Fractional Order Darwinian Particle Swarm Optimization

Abstract

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Multilevel Image Segmentation Based on Fractional-Order Darwinian Particle Swarm Optimization

“…The PSO basically takes advantage of the swarm intelligence concept, which is the property of a system whereby the collective behaviors of unsophisticated agents that are interacting locally with their environment, create coherent global functional patterns. More recently, and based on the concepts inherent to the PSO, the DPSO [36] and the FOPSO [37], an extended version denoted as FODPSO was presented in [35], in which several swarms compete using Darwin's survival-of-the-fittest principles and fractional calculus to control the convergence rate of the algorithm. Using those principles, the FODPSO enhances the ability of the PSO algorithm to escape from local optima by running several simultaneous parallel PSO algorithms, each being a different swarm, on the same test problem and apply a simple selection mechanism.…”

“…In the DPSO, multiple swarms of test solutions performing just like an ordinary PSO may exist at any time with rules governing the collection of swarms that are designed to simulate natural selection. More recently, Couceiro et al [35] further extended the DPSO using fractional calculus to control the convergence rate of the algorithm. In [35], fractional-order DPSO (FODPSO) was successfully compared to both the fractional-order PSO (FOPSO) from Pires et al [37] and the traditional DPSO.…”

“…More recently, Couceiro et al [35] further extended the DPSO using fractional calculus to control the convergence rate of the algorithm. In [35], fractional-order DPSO (FODPSO) was successfully compared to both the fractional-order PSO (FOPSO) from Pires et al [37] and the traditional DPSO.…”

“…The PSO consists of a number of particles that collectively move in the search space (e.g., pixels of the image) in search of the global optimum (e.g., maximizing the betweenclass variance of the distribution of intensity levels in the given image). However, a general problem with the PSO and similar optimization algorithms is that they may get trapped in local optimum points, and the algorithm may work in some problems but fail in others [35]. To overcome such a problem, Tillett et al [36] presented the Darwinian PSO (DPSO).…”

“…Some optimization methods are fast but not efficient (for finding the global optimum) and viceversa. It has been recently proved in [35] for benchmarking optimization problems that the FODPSO is faster than the PSO (the most well-known optimization algorithm in terms of speed) and more efficient than the DPSO (in order to find the global optimum while avoiding local optima). Therefore, applying the FODPSO to the segmentation of images may allow achieving both vital important goals at once.…”