Why Should Mathematicians And Computer Scientists Be Interested In Evolutionary Computation

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What is Evolutionary Computation?. Evolutionary computation (EC) is a biologically inspired computational concept that is derived from the evolutionary process of nature.. Flavors" of Evolutionary Computation. Genetic AlgorithmsGenetic ProgrammingEvolutionary ProgrammingEvolutionary Strategie

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Why Should Mathematicians And Computer Scientists Be Interested In Evolutionary Computation

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1. Why Should Mathematicians And Computer Scientists Be Interested In Evolutionary Computation? Gary R. Greenfield Mathematics and Computer Science University of Richmond Richmond, Virginia USA May, 2006

2. What is Evolutionary Computation? Evolutionary computation (EC) is a biologically inspired computational concept that is derived from the evolutionary process of nature.

3. “Flavors” of Evolutionary Computation Genetic Algorithms Genetic Programming Evolutionary Programming Evolutionary Strategies Ant Colony, Particle, and Swarm Methods Metaheuristics Hybrid Methods

4. EC Applications Simulation Robotics Economics Security Industrial Design Computer Graphics Evolvable Hardware Optimization Bioinformatics Art and Music

5. EC Conferences GECCO – Genetic and Evolutionary Computation Conference CEC – IEEE Congress on Evolutionary Computation EuroGP, EvoCOP, et al – European Conference on Genetic Programming, Evolutionary Computation in Combinatorial Optimization, and EvoWorkshops (re-emerging in ’07 as EvoCOMP) FOGA – Foundations of Genetic Programming

6. AL – Artificial Life Conference ECAL – European Conference on Artificial Life ACO – Ant Colony Optimization MIC – International Metaheuristics Conference SAB – Simulation of Adaptive Behavior PPSN – Parallel Problem Solving from Nature

7. EC Journals and Books Evolutionary Computation Artificial Life Genetic Algorithms – Goldberg Genetic Algorithms – Mitchell Genetic Programming I, II, III, IV – Koza Genetic Programming - Banzhaf Emergent Computation - Forrest Ant Colony Optimization – Dorigo et al Evolutionary Robotics – Nolfi et al Evolutionary Computation – De Jong

8. EC Origins John Holland (’75?) - Genetic Algorithms (for classifier systems): “Computer programs that `evolve’ in ways that resemble natural selection can solve complex problems even their creators do not fully understand” Robert Axelrod (’84?) – Iterated Prisoner’s Dilemma

9. Genetic Algorithms -- Particulars Population of binary strings Genotypes – contiguous segments are genes Fitness Evaluation Genotype to Phenotype Population Culling Elistist Proportional Fitness Tournament Selection Population Replacement Genetic Operators Recombination (crossover) Mutation (bit flipping)

10. Toy Example #1 Chaotic 1-dim CA’s: Genotype – 00010111 Phenotype – Rule Table: 000 -> 0 000 -> 0 010 -> 0 011 -> 1 . . 111 -> 1

11. Toy Example #2 (cf. D. Hillis) Sorting Networks Genotype: coded pairs Phenotype: compare/swap e.g. 0001 0110 … (0,1) (1,2)

12. Genetic Programming -- Particulars Population – binary trees Leaf nodes – terminals Variables Constants Internal nodes – operators +, -, *, (protected) /, etc. Evaluation – (post-order) traversal Genetic Operators Recombination (subtree crossover) Mutation (various?)

13. Toy Example: Even Parity

14. Koza’s Original GP Test Suite Force Balancing Controller Ant Trail Learning Problem Regression Problem Boolean Multiplexer Problem

15. The “HUMIES” Human Competitive Awards http://www.genetic-programming.org/hc2005/cfe2005.html Backgammon playing (Sipper) Image compression (Miikkulainen ) Quantum computer algorithms (Clark) Photonic crystal design (Lipson) Optical lens systems (Koza) Mars rover mission planning (Terrile)

16. Combinatorial Optimization Idea: Find satisfactory algorithms for “solving” NP-hard graph problems arising in scheduling, distribution, routing, etc. Subgraph isomorphism problem Graph bisection problem Graph edit distance problem Maximal common subgraph problem Graph coloring problem Three index assignment problem Traveling salesperson problem Maximum clique problem

17. Early Work of Karl Sims (’91) Artificial evolution of images (’94) Evolved Behavior

18. Getting Started… … or how I learned to stop worrying and love interactive artificial evolution. Sample image processing primitives for use in the method of “evolving expressions”

19. Sample Evolved Image

22. Expressionism IV

23. Fast Forward to 1999 Non-interactive image evolution using a co-evolutionary model with images as hosts and digital convolution filters as prey.

24. The Co-evolutionary Arms Race

25. The Fitness “Contest”

26. Fast Forward to 2001 Evolving Expressions coupled with an image segmentation algorithm parameterized by a vector of coefficients admits a non-interactive approach… High res -> low res -> 50 segs -> 25 segs

27. Fitness Functions! With image fitness evaluated using functions such as:

28. Evolved Images

29. Planar Graphs? What does one make of the following images evolved using which maximizes the number of segmented region adjacencies, where two regions are adjacent if and only if they have a common boundary edge?

30. (Segmented) Examples

31. Constructing G from I Let G be the graph whose vertices correspond to the segmented regions of I, where two vertices are joined by an edge if and only if their corresponding segments are adjacent. Theorem. G is a simple, connected planar graph. Recall. A planar graph G is maximal planar if and only if e = 3v-6. Moral. Maximizing F(I) is equivalent to finding (evolving?) an image with a segmentation that yields a maximal planar graph.

32. Maximal Planar (v = 25) Gallery

33. An Aside Theorem: A planar graph G can be realized as the graph arising from the adjacencies of a region decomposition (i.e., partition of some s x t array) if and only if for every face f - except possibly the face at infinity - the maximum length of a “cycle of f” is four.

34. Take-Away Messages EC is here to stay! Computer science applications Combinatorial Optimization Applied Mathematics Experimental mathematics Ignore EC at your peril! EC vis-a-vis theoretical computer science and mathematics may be complementary!

35. Thank-you! [email protected] http://www.mathcs.richmond.edu/~ggreenfi/ Questions??

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