Genetic Algorithm - Pohlheim

Andrew Chipperfield Peter Fleming Hartmut Pohlheim Carlos Fonseca Version 1.2 User’s Guide Genetic Algorithm TOOLBOX For Use with MATLAB Genetic Algorithm Toolbox User’s Guide Acknowledgements The production of this Toolbox was made possible by a UK SERC grant on “Genetic Algorithms in Control Systems Engineering” (GR/J17920). Many thanks are due to Hartmut Pohlheim, a visiting researcher from the Technical University Ilmenau, Germany, for the support for real-valued genetic algorithms and his hard work in coding and revising many of

the routines in this Toolbox. Thanks are also due to Carlos Fonseca for providing the initial prototype for this Toolbox. Genetic Algorithm Toolbox User’s Guide Table of Contents 1 Tutorial.....................................................................................................1-1 Installation ..................................................................................................1-2 An Overview of Genetic Algorithms .........................................................1-3 What are Genetic Algorithms .........................................................1-3 GAs versus Traditional Methods ....................................................1-5 Major Elements of the Genetic Algorithm ................................................1-6 Population Representation and Initialisation ..................................1-6 The Objective and Fitness Functions..............................................1-8 Selection .........................................................................................1-9 Roulette Wheel Selection Methods ....................................1-10 Stochastic Universal Sampling ..........................................1-12 Crossover ........................................................................................1-12 Multi-point Crossover.........................................................1-12 Uniform Crossover ............................................................1-13 Other Crossover Operators .................................................1-14 Intermediate Recombination...............................................1-14 Line Recombination ...........................................................1-15 Discussion ..........................................................................1-15 Mutation .........................................................................................1-16 Reinsertion ......................................................................................1-18 Termination of the GA ...................................................................1-18 Data Structures ...........................................................................................1-20 Chromosomes .................................................................................1-20 Phenotypes .....................................................................................1-20 Objective Function Values .............................................................1-21 Fitness Values .................................................................................1-22 Support for Multiple Populations ..............................................................1-23 Examples ....................................................................................................1-26 The Simple GA ..............................................................................1-26 A Multi-population GA ..................................................................1-30 Demonstration Scripts.....................................................................1-36 References...................................................................................................1-37 2 Reference..............................................................................................2-1 Genetic Algorithm Toolbox User’s Guide 1-1 1 Tutorial MATLAB has a wide variety of functions useful to the genetic algorithm practitioner and those wishing to experiment with the genetic algorithm for the first time. Given the versatility of MATLAB’s high-level language, problems can be coded in m-files in a fraction of the time that it would take to create C or Fortran programs for the same purpose. Couple this with MATLAB’s advanced data analysis, visualisation tools and special purpose application domain toolboxes and the user is presented with a uniform environment with which to explore the potential of genetic algorithms. The Genetic Algorithm Toolbox uses MATLAB matrix functions to build a set of versatile tools for implementing a wide range of genetic algorithm methods. The Genetic Algorithm Toolbox is a collection of routines, written mostly in m-files, which implement the most important functions in genetic algorithms. Genetic Algorithm Toolbox User’s Guide 1-2 Installation Instructions for installing the Genetic Algorithm Toolbox can be found in the MATLAB installation instructions. It is recommended that the files for this toolbox are stored in a directory named genetic off the main matlab/toolbox directory. A number of demonstrations are available. A single-population binary-coded genetic algorithm to solve a numerical optimization problem is implemented in the m-file sga.m. The demonstration m-file mpga.m implements a real-valued multi- population genetic algorithm to solve a dynamic control problem. Both of these demonstration m-files are discussed in detail in the Examples Section. Additionally, a set of test functions, drawn from the genetic algorithm literature, are supplied in a separate directory, test_fns, from the...

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