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Evolutionary Algorithms An Introduction "[G]enetic algorithms are based on a biological metaphor: They view learning as a competition among a population of evolving candidate problem solutions. A 'fitness' function evaluates each solution to decide whether it will contribute to the next generation of solutions. Then, through operations analogous to gene transfer in sexual reproduction, the algorithm creates a new population of candidate solutions." Matthias Trapp, Diploma Student - Computer Science, Theoretical Ecology Group - University of Potsdam, Stanislaw Lem Workshop on Evolution – 10.-14. October - Lviv 2005, trapp.matthias@freenet.de

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Agenda Introduction Structure of an EA Genetic Operators Classification Implementation Discussion

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Introduction

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Evolutionary Algoritms - Introduction4 Motivation - The Problem(s) Global optimization problem: –Function has many local optima –Function is changing over time –Function have many parameters very large search space Combinatorial problems / Data Mining Classical NP-hard problems: –TSP –SAT …

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Evolutionary Algoritms - Introduction5 Overview Application Domains

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Evolutionary Algoritms - Introduction6 Evolution and Problem Solving Algorithm = Automated Problem Solver Broad Scope: Natural Computing Family of algorithms which mimicking natural processes: –Neural Networks –Simulated Annealing –DNA Computing –Evolutionary Algorithms Evolutionvs.Problem Solving Environment Problem Individual Candidate Solution Fitness Quality Approximation Optimization

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Evolutionary Algoritms - Introduction7 Evolutionary Algorithms EAs are adaptive heuristic search algorithms Metaphor: trail and error (a.k.a generate and test) EAs are inspired by Darwin's theory of evolution: problems are solved by an evolutionary process resulting in a best (fittest) solution (survivor) from a population of solution candidates EAs has been successfully applied to a wide range of problems: Aircraft Design, Routing in Communications Networks, Tracking Windshear, Game Playing, Robotics, Air Traffic Control, Design, Scheduling, Machine Learning, Pattern Recognition, Job Shop Scheduling, VLSI Circuit Layout, Strike Force Allocation, Market Forecasting, Egg Price Forecasting, Design of Filters and Barriers, Data-Mining, User-Mining, Resource Allocation, Path Planning, Theme Park Tours …

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Evolutionary Algoritms - Introduction8Characteristics Differences to classical algorithms/optimization methods: EAs search a set of possible solutions in parallel EAs do not require derivative information EAs use probabilistic transition rules EAs are generally straightforward to apply EAs provide a number of potential solutions EAs are able to apply self-adaptation Another useful hammer ? If yes, then how can that be achieved ?

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Structure of an EA

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Evolutionary Algoritms - Structure of an EA10 EA Components Representation mechanism (definition of individuals) Evaluation function (or fitness function) Population as container data structure Parent/Survivor selection mechanism Variation operators (Recombination, Mutation) Initialization procedure / Termination condition

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Evolutionary Algoritms - Structure of an EA11 General Schema EA Evolutionary Search (Flow Chart Model)

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Evolutionary Algoritms - Structure of an EA12 General Schema EA Evolutionary Search (Pseudo Code) procedure EA { t = 0; Initialize(Pop(t)); Evaluate(Pop(t)); while(!TerminalCondition(Pop(t)) { Parents(t) = ParentSelection(Pop(t)); Offspring(t) = Recombination(Parents(t)); Offspring(t) = Mutation(Offspring(t)); Evaluate(Offspring(t)); Pop(t+1)= Replace(Pop(t),Offspring(t)); t = t + 1; }

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Evolutionary Algoritms - Back Matter13 Representation x = E(D(x)) Mapping: Problem context Problem solving space: –Phenotype space P (candidate solution,individuals) –Genotype space G (chromosomes, individuals) –Encoding E : P G –Decoding D : G P Encoding: Technical representation of individuals –GA:Binary Encoding: (1110110000100) = 7556 –ES: Valued vectors: (ABDJEIFJDHDIE)||(136578924) –EP: Finite state machines: –GP: Tree of objects (LISP): (IF_THEN_ELSE(> x 0)(SetX(*(* x 3) (- 4 y)))(SetY(+ x (- y 1))))

