Eastern Michigan University Introduction to Evolutionary Computation Matthew

Eastern Michigan University Introduction to Evolutionary Computation Matthew Evett

Evolutionary Computation is…. § Umbrella term for machine learning techniques that are modeled on the processes of neo-Darwinian evolution. l l Genetic algorithms, genetic programming, artificial life, evolutionary programming Survival of the fittest, evolutionary pressure § Techniques for automatically finding solutions, or near solutions, to very difficult problems.

Why is EC Cool? § EC techniques have found solutions better than any previously known for many domains l Electronic circuit design, scheduling, pharmaceutical design § Autonomous solution discovery is fun l Look Ma! No hands!

Darwinian Evolution § Works on population scale, not individual § Chance plays a part l l Variation affects viability Fittest don’t always survive! § Heredity of traits § Finite resources to yield competition

EC is not. . . § “Real” evolution, or “real” genetics § It is modeled on natural genetic systems only in a simple sense. l l Term “genetic” is really used to mean “heredity” Real genetics is much more complicated

Overview of the Talk § We’ll look at two related techniques. . . l l genetic algorithms genetic programming § We’ll look at some demos of evolutionary systems.

History of EC § Friedberg’s induced compilers (1958) § Evolutionary Programming (1965) l Fogel, Owens & Walsh § Evolutionary Strategies (Recehenberg ‘ 72) § Genetic Algorithms (Holland ‘ 75) § Genetic Programming l l Tree-based GA (Cramer ‘ 85, Koza ‘ 89) “True” GP (Koza ‘ 92)

Basic evolutionary algorithm § Population of individuals, each representing a potential solution to the problem in question.

Genetic Algorithms (GA) § Population individuals are (fixed-length) binary strings (“genome”) § Start with a population of random strings. § Measure “fitness” of individuals. § Each generation forms a new population from old via recombination and mutation. § Solutions improve over generations.

Three steps to setting up a GA § 1) Devise a binary encoding representing the potential solutions to a problem. § 2) Define a fitness function. l Objective measure of quality of individual § 3) Set control parameters. l l l population size maximum number of generations probability of mutation and crossover, etc.

Example: Designing a Truss § 10 members § 16 diameters avail. l l Different costs Different strengths A 10 A 2 A 8 A 6 A 7 A 3 A 5 A 9 A 4 § Find cheapest that is strong enough 0010 1110 0001 0010 1111 0001 0110 1010 § 40 -bit genome 50 lb l Each 4 bit sequence reps. diam. of 1 member 50 lb

Running a GA § Generate an initial population of random binary strings § Calculate “fitness” of each individual l Fitness is cost of design, + penalty for fails § Create next generation l l l Select on the basis of “fitness” Recombination/mating Select some elements for mutation. • Typically one or two random bits will be flipped

Crossover in GA § Single-point crossover l 00101101 00101011 10010101 Parents Children There are many other forms § Randomly select crossover point § Swap crossover fragments § Offspring will have a combination of randomly selected parts of both parents

Running a GA (continued) § Repeatedly create new generations l Calculate fitness § Terminate when an acceptable solution is been found or when the specified maximum number of generations is reached.

Running a GA/GP § Major phases of evolutionary algorithms:

Results of Truss Example § Optimal solution is known, but rare l Number of possible designs is 240 § Typical run l 200 individuals/pop. ; 40 generations § Yields answer within 1% of optimal l …but examines only 8000 individuals! (. 0000007% of designs)

Genetic Programming (GP) l l GP is a domain-independent method for inducing programs by searching a space of Sexpressions. GP’s search technique is similar to GA’s. The elements of a population are programs, encoded as s-expressions. The Lisp programming language is based on sexpressions. • Original GP work was done in Lisp.

Genetic Programming Elements § S-expressions l l Prefix notation Programs, encoded as trees, evaluated via postorder traversal § Ex: tree corresponding to the S-expression l (sqrt ( / (+ a b) 2. 0 ) )

Representation of a Program § S-expressions can be converted to C…. float tree. Func(float a) { if ( a > 10. 0) { return 20. 0; } else { return a/2. 0; } } Looping constructs and subroutine calls are also possible.

Three steps to setting up a GP § Define appropriate set of functions and terminal set = {a, b, c, 0, 1, 2} terminals. l l Must have closure. function set ={+, -, *, /, SQRT} Functions and Terminals must be sufficient. § Define a fitness function. § Set control parameters. l l l GA population size, maximum size or depth of the individual trees size and the shape of the original trees, etc.

