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1 Evolutionary Systems Paul CRISTEA Politehnica University of Bucharest Spl. Independentei 313, 77206 Bucharest, Romania, Phone: +40 -21- 411 44 37, Fax: +40 -21- 410 44 14 e-mail: pcristea@dsp.pub.ro Eindhoven University of Technology April 16 th, 2003 Slide 2 2 Evolutionary Systems Lecture Outline Slide 3 3 Biological Evolution Current estimates: the universe began 15 billion years ago; the earth was formed 5000 million years ago, the first living organism appeared 3500 million years ago The ancestral cell - simple bag of chemicals enclosed in a membrane. It contained a program of instructions encoded on a DNA molecule. The program consisted of sub-programs called genes, which directed various chemical reactions inside the cell: reactions to import food, reactions to convert food into energy, reactions to maintain the membrane, and so on. Most significantly, some genes directed chemical reactions that enabled the cell to replicate itself. As the ancestral cell replicated itself, the genes gradually changed, creating different species of progeny which were adapted to different environments. Slide 4 4 Evolution Evolution is seen as based on the trial-and-error process of variation and natural selection of systems at all levels of complexity. Artificial selection -- specific features are retained or eliminated depending on a goal or intention. (e.g., the objective of a cattle breeder who would like to have cows that produce more milk). Natural selection -- from Darwinian theory of biological evolution. Implicit goal of natural selection is maintenance or reproduction of a configuration at some level of abstraction. The selection is natural in the sense that there is no actor or purposive system making the selection. The selection is purely automatic or spontaneous, without plan or design involved. Evolution typically leads to greater complexity. Slide 5 5 Selection or self-organization? Criticisms against Darwinian view of evolution. (1) There are designs or plans guiding evolution (not discussed here), (2) Natural selection must be complemented by self- organization in order to explain evolution. (Jantsch, 1979; Kauffman, 1993; Swenson, 1997). The specific interpretation of Darwinism sees evolution as the result of selection by the environment acting on a population of organisms competing for resources. The winners of the competition -- those most fit to gain the resources necessary for survival and reproduction -- are selected, the others are eliminated. Slide 6 6 Over Darwinian view This view of evolution entails two strong restriction: 1. it assumes that there is a multitude ("population") of configurations undergoing selection; 2. assumes that selection is carried out by their common environment. It cannot explain the evolution of a "population of one". In the current, more general interpretation, there is no need for competition between simultaneously present configurations: A configuration can be selected or eliminated independently of the presence of other configurations: a single system can pass through a sequence of configurations, some of which are retained while others are eliminated. The only "competition" is one between subsequent states of the same system, but the selection is still "natural". Slide 7 7 Self-organization Selection does not presuppose the existence of an environment external to the configuration undergoing selection. The selection is inherent in the configuration itself. E.g., configurations can be intrinsically stable or unstable: A crystal vs a cloud of gas molecules, both in vacuum, will retain or not their structure. Self-organization -- the asymmetric transition from varying to stable. Natural selection encompasses both external, Darwinian selection, and internal, self-organizing selection. Slide 8 8 Evolutionary Algorithms Evolutionary algorithms are good coarse search techniques that can search enormous problem spaces. A population of possible solutions are scored on how well they solve some problem. The more fit a solution is, the more part it plays in parenting the next generation. New solutions are bred by combining components of the parents, and applying mutation to introduce variability (new aspects to the solutions). Evolution is slow and prone to loss of diversity, even if forced with higher mutation rate. The greedier the EA version, the faster the population will converge but the less likely they are to converge to the true optimum. Slide 9 9 A genetic algorithm (GA) is a computer model of the evolution of a population of artificial individuals. Each individual (k = 1,..., n; n is the population size) is characterized by a chromosome (genotype) S k, which determines the individual fitness (phenotype) f(S k ). The chromosome (genotype) is a string of symbols, S k = (S k1, S k2,...,S kN ), where N is the string length. The symbols S k1 are interpreted as genes of the chromosome S k. The evolution process consists