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Evolutionary Algoritms - Back Matter14 Population P(t) = {x 1 t,..., x n t } Multi-set of genotypes = unit of evolution Invariants: –Population Size n: static (common) dynamic (unusually) –Non-overlapping (Simple GA): entire population is replaced each generation –Overlapping (Steady-State GA): few individuals are replaced each generation Sometimes associated with spatial structure Diversity: number of different solutions in P(t) Multi-Population approaches (Pohlheim, 1995)

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Genetic Operators

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Evolutionary Algoritms - Genetic Operators16 Selection/Sampling Operators Distinguish between parent and survivor selection Typically probabilistic; work on population level Use fitness assignment of solution candidates Role: pushing quality improvement Generational selection vs. steady-state selection Common steady state selection methods: Elitist Selection Roulette Wheel Selection Tournament Selection Scaling Selection Rank Selection Fitness-proportionate Selection Hierarchical Selection Boltzmann Selection Remainder stochastic sampling Stochastic uniform sampling

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Evolutionary Algoritms - Genetic Operators17 Mutation Operator m i : G G Unary operator, always stochastic Bit-Strings: Bit-flips (00101) (10101) Tree: –Sub tree destructive –Sub tree/Node swap List: –Generative/Destructive –Node/Sequence Swap Array: –Destructive –Element Flip/Swap

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Evolutionary Algoritms - Genetic Operators18 Recombination c i : G ×…× G G Inherit genotype traits, typically stochastic Often binary operator: Offspring = Sex(Mum, Dad) Bit-Strings: –k-Point Recombination –Uniform Recombination Genetic Programming: (seldom used)

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Evolutionary Algoritms - Genetic Operators19 A Simple Example Representation{0,1} n Recombination1-Point Crossover Recombination probability70% MutationUniform Bit-Flip Mutation probability p m 1/n Parent selectionBest out of random two Survival selectionGenerational Population size500 Number of offspring500 InitializationRandom Termination conditionNo improvement in last 25 generations EA for Knapsack Problem

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Evolutionary Algoritms - Genetic Operators20 Effects of Genetic Operators Selection alone will tend to fill the population with copies of the best individual Selection and crossover operators will tend to cause the algorithms to converge on a good but sub-optimal solution Mutation alone induces a random walk through the search space. Selection and mutation creates a parallel, noise- tolerant, hill-climbing algorithm

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Evolutionary Algoritms - Genetic Operators21 Terminal Conditions Discovery of an optimal solution (precision ε > 0), Discovery of an optimal or near optimal solution, Convergence on a single or set of similar solutions, A user-specified threshold has been reached, A maximum number of cycles are evaluated, EA detects the problem has no feasible solution often disjunction of different conditions

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Classification

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Evolutionary Algoritms - Classification23 Classification - Overview 1948 Alan Turing: genetically or evolutionary search >1950 Idea: simulate evolution to solve engineering and design problems Box, 1957 Friedberg, 1958 Bremermann, 1962

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Evolutionary Algoritms - Classification24 Genetic Algorithms (GA) By Holland (1975), USA concerned with developing robust adaptive systems Initially as abstraction of biological evolution Use of bit-strings for solution representation First EA which uses recombination Recombination seen as main operator very successful for combinatory optimization problems

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Evolutionary Algoritms - Classification25 By Rechenberg (1973), Schwefel (1981), Germany Parameter optimization of real-valued functions Accentuation on mutation Selection (μ – Parents, λ – Offspring): –(μ, λ): choose fittest of λ > μ offspring –(μ + λ): choose fittest of λ + μ solutions Recombination (u,v parent vectors, w child vector): More soon… (Implementation Example) Evolutionary Strategies (ES)

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Evolutionary Algoritms - Classification26 Evolutionary Programming (EP) By Fogel, Owens, and Walsh (1966), USA Application: Artificial Intelligence, Initially for evolution of finite-state machines, Using mutation and selection, Later applications to mainly real-valued functions Strong similarity to evolutionary strategies Example: Prediction of binary cycles

