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Publication# Meta Morphic Particle Swarm Optimization

Abstract

Particle Swarm Optimization is a simple and elegant optimization algorithm used to solve a large variety of different real-valued problems. When it comes to solving combinations of continuous and discrete problems however, PSO by itself is not very well suited for the task. There have been previous works addressing the issue of solving solely discrete problems with PSO, but solving problems involving both discrete and continuous parameters at the same time with a PSO-like algorithm has not yet been fully explored. In this paper we provide a novel PSO-based algorithm, called Meta Morphic Particle Swarm Optimization, which looks at solving a particular class of problems for which there exists a discrete set of possible ways to solve the problem where each possibility uses a different subset of a continuous, real-valued parameter space. We introduce a two-layered approach, a PSO in the inner layer for the continuous space, and an outer layer, guided migration scheme using probabilities to choose between the different possible solution sets. We analyze the performance and characteristics of this new algorithm and show how it can be used for real-world applications.

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In mathematics and statistics, a quantitative variable may be continuous or discrete if they are typically obtained by measuring or counting, respectively. If it can take on two particular real values such that it can also take on all real values between them (even values that are arbitrarily close together), the variable is continuous in that interval. If it can take on a value such that there is a non-infinitesimal gap on each side of it containing no values that the variable can take on, then it is discrete around that value.

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