Genetic Programming in Python

Genetic Algorithms and Genetic Programming in Python

What are Genetic Algorithms and Genetic Programs?

Search algorithms based on the mechanics of natural selection and natural genetics

John Holland, University of Michigan

They seem to do well when... There is a huge solution space

The solution space is dynamic, non-linear, or otherwise complex

The solution space is poorly understood

Domain knowledge is scarce or difficult to encode

No mathematical analysis is available

Fitness, payoff, or suitability of a solution can be determined

Traditional search methods fail

What are the “mechanics” of natural selection and natural genetics?

Genotype and Phenotype “ blueprint”, chromosomes “ Physical manifestation”

Pyevolve Built-In Genotypes One-Dimensional Binary String

Genetic Program (Tree specific to GP)

1-D Binary String from pyevolve import G1DBinaryString genome = G1DBinaryString.G1DBinaryString(16)

2-D Binary String from pyevolve import G2DBinaryString genome = G1DBinaryString.G2DBinaryString(12, 18)

1-D and 2-D Lists from pyevolve import G1DList, G2DList genome = G1DList.G1DList(140) genome = G2DList.G2DList(8, 5) “ Alleles” are the object types the list is made of... by default integers You can pass in a function to construct the list with whatever object you want genome.setParams(rangeMin=-5.12, rangemax=5.13) genome.initializator.set(Initializators.G1DListInitializatorReal)

Tree and Genetic Program from pyevolve import GTree genome = GTree.GTree() gp_genome = GTree.GTreeGP()

Now that we have our genome, how is it expressed, and how do we know how “good” it is?

Find the global minima of Schaffer F6

The genotype is the (x,y) point, eg. (3.2,-4.7)

Phenotype is the value that results from putting in the (x,y) point into the function

Fitness is how close that resultant value is to the global minimum value (in this case, zero)

The Fitness Function def schafferF6(genome): x2y2 = genome[0]**2 + genome[1]**2 t1 = math.sin(math.sqrt(x2y2)); t2 = 1.0 + 0.001*(x2y2); score = 0.5 + (t1**2 - 0.5)/(t2*t2) return score genome = G1DList.G1DList(2) genome.setParams(rangemin=-100.0, rangemax=100.0, bestrawscore=0.0000, rounddecimal=4) genome.initializator.set(Initializators.G1DListInitializatorReal) genome.evaluator.set(schafferF6)

The GA Engine from pyevolve import GSimpleGA … create genome … ga = GSimpleGA.GSimpleGA(genome, seed=123) ga.setMinimax(Consts.minimaxType["minimize"]) ga.evolve(freq_stats=1000) print ga.bestIndividual() Output: Gen. 0 (0.00%): Max/Min/Avg Fitness(Raw) [0.60(0.82)/0.37(0.09)/0.50(0.50)] Gen. 1000 (12.50%): Max/Min/Avg Fitness(Raw) [0.30(0.97)/0.23(0.01)/0.25(0.25)] Gen. 2000 (25.00%): Max/Min/Avg Fitness(Raw) [0.21(0.99)/0.17(0.01)/0.18(0.18)] Gen. 3000 (37.50%): Max/Min/Avg Fitness(Raw) [0.26(0.99)/0.21(0.00)/0.22(0.22)] Evolution stopped by Termination Criteria function ! Gen. 3203 (40.04%): Max/Min/Avg Fitness(Raw) [0.30(0.99)/0.23(0.00)/0.25(0.25)] Total time elapsed: 14.357 seconds. - GenomeBase Score: 0.000005 Fitness: 0.232880 - G1DList List size: 2 List: [0.0020881039453384299, 0.00043589670629584631]

Pyevolve Built-In Selection Operators Rank Selection Choose the best (default) Uniform Selection Choose at random Tournament Selection Choose best from a random subset of population Roulette Wheel Selection More fit more likely to be chosen

Setting the selector from pyevolve import Selectors ga = GSimpleGA.GSimpleGA(genome) ga.selector.set(Selectors.GRouletteWheel) ga.selector is a “FunctionSlot.” It can accept any number of functions that will be used in order. ga.evaluator is another.

