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TopParticle Swarm Optimization (Pso) Applied To Inverse Problems
Particle swarm optimization is a stochastic evolutionary computation technique inspired by the social behavior of individuals (called particles) in nature, such as bird flocking and fish schooling (Kennedy & Eberhart, 1995).
Let us consider an inverse problem of the form , where are the model parameters, the discrete observed data, and
is the vector field representing the forward operator and
is the scalar field that accounts for the
j-th data. Inverse problems are very important in science and technology and sometimes referred to as, parameter identification, reverse modeling, etc. The “classical” goal of inversion given a particular data set (often affected by noise), is to find a unique set of parameters
m, such the data prediction error
in a certain norm
p, is minimized.
The PSO algorithm to approach this inverse problem is at first glance very easy to understand and implement:
where
are the lower and upper limits for the
j-th coordinate of each particle in the swarm,
n is the number of parameters in the optimization problem and
is the swarm size.