of successive generations t = 0, 1, described by their population {S k (t)}. Genetic Algorithms Slide 10 10 Step 0. Generate a (random) initial population {S k (0)}. Step 1. Evaluate the fitness f(S k ) of each individual S k in the population {S k (t)}. Step 2. Select the individuals S k according to their fitness f(S k ) and apply to selected chromosomes the genetic operators: recombinations, point mutations, to generate the offspring population {S k (t+1)}. Step 3. Repeat the steps 1,2 for t = 0, 1, 2,..., until some convergence criteria (the maximum fitness in the population ceases to increase, t reaches the certain value) is satisfied. GA Steps Slide 11 11 Genetic Algorithm Flow Diagram Slide 12 12 General Features of GA 1 GAs are optimization techniques that posses an implicit parallelism: different partial effective gene combinations (called schemata) are searched in a parallel manner, simultaneously, for all combinations. Note: the smaller a combination is, the quicker it can be found. The GA scheme is very similar to that of quasispecies. Main difference: recombinations are not included in quasispecies model, whereas namely recombinations play the main role to find new good solutions in GAs (mutation intensity is usually very small in GAs). Slide 13 13 General Features of GA 2 In principle, GA are general algorithms, but the genetic operators (population crossover and mutation) are application-specific ; The GA itself is extremely simple. The power of the algorithm comes from the fact that it does two basic things: 1) it continuously improves and, 2) it explores solutions which may provide additional improvements. Both operations are encompassed in the genetic operators of population crossover and mutation, which manipulate the genes of the individuals to produce the continuously improving and experimentation properties of the GA. Slide 14 14 Specificity vs Versatility The genes of the individuals -- the genotype -- are used to determine how it behaves (i.e., how well it solves the problem) -- the phenotype. The genetic operators manipulate the genes, thus they must be tied to the representation of the genes. Genetic operators that are specific to the problem domain. Significant research has been done, attempting to determine universal genetic operators, based on universal gene representations. Unfortunately, these attempts have not been successful and it has been shown that problem specific encodings typically out perform universal encodings [DeJong and Spears, 1993], [Radcliff and George, 1993]. Slide 15 15 Crossover One-point crossover (analog to the biological one) For the parents S 1 = (S 11, S 12,...,S 1N ) and S 2 = (S 21, S 22,..., S 2N ), the children are (S 11,..., S 1m, S 2,m+1,...,S 2N ) and (S 21,..., S 2m, S 1,m+1,...,S 1N ); i.e., a head and a tail of an offspring chromosome are taken from different parents. Two-point and several point crossovers can be used similarly. Crossovers are sometimes supplemented by inversions, which consist in reverses of the symbol order in a part of a chromosome -- can help finding the best combinations of symbols in the chromosome strings. Slide 16 16 Uniform recombination The symbols of the chromosome of the first offspring are taken from either of the parents (S 1 or S 2 ) randomly for any symbol position, whereas the second offspring has the remainder symbols. E.g., two children of S 1 and S 2 can have the chromosomes: (S 11, S 22, S 13, S 14,...,S 2N ) and (S 21, S 12, S 23, S 24,...,S 1N ). Slide 17 17 GA Schemes There are a number of particular GA schemes, which differ in: methods of selection, recombination, chromosome representation, etc. A standard GA works on a binary string chromosome (symbols S ki take the values 0 or1) of fixed length (N = const) and applies fitness-proportionate selection, one-point crossovers, and one-flip mutations. Fitness-proportionate selection: the parents S k of the individuals in the new population are selected with probabilities proportional to their fitness f(S k ). Ranking selection: a certain number of best the individuals of the population {S k (t)} are used as parents of a new generation. Slide 18 18 Faster Evolution Elitist approach: G ood solutions are copied into the next generation (elites); Islands: physical, casts, in time (reincarnation); Local search: Using a local heuristic; Avoid greedy algorithms for better but slower results; Using computer clusters. Slide 19 19 Estimating Fitness Fitness evaluation takes most of the computing time; Reduce the number of true fitness evaluations in favour of quick fitness estimates; Need to keep track of how reliable the fitness estimate is; A solution with too low a reliability needs to be truly evaluated. where f is the fitness, R the reliability of the child (0-1). S 1, S 2 - the similarity between the child and parent 1, 2; R 1, R 2 - reliability of parent 1, 2. Slide 20 20 Partial Fitness Estimation 1 After Tim Hendtlass, Swinburne University of Technology, Mel