Computational intelligence methods GA, schemas, diversity Pavel Kordík, Martin Šlapák Katedra teoretické informatiky FIT České vysoké učení technické v Praze MI-MVI, ZS 2011/12, Lect. 5 https://edux.fit.cvut.cz/courses/mi-mvi/ Evropský sociální fond Praha & EU: Investujeme do vaší budoucnosti Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 1 / 13
Islands model in EA Introduced by Cohoon et al. (1987). On N isolated islands run N independent evolutionary algorithms. After some iterations the migration will start: 1 On each island, there are selected few most perspective individuals. 2 This best individuals are put to boat/plane and sent to other island(s). 3 After arrival, they are mixed into local pop. with some probababilistic method. Powerful method to parallelization of EAs distributed computing. Ideas: different enviroment on each island, simulate catastrophe, tune attributes of selection the best individuals,... Image source: http://www.maths.tcd.ie/~rmurphy/project/report/report_html_e8ffb07.gif Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 2 / 13
Elitism Method when we take 1 or more individuals directly from the population P t to new population P t+1 without aplying any crossover or mutate operators. Guarantees that the quality of population P t+1 will not became worse then the quality of P t. Figure: Example of run of GA with elitsm Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 3 / 13
Premature Convergence & Stagnation Premature convergence A premature loss of diversity in the population with the search converging to a sub-optimal solution. (Early stages of the evolution search process.) Stagnation Ineffective search due to a weak selective pressure. (Later stages of the evolution search process.) population diversity selective pressure Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 4 / 13
Prem. Convergence & Stagnation How to Deal with it? 1 Balance between exploration and exploitation. How to achieve the optimal selective pressure during the whole evolution search? We have many options: Linear scaling scaling techniques proper selection mechanisms fitness sharing and crowding... It is adjustment of the fitness values distribution in order to get desired selection pressure. σ = f max f avg The actual chromosomes fitness is scaled as f i = a f i + b Parameters a and b are selected so that the f avg is mapped to itself, and the best fitness is increased by a desired multiple of the f avg. Typical value of σ is from (1.5, 2.0). 1 Based on X33SCP slides. [2] Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 5 / 13
Schemas Questions [2] How can an EA identify parts of chromosomes that are important for completion of the sought solution? How can an EA combine two solutions in a new one in an efficient way? What is an amount of information that is processed efficiently through the simulated evolution? Schema theory tries to analyze effect of selection, crossover and mutation in order to answer the above questions. In its original form it assumes: binary representation, proportionate roulette wheel selection, 1-point crossover and bit-flip mutation. Schema A template, which defines set of solutions from the search space with certain specific similarities. Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 6 / 13
Schema structure Example Schema consists of: 0s, 1s (fixed values) and wildcard symbols * (any value) covers 2 r strings, where r is a number of used in the schema. Example: schema S = 11 0 covers strings 11000, 11001, 11100, and 11101 Schema properties: Defining length δ(s) (compactness) distance between first and last non-* in a schema (= number of positions where 1-point crossover can disrupt it). Order o(s) (specificity) a number of non-* s (= number of positions where simple bit swapping mutation can disrupt it). Chromosomes are order l schemata, where l is length of chromosome (in bits or loci). Chromosomes are instances (or members) of lower-order schemata. How many schemata is matched by a string of length l? Fitness f(s) (quality) average fitness computed over all covered strings. S = ( 1 01 0 ) : δ(s) = 5, o(s) = 4 Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 7 / 13
Schema Properties: Example 8-bit Count Ones problem maximize a number of ones in 8-bit string. string fitness string fitness 00000000 0 11011111 7 00000001 1... 10111111 7 00000010 1 01111111 7 00000100 1 11111111 8 Assume schema S a = 1 1 10 vs. S b = 0 0 defining length: δ(s a ) = 7 1 = 6, δ(s b ) = 4 2 = 2 order: o(s a ) = 4, o(s b ) = 2 fitness of S a : S a covers 2 4 strings in total. 1 string of fitness 3, 4 with f=4, 6 with f=5, 4 with f=6, 1 with f=7 f(s a ) = (1 3 + 4 4 + 6 5 + 4 6 + 1 7)/16 = 80/16 = 5 Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 8 / 13
Schema Properties: Example 2 Once more: S b = 0 0 fitness of S b : S b = (1 0 + 6 1 + 15 2 + 20 3 + 15 4 + 6 5 + 1 6)/26 = 192/64 = 3 Question: What would be a fitness of S = 0 1 compared to S b? 1 Count length and order of schema... 2 How many strings is covered? 3 What is the final fitness? Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 9 / 13
Darwinism Charles Darwin, the English Naturalist in his main work The Origin of the species, en 1859. Darwin s theory of evolution proposed natural selection as the basis of evolution and human origin. Individuals display differences. Shortage of food leads them to fight for existence. Individuals with superior differences have more chance to reach adulthood, reproduce and transmit these variations to their offspring. [1] Figure: Charles Darwin(1809-1882) Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 10 / 13
Lamarck s theory Lamarck s theory of evolution appeared in his Zoological Philosophical Work written in 1809. Environmental changes generate new needs. These needs determine the use or disuse of some organs. Such organs develop or are diminished. The acquired characters are hereditary. A typical example of Lamarck s theory is the evolution of the necks of giraffes, due to the effort of eating leaves from the trees. [1] Figure: Jean-Baptiste de Monet Lamarck (1744-1829) Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 11 / 13
Books Richard Dawkins, The Selfish Gene. New York City: Oxford University Press, 1976. ISBN 0-19-286092-5. John Holland, Hidden Order: How Adaptation Builds Complexity. Helix Books, 1996. ISBN 978-0201442304 John Koza, A Field Guide to Genetic Programming ISBN 978-1-4092-0073-4, download at: http://www.springerlink.com/content/h46r77k291rn/ Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 12 / 13
References M José T. Molina, General theory conditional evolution of life [online], [cited on 2011-05-10] available at http://www.molwick.com/en/evolution/ Kubalík, J., Evolutionary Algorithms slides from X33SCP Pavel Kordík, Martin Šlapák (FIT ČVUT) Computational intelligence methods MI-MVI, ZS 2011/12, Lect. 5 13 / 13