The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
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Aspects of Modelling and Simulation of Genetic Algorithms: a Formal Approach
Sam Sandqvist
Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Computer Science and Engineering, for public examination and debate in Auditorium T2 at Helsinki University of Technology (Esbo, Finland) on the 1st of November, 2002, at 12 o'clock noon.
Dissertation in PDF format (ISBN 951-22-6082-4) [1074 KB]
Dissertation is also available in print (ISBN 951-22-6115-4)
Abstract
Genetic algorithms (GAs) are widely used in solving search and optimisation problems involving very large search spaces, or very many variables where closed form solutions are impractical due to the very size of the problems. This dissertation combines the two salient features of GAs, namely the temporal aspect of the evolutionary approach to solving problems at the heart of the GA, and the stochastic aspect of evolution arising from its reliance on basically random generation of new individuals with stringent selection in determining survival.
The work centres around describing the formal modelling of GAs using a logical approach based on standard first-order logic combined with temporal logic and with probabilistic logic. These logics are combined into a unified logic, temporal-probabilistic logic (TPL) which is formulated in this work.
The GA is then described using TPL as the main tool, and the working of the GA is detailed from its components to the actual processes by formulating a model of the GA. Several important parameters are described and analysed, as is the important mechanism of selection. A simple axiomatisation of the GA using TPL is described as well.
Also presented are simulation of the workings of the genetic algorithm based on high-level Petri nets and experimentation with a genetic algorithm package providing experimental evidence centring on the various selection mechanisms for some of the theoretical results.
Keywords: genetic algorithm, temporal logic, probabilistic logic, modelling, simulation, Petri net
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© 2002 Helsinki University of Technology
Last update 2011-05-26