Evolutionary Algorithms

1. 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

2. Agenda Introduction Structure of an EA Genetic Operators Classification Implementation Discussion

3. Introduction

4. 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 • … Evolutionary Algoritms - Introduction

5. Overview Application Domains Evolutionary Algoritms - Introduction

6. Evolution and Problem Solving • Algorithm = Automated Problem Solver • Broad Scope: Natural Computing • Family of algorithms which mimickingnatural processes: • Neural Networks • Simulated Annealing • DNA Computing • Evolutionary Algorithms Evolutionary Algoritms - Introduction

7. 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 ShopScheduling, VLSI Circuit Layout, Strike Force Allocation, Market Forecasting,Egg Price Forecasting, Design of Filters and Barriers, Data-Mining, User-Mining, ResourceAllocation, Path Planning, Theme Park Tours … Evolutionary Algoritms - Introduction

8. Characteristics 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 ? Evolutionary Algoritms - Introduction

9. Structure of an EA

10. 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 Evolutionary Algoritms - Structure of an EA

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

12. 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; } Evolutionary Algoritms - Structure of an EA

13. 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)))) Evolutionary Algoritms - Back Matter

14. Population P(t) = {x1t,..., xnt} • 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) Evolutionary Algoritms - Back Matter

15. Genetic Operators

16. 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: Evolutionary Algoritms - Genetic Operators

17. Mutation Operator mi : 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 Evolutionary Algoritms - Genetic Operators

18. Recombination ci : 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) Evolutionary Algoritms - Genetic Operators

19. A Simple Example EA for Knapsack Problem Evolutionary Algoritms - Genetic Operators

20. 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 Evolutionary Algoritms - Genetic Operators

21. 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 Evolutionary Algoritms - Genetic Operators

22. Classification

23. 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 Evolutionary Algoritms - Classification

24. 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 Evolutionary Algoritms - Classification

25. Evolutionary Strategies (ES) • 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 Algoritms - Classification

26. 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 Evolutionary Algoritms - Classification

27. 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 Evolutionary Algoritms - Classification

28. void ga::rank(void) { fitness_struct temp; int pos; calc_fitness(); for (int pass=1; pass<POP_SIZE; ++pass) { temp = rankings[pass]; pos = pass; while ((pos > 0) && temp.fitness < rankings[pos-1].fitness) { rankings[pos] = rankings[pos-1]; --pos; } rankings[pos] = temp; } best_sol = rankings[0].fitness; worst_sol = rankings[POP_SIZE-1].fitness; if (best_sol < best_overall) best_overall = best_sol; if (worst_sol > worst_overall) worst_overall = worst_sol; } Implementation and Software

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

30. 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: Evolutionary Algoritms - Implementation

31. 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 Evolutionary Algoritms - Implementation

32. API Comparison Evolutionary Algoritms - Implementation

33. Discussion

34. 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.” Evolutionary Algoritms - Discussion

35. 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 Evolutionary Algoritms - Discussion

36. Summary „an EA is the second best algorithm for any problem“ • 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.“ Evolutionary Algoritms - Discussion

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

38. 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