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TopThe Bees Algorithm
The Bees Algorithm (Pham et al., 2006a; Pham & Castellani 2009) is a nature-inspired optimisation method based on the foraging behaviour of honey bees. It uses a population of agents (artificial bees) to explore randomly the solution space, looking for regions of high performance. These regions are selected for more detailed local search. The Bees Algorithm repeats cycles of global (random) and local search until an acceptable solution is discovered, or a given number of iterations have elapsed. In its standard formulation (Pham & Castellani 2009), the Bees Algorithm makes no assumption on the nature of the solution space, such as its derivability or continuity. For this reason it is applicable to a wide range of continuous and combinatorial problems. Henceforth, unless explicitly stated, continuous optimisation problems will be considered.
Bees Foraging Process in Nature
In a bee colony, a portion of the population explores the environment surrounding the hive in search of food (von Frisch, 1976). These scouts look for patches of flowers where pollen or nectar is easily available and rich in sugar. Upon their return to the hive, the scouts unload the food they collected. Scouts that discovered a high-quality flower patch communicate to idle foragers the position of their find through a ritual called the waggle dance (Seeley, 1996). The duration of the waggle dance depends on the scout’s quality rating of the patch: highly rated patches are advertised via long dances, which mobilise a large number of free foragers (Seeley, 1996). Once the waggle dance is terminated, the scout returns to the food source together with the recruited foragers. When they return to the hive, recruited bees may in turn waggle dance to call more workers on the food source. Thanks to this autocatalytic mechanism, a bee colony is able to exploit efficiently the most profitable food sources (Tereshko & Lee, 2002).
Key Terms in this Chapter
Bees Algorithm: Optimisation algorithm inspired by the foraging behaviour of bees in nature.
Artificial Neural Networks (ANN): Computational models inspired by the properties of biological nervous systems. Usually composed of layers of highly interconnected simple processing units, they are characterised by learning capabilities and can be implemented in software and hardware.
Multi-Layer Perceptron (MLP): Arguably the most popular artificial neural network model. It is usually composed by three or four layers of units. Each unit is fully connected to the units of the previous layer. Learning is customarily performed via the backpropagation rule.
Metaheuristics: A higher-level procedure that manages and guides a lower-level heuristic in search. In the Bees Algorithm, the bees foraging metaheuristics manages the random local and global search heuristics.
Swarm Intelligence (SI): Collective intelligence of societies of biological (social animals) or artificial (robots, computer agents) individuals. In artificial intelligence, it gave rise to a computational paradigm based on decentralisation, self-organisation, local interactions, and collective emergent behaviours.
EA: Evolutionary algorithm.
Optimisation: Search for the element that best satisfies some given quality criteria from a set of feasible alternatives.
Backpropagation Rule (BP): Learning rule customarily used by multi-layer perceptron artificial neural network models. It is based on gradient descent minimisation of the squared output error.