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Stefano Cagnoni (Università degli Studi di Parma, Italy) and Monica Mordonini (Università degli Studi di Parma, Italy)

DOI: 10.4018/978-1-59904-849-9.ch191

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TopOne of the most attractive features of PSO, apart from its effectiveness and robustness with respect to local minima, is certainly its simplicity, which makes it trivial to implement in any programming language. It is also very versatile and applicable to a large number of optimization problems, virtually to any problem defined within a space for which a metric can be defined. However, its behavior, which mainly depends on the values of three constants, is still far from being fully understood. Extensive work (Engelbrecht2005, Clerc2006, Poli2007a) has provided very important insights into the properties of the algorithm, in studies where the dynamic properties of the swarm have been studied, even if under some restrictive assumptions.

The model which underlies PSO describes the motion of a swarm of particles within the domain of a function, usually termed *fitness function* as for evolutionary algorithms (Eiben 2004, de Jong 2006), seeking for its optimum. Such a motion is comparable to the random motion of a set of independent non-interacting particles within a force field generated by two attractors, one of which is specific to each cell.

The basic PSO equations for a generic particle P within the swarm are_{P}(t) = _{P}(t-1) + _{P}(t) *(1)*_{P}(t) = ω * _{P}(t-1) + C_{1} * rand() * [_{Pbest} - _{2} * rand() * [_{gbest} - *(2)* where _{P} is the velocity of particle P, C_{1} and C_{2} are two positive constants, ω is the so-called inertia weight, _{P} is the position of particle P, _{Pbest} is the best-fitness point reached by P up to time t-1, _{gbest} is the best-fitness point found by the whole swarm, rand() is a random value taken from a uniform distribution in the interval [0,1].

Sub-Swarm: In particle swarm optimization, subset of a swarm, within which the distance between any particle and the closest one is below a pre-set threshold.

Segmentation: In computer vision, a process by which an image is subdivided into regions having homogeneous visual features.

Image Analysis: Collection of techniques by which high-level information content is extracted from a digital image using image processing and computer vision techniques.

Particle Swarm Optimization: Optimization technique inspired by the exploratory behavior of animal swarms/flocks/herds in search of food.

Fitness Function: In evolutionary computation the objective function which is to be optimized.

Evolutionary Computation: Collection of techniques, basically aimed at function optimization but applicable to a huge variety of problems, by which the optimum of a function (fitness function) is sought through iterative refinements, according to rules inspired by the laws of natural evolution.

Swarm Intelligence: Collection of techniques, usually inspired by nature, in which high-level intelligent behaviors emerge as a result of the interaction among a high number of agents which, individually, perform apparently trivial, low-level tasks.

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