model defines two leading modes of the behaviour: the recruitment to a nectar source and the abandonment of a source.
i) Food Sources: The value of a food source depends on many
factors such as its proximity to the nest, its richness or concentration
of its energy, and the ea of extracting this energy. For the sake of
simplicity, the “profitability” of a food source can be reprented with
a single quantity [8].
ii) Employed foragers: They are
associated with a particular food source which they are currently
菠萝蜜的营养价值
exploiting or are “employed” at. They carry with them information
about this particular source, its distance and direction from the nest,
the profitability of the source and share this information with a
certain probability.
iii) Unemployed foragers: They are continually at look out中学生圆山
for a food source to exploit. There are two types of unemployed
foragers: scouts, arching the environment surrounding the
nest for new food sources and onlookers waiting in the nest and
establishing a food source through the information shared by employed foragers. The mean number of scouts averaged over conditions is about 5-10% [8].
The exchange of information among bees is the most important occurrence in the formation of the collective knowledge. While examining the entire hive it is possible to distinguish between some parts that commonly exist in all hives. The most important part of the hive with respect to exchanging information is the dancing area. Communication among bees related to the quality of food sources takes place in the dancing area. This dance is called a waggle dance.
Since information about all the current rich sources is available to an onlooker on the dance floor, probably she can watch numerous dances and decides to employ herlf at the most profitable source. There is a greater probability of onlookers choosing more profitable sources since more information is circulated about the more profitable sources. Employed foragers share their information with a probability proportional to the profitability of the food source, and the sharing of this information through waggle dancing is longer in duration. Hence, the recruitment is proportional to the profitability of the food source [9].
我想你了英语In order to understand the basic behaviour characteristics of foragers better, let us examine Figure 1. Assume that there are two discovered food sources: A and B. At the very beginning, a potential forager will start as unemployed forager. That bee will have no knowledge about the food sources around the nest. There are two possible options for such a bee:
i) It can be a scout and starts arching around the nest spontaneously for a food due to some internal motivation or possible external clue (S on Figure 1).
ii) It can be a recruit after watching the waggle dances and starts arching for a food source (R on Figure 1).
After locating the food source, the bee utilizes its own capability to memorize the location and then immediately starts exploiting it. Hence, the bee will become an “employed forager”. The
洋葱的功效和作用foraging bee takes a load of nectar from the source and returns to the hive and unloads the nectar to a food store. After unloading the food, the bee has the following three options:
i) It becomes an uncommitted follower after abandoning the food source (UF).
ii) It dances and then recruits nest mates before returning to the same food source (EF1) iii) It continues to forage at the food source without recruiting other bees (EF2).
It is important to note that not all bees start foraging simultaneously. The experiments confirmed that new bees begin foraging at a rate proportional to the difference between the eventual total number of bees and the number of prent foraging.
Figure 1. The behaviour of honey bee foraging for nectar
In the ca of honey bees, the basic properties on which lf organization relies are as follows:
i)Positive feedback: As the nectar amount of food sources increas, the number of
onlookers visiting them increas, too.
ii)Negative feedback: The exploration process of a food source abandoned by bees is stopped.
iii)Fluctuations: The scouts carry out a random arch process for discovering new food sources.
iv)Multiple interactions: Bees share their information about food source positions with their nest mates on the dance area.
