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Tutorial 1 Temi avanzati di Intelligenza Artificiale - Lecture 3 Prof. Vincenzo Cutello Department of Mathematics and Computer Science University of Catania Types of Evolutionary Algorithms 1) Genetic Algorithms (GAs) Proposed and studied by John Holland and his students Numerical optimization and adaptive systems design Simulate Darwinian Evolution Recombination (Crossover) important Mainly binary representation Schema Theorem classical GA theory Tutorial 1 - Lecture 3 2 Types of Evolutionary Algorithms 2) Genetic Programming (GP) Developed by Koza et al. Evolved LISP programs Tree Representation Widest variety of application Term also used by De Garis for evolution of artificial neural networks Tutorial 1 - Lecture 3 3 Types of Evolutionary Algorithms 3) Evolutionary Programming (EP) Developed by Fogel for simulated intelligence Finite State Machine (FSM) representation close to Lamarckian inheritance No recombination Adaptive Mutation (and others) Applied to Phenotypes Tutorial 1 - Lecture 3 4 Types of Evolutionary Algorithms 4) Evolution Strategies Introduced by Rechenberg and Schwefel for numerical optimzation Real-valued representation Mutation Based Adaptive Mutation Tutorial 1 - Lecture 3 5 Search Operators and Bias 1) Mutation Bias Example: Integer variables in binary representation 2 variables, each 3 bit integer - 6 bit genotype Current value:<4,4> (<100100>) Single-bit bitflip mutation Where can we go in one mutation? How many mutations are required to get to <3,3> ? Tutorial 1 - Lecture 3 6 Search Operators and Bias Crossover Bias One-Point vs. Uniform Crossover Example Representation: Strings of integer values (0 - m) of length n Two fitness functions: 1: Fitness = n 2 i 0 ( xi xn i ) 2 n 2 i 0 ( x2i x2i 1 ) 2 2: Fitness = Minimzation problem Suggestions ? Tutorial 1 - Lecture 3 7 Search Operators and Bias Crossover Bias Example System m=4 n=200 Population size: 400 Mutation: single-gene random raplacement, 1.0 perindividual mutation probability Crossover: uniform or one-point crossover, 1.0 crossover probability Replacement: keep best Termination: when fitness == 0 Tutorial 1 - Lecture 3 8 Selection Pressure Different selection operators produce different behaviour Exploration vs. Exploitation Example: Roulette Wheel and Tournament selection Tutorial 1 - Lecture 3 9 Selection Pressure Example Case Two-optima function Genotype: real-valued vector, -10.0 to 10.0 Mutation: gaussian mutation, 1.0 probability, 0.7 deviation; Crossover: none Population size: 20, Replacement: keep best Maximization problem Tutorial 1 - Lecture 3 10 Excercise sheet 1. Write an evolutionary algorithm... ... to find the maximum of the function on slide 10: f(x,y) = e(- 0.7 * (x+2.0) *(x+2.0)) * e(-0.9 * y * y) + 2.0 * e(- (x -5.0) * (x-6.0)) * e (-(y-2.0) * (y-2.0)) For values -10.0 < x,y < 10.0 Two versions... Describe the differences Version one: binary representation (e.g. 2 x 16 bit) Version two: real-value representation (see next week's lectures) Run a few runs, and write a short (1/2 page) description of the differences in search behaviour between the two representations. E.g. how long does it need to find the optimum? Does it always find the global optimum? How close to the optimum does it get? 2. Think about... If you have a genotype of length n, what is the difference between n-1 point crossover and uniform crossover ? Describe the difference in a few lines. Tutorial 1 - Lecture 3 11