Aspects of Modelling and Simulation of Genetic Algorithms: A Formal Approach

Reference:

Sam Sandqvist. Aspects of modelling and simulation of genetic algorithms: A formal approach. Research Report A74, Helsinki University of Technology, Department of Computer Science and Engineering, Laboratory for Theoretical Computer Science, Espoo, Finland, September 2002. Doctoral dissertation.

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. GAs have been modelled in various ways, from the seminal work by Holland describing an approach based on sets, to works based on Markov chains in the 1990s. 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

Suggested BibTeX entry:

@techreport{HUT-TCS-A74,
    address = {Espoo, Finland},
    author = {Sam Sandqvist},
    institution = {Helsinki University of Technology, Department of Computer Science and Engineering, Laboratory for Theoretical Computer Science},
    month = {September},
    note = {Doctoral dissertation},
    number = {A74},
    pages = {164},
    title = {Aspects of Modelling and Simulation of Genetic Algorithms: A Formal Approach},
    type = {Research Report},
    year = {2002},
}