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Evolutionary Algoritms - Classification27 Genetic Programming (GP) Koza (1992), developed to simulate special functions Application: Function fitting f(x) Using parse trees of Terminal and Non-Terminals: Assumptions: –Completeness –Seclusion Problems: –Variable count –Variable types

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void ga::rank(void) { fitness_struct temp; int pos; calc_fitness(); for (int pass=1; pass

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Evolutionary Algoritms - Implementation29 Search Space: Evolutionary strategy: Solution candidate (no encoding necessary): Fitness-Function : Parent selection: Elitist Recombination: 1-Point, fixed Non-overlapping population Another Simple Example Hybrid approach: evolutionary strategy and genetic program

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Evolutionary Algoritms - Implementation30 Applying Self-Adaptation Evolution of the Evolution: Self-adaptation = specific on-line parameter calibration technique Random number from Gaussian distribution with zero mean and standard deviation σ Mutation operator: Extending the candidate representation:

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Evolutionary Algoritms - Implementation31 Working of an EA Distinct search phases: –Exploration –Exploitation Trade-Off between exploration and exploitation: –Inefficient search vs. Propensity to quick search focus Premature Convergence: climbing the wrong hill –Losing diversity Converge in local optimum –Techniques to prevent this well-known effect Any-time behaviour

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Evolutionary Algoritms - Implementation32 Multiobjective EA Multiobjective GA (MOGA) (Fonseca und Fleming (1993)), Niched Pareto GA (NPGA) (Horn und Nafpliotis (1993)), Nondominated Sorting GA (NSGA-II) (Deb u. a. (2000)), Strength Pareto EA (SPEA) (Zitzler und Thiele (1998)), Strength Pareto EA (SPEA2) (Zitzler u. a. (2001))

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Evolutionary Algoritms - Implementation33 Parallel Implementation of EA Subpopulation on MIMD (Belew and Booker (1991)) Decrease of execution time Migration Model –Unrestricted migration –Ring migration –Neighbourhood migration Global Model (Worker/Farmer) Diffusion Model: –handles every individual separately –selects the mating partner in a local neighbourhood –diffusion of information takes place

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Evolutionary Algoritms - Implementation34 API Comparison NameLanguageLicenceTarget PGAPackFortran / CFreewareAll EOC++GNU LGPLAll GALibC++BSDLnx,Win GAGSC++FreewareLnx,Win JAGAJavaFreewareAll JGAPJaveFreewareAll

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Discussion

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Evolutionary Algoritms - Discussion36 EA Advantages +Applicable to a wide range of problems +Useful in areas without good problem specific techniques +No explicit assumptions about the search space necessary +Easy to implement +Any-time behaviour..is a good designer of complex structures that are well adapted to a given environment or task.

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Evolutionary Algoritms - Discussion37 EA Disadvantages –Problem representation must be robust –No general guarantee for an optimum –No solid theoretically foundations (yet) –Parameter tuning: trial-and-error Process (but self-adaptive variants in evolution strategies) –Sometimes high memory requirements –Implementation: High degree of freedom

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Evolutionary Algoritms - Discussion38Summary EAs are different from classical algorithms Less effort to develop an EA which: –Delivers acceptable solutions, –In acceptable running time, –Low costs of men and time EAs are distributable (Belew and Booker (1991)): –Subpopulations on MIMD, –Via network EAs are easy to implement In order to make evolutionary computing work well, there must be a programmer that sets the parameters right. an EA is the second best algorithm for any problem

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Thank You ! Questions, Concerns, Comments, Sarcasm, Insults…

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Sources Spears, W. M., De Jong, K. A., Bäck, T., Fogel, D. B., and de Garis, H. (1993). An Overview of Evolutionary Computation, The Proceedings of the European Conference on Machine Learning, v667, pp. 442-459. A.E. Eiben, Evolutionary computing: the most powerful problem solver in the universe? Zbigniew Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, 1999, 3-540-60676-9 Lawrence J. Fogel, Alvin J. Owens, Michael J. Walsh: Artificial intelligence through simulated evolution, Wiley Verlag 1966 John R. Koza: Genetic Programming on the programming of computers by means of natural selection, MIT Verlag 1992

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