Starting a GP § Generate an initial population of random Sexpression trees. § Calculate fitness value for each individual l Often over a set of test cases.

Running a GP § Create the next generation (population) l Select elements for reproduction • Random, fitness-proportionate, tournament. l Reproduce: • Direct reproduction (cloning) • Mating – Mating method differs from GA’s. • Mutation – Also differs from GA’s.

GP Crossover § Randomly choose crossover points. § Swap rooted subtrees. § “Closure” property guarantees viability of offspring

Mutation with GP § Elements that are selected for mutation will have some randomly selected node (and any subtree under it) replaced with a randomly generated subtree. § Point mutation § Tree growth (shown here)

Running a GP (continued) § Repeatedly create new generations. § Terminate when an acceptable solution is found or when a specified maximum number of generations is reached. l The termination criteria is often based on a number of hits, where a hit is defined as the successful completion of some subgoal.

Example: Santa Fe Trail § Ant animats, acquiring food. l l Some gaps in trail 89 food “pellets” § Evolve control strategy to consume all pellets l In acceptable time

Representing “Ants” T = {ahead, left, right} F ={if-food-ahead, progn 2, progn 3} § “Terminals” are functions, whose evaluation causes ant to move. § Fitness = # of pellets consumed in 400 terminal evaluations. l Prevents infinite runs, and weak solutions. (if-food-ahead (move) (progn 2 (left) (move)))

Demo: Santa Fe Ant § During run, shows path of best-of-generation, best-of-run § Chong, 1998 l

Santa Fe Ant Demo (done) § http: //studentweb. cs. bham. ac. uk/~fsc/DGP. html § The applet

GP Generated Military Tactics § Squadron has a destination § Ordered either to: evade or attack § Porto, Fogel & Fogel, 1998 § Population of strategies

Generating tactics § Every 20 seconds of real time, do GP run, 40 generations. § Predicts 20 mins ahead. § Allows adaptation to changing situation. § Here, order is changed from “evade” to “attack”.

Co-evolution § Simulation uses GP-developed strategy for both squadrons.

Real-time success § Platform: Sparc 20 § Actual Pentagon military simulation. § Blue squad fires on red.

Learning to Walk with GP § Evolve control strategies for movement of arbitrarily articulated animats. l Karl Sims, 1995 § Fitness is rate of travel l l physics model LOTS of CPU cycles!

GA-learned bipedal motion § Individual strategies can be observed on the applet. (http: //www. jsh. net/and y/gat/environ. html) § User can view all trials, or just the best-ofgeneration. § Constrained skeletons. § Dick, 1998

Financial Symbolic Regression § The goal is time series prediction, where the target points are a financial time series. § In this case we are using a target time series derived from the daily closing prices of the S&P 500 from the years 1994 and 1995. § Uses 33 independent variables taken from time series that are derived from the S&P 500 itself and from the closing daily prices of 32 Fidelity Select Mutual Funds. § Evett & Fernandez, 1996, 1997.

Solving Financial Problems § The top line in the graph is the daily closing price of the S&P 500. The solid line below it is the graph of the target time series after preprocessing. § The dotted line is a function evolved using GP. It is included here only as an example to illustrate that criterion for success does not require a great deal of accuracy.

The Example Evolved Function § y = (((0. 38)-((-0. 20923)-(FSPTX-(((-0. 79706) /(0. 38))*((FSUTX-FSCSX)*(FSCGX-(0. 34247))))))) *(SPX*((0. 82794)/(0. 54431)))) l The independent variables that were used by this evolved function are derived from the following time series. • • • FSPTX FSUTX FSCSX FSCGX SPX Fidelity select Technology Portfolio. Fidelity Select Utility Portfolio Fidelity Select Software Portfolio Fidelity Select Capital Goods Portfolio S&P 500 Index

Conclusions § Evolutionary algorithms are a powerful technique for problem solving in domains that: l l are variable difficult, if not impossible to optimize § GP is especially useful for problems for which the form of the solution is not known. § Evolutionary techniques are becoming widespread.

Overview of the Software § § § Object Oriented C++. Windows 95 (MS Visual C++ 5. 0) Ported to UNIX. (GNU C++) Extended to run cooperatively on multiple machines using MPI.

Thank You! Are there any Questions?