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G5BAIM Artificial Intelligence Methods Graham Kendall Evolutionary Algorithms

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms How can programs learn? This lecture is only an introduction This techniques can be used as an optimisation strategy but we are going to look at a learning example

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms Chapter 8 of –Michalewicz, Z. (1996). Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, ISBN 3-540-60676-9 Almost anything by David Fogel –Fogel, D. B. (1994) IEEE Transactions on Neural Networks, Vol 5:1, pp3-14 –Fogel, D.B. (1998) Evolutionary Computation The Fossil Record, IEEE Press, ISBN 0-7803-3481-7, pp 3-14 –Michalewicz, Z. and Fogel, D. (2000). How to Solve It : Modern Heuristics. Springer-Verlag, ISBN 3-540-66061-5

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms There are other ways that we could design computer programs so that they “learn” –For example, knowledge based on some suitable logic symbolism Use inference rules We should also be careful not confuse evolutionary strategies with evolutionary programming (EP). EP is about writing programs that write programs

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms vs GA’s ES’s are an algorithm that only uses mutation and does not use crossover This is not a formal definition and there is no reason why we cannot incorporate crossover (as Michalewicz, 1996 shows)

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms vs GA’s ES’s are normally applied to real numbers (continuous variables) rather than discrete values. Again, this is not a strict definition and work has been done on using ES’s for discrete problems (Bäck, 1991) and (Herdy, 1991)

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms vs GA’s ES’s are a population based approach Originally only a single solution was maintained and this was improved upon.

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms vs GA’s In summaryES’s are –Like genetic algorithms but only use mutation and not crossover –They operate on real numbers –They are a population based approach –But we can break any, or all, of these rules if we wish!

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work An individual in an ES is represented as a pair of real vectors, v = (x,σ) x, represents a point in the search space and consists of a number of real valued variables The second vector, σ, represents a vector of standard deviations

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work Mutation is performed by replacing x by x t+1 = x t + N(0, σ) N(0, σ) is a random Gaussian number with a mean of zero and standard deviations of σ

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work This mimics the evolutionary process that small changes occur more often than larger ones An algorithm (in C++) that produces Gaussian random numbers is supplied in the handout

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work In the earliest ES’s (where only a single solution was maintained), the new individual replaced its parent if it had a higher fitness In addition, these early ES’s, maintained the same value for σ throughout the duration of the algorithm It has been proven that if this vector remains constant throughout the run then the algorithm will converge to the optimal solution

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work Problem –Although the global optimum can be proved to be found with a probability of one, it also states that the theorem holds for sufficiently long search time The theorem tells us nothing about how long that search time might be

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work To try and speed up convergence Rechenberg has proposed the “1/5 success rule.” It can be stated as follows The ratio, , of successful mutations to all mutations should be 1/5. Increase the variance of the mutation operator if is greater than 1/5; otherwise, decrease it

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work Motivation behind 1/5 rule –If we are finding lots of successful moves then we should try larger steps in order to try and improve the efficiency of the search –If we not finding many successful moves then we should proceed in smaller steps

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work The 1/5 rule is applied as follows if (k) < 1/5 then σ = σc d if (k) > 1/5 then σ = σc i if (k) = 1/5 then σ = σ

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work if (k) < 1/5 then σ = σc d if (k) > 1/5 then σ = σc i if (k) = 1/5 then σ = σ k dictates how many generations should elapse before the rule is applied c d and c i determine the rate of increase or decrease for σ c i must be greater than one and c d must be less than one Schwefel used c d = 0.82 and c i = 1.22 (=1/0.82)

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work Problem with the applying the 1/5 rule It made lead to premature convergence for some problems Increase the population size, which now turns ES’s into a population based approach search mechanism

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work Increase population size –The population size is now (obviously) > 1. –All members of the population have an equal probability of mating - compare with GA –We could now introduce the possibility of crossover –As we have more than one individual we have the opportunity to alter σ independently for each member –We have more options with regards to how we control the population (discussed next)

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work In evolutionary computation there are two variations as to how we create the new generation

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work ( + ), uses parents and creates offspring After mutation, there will be + members in the population All these solutions compete for survival, with the best selected as parents for the next generation

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work ( , ), works by the parents producing offspring (where > ) Only the compete for survival. Thus, the parents are completely replaced at each new generation Or, to put it another way, a single solution only has a life span of a single generation

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - How They Work The original work on evolution strategies (Schwefel, 1965) used a (1 + 1) strategy This took a single parent and produced a single offspring Both these solutions competed to survive to the next generation

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - Case Study Learning how to play Poker –fold(x) = exp(-eval(b) * (x – a)) –call(x) = eval(c) * exp(-eval(b) 2 * (x-a) 2 ) –raise(x) = exp(eval(b) * (x + a – 1.0))

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - Case Study Learning how to play Poker –Two-dimensional hypercube of solutions –Betting Position –Risk Management –N solutions of seven real values in each hyprcube element –The poker playing agent evolves the variables

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - Case Study Simplified Blackjack Blackjack is a two player game comprising of a dealer and a player. The dealer deals two cards (from a normal pack of 52 cards) to the player and one card to himself. All cards are dealt face up. All cards take their face value, except Jack, Queen and King which count as 10 and Aces which can count as one or eleven The aim for the player is to draw as many cards as he/she wishes (zero if they wish) in order to get as close as possible to 21 without exceeding 21

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - Your Go Simplified Blackjack –How might we write an agent that learns how to play blackjack? –Learn Probabilities?

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - Your Go Questions Do you think this would work? Should we use a single candidate for each probability or should we have a population greater than one? What sort of evolutionary scheme should we use; ( + ) or ( , ); and what values should we give and ? Can you come up with a better representation; other than trying to learn probabilities?

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G5BAIM Evulutionary Algorithms Evolutionary Algorithms - Finally Evolutionary algorithms can be used as search methods as well as a learning mechanism It just needs saying!

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G5BAIM Artificial Intelligence Methods Graham Kendall End of Evolutionary Algorithms

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