Take two (or more) individuals and combine them in some way to create children

Pyevolve Built-In Crossover Operators 1D Binary String Single Point Crossover, Two Point Crossover, Uniform Crossover 1D List Single Point Crossover, Two Point Crossover, Uniform Crossover, OX Crossover, Edge Recombination Crossover, Cut and Crossfill Crossover, Real SBX Crossover 2D List Uniform Crossover, Single Vertical Point Crossover, Single Horizontal Point Crossover 2D Binary String Uniform Crossover, Single Vertical Point Crossover, Single Horizontal Point Crossover Tree Single Point Crossover, Strict Single Point Crossover GP Tree Single Point Crossover

Pyevolve Built-In Mutation Operators 1D Binary String Swap Mutator, Flip Mutator 2D Binary String Swap Mutator, Flip Mutator 1D List Swap Mutator, Integer Range Mutator, Real Range Mutator, Integer Gaussian Mutator, Real Gaussian Mutator, Integer Binary Mutator, Allele Mutator, Simple Inversion Mutator 2D List Swap Mutator, Integer Gaussian Mutator, Real Gaussian Mutator, Allele Mutator, Integer Range Mutator Tree Swap Mutator, Integer Range Mutator, Real Range Mutator, Integer Gaussian Mutator, Real Gaussian Mutator GP Tree Operation Mutator, Subtree mutator

Genetic Programs are basically just a type of Genetic Algorithm

John Koza, University of Michigan, Stanford

Plug for Python and Entrepreneurship Karl Sims A founder of GenArts

Visual Effects plug-ins for film and video John Koza Cofounder of Scientific Games Corp.

Scientific Games now a near $1B company

65% of all scatch-off tickets created

A genetic program is just a tree with nodes

Simple Operator Node Examples Addition, Subtraction, Multiplication, Division Two inputs Cosine, Sine, Absolute Value One input Max, Min, Average Two inputs (or more) If Greater Than, If Less Than Four inputs: if A is greater than B then C else D

Terminal Node Examples Ephemeral Constants Generated at runtime Specified Constants Defined by you Variables Value determined when evaluated

Putting it all together: Creating a better unskilled forecast

Defining The Problem Columbus Next-Day High Temperatures From February 2005 to June 2010 Average Absolute Error Today's High: 5.74 degrees

Yesterday's High: 8.01 degrees

Last Year's High: 10.87 degrees Can we beat that?

Create The Genome genome = GTree.GTreeGP() genome.setParams(max_depth=4, method="ramped") genome.evaluator.set(eval_func)

Initialize The Engine ga = GSimpleGA.GSimpleGA(genome) ga.setParams(gp_terminals = ['per', 'perlast', 'clm'], gp_function_prefix = "gp") ga.setMinimax(Consts.minimaxType["minimize"]) ga.setGenerations(50) ga.setCrossoverRate(1.0) ga.setMutationRate(0.25) ga.setPopulationSize(800)

Define The Fitness Function def eval_func(chromosome): code_comp = chromosome.getCompiledCode() error = 0.0 count = 0.0 for day,per,peryest,perlast,clm,actual in data: forecast = eval(code_comp) error += abs(forecast-actual) count += 1 return error/count

Define The Operators @GTree.gpdec(representation="+", color="red") def gp_add(a, b): return a+b @GTree.gpdec(representation="-", color="red") def gp_sub(a, b): return a-b @GTree.gpdec(representation="avg", color="green") def gp_avg(a, b): return (a+b)/2.0 @GTree.gpdec(representation="if_gt", color="blue") def gp_gt(a, b, c, d): if a>b: return c else: return d

Run ga = GSimpleGA.GSimpleGA(genome) ga.setParams(gp_terminals = ['per','perlast','clm'], gp_function_prefix = "gp") ga.setMinimax(Consts.minimaxType["minimize"]) ga.setGenerations(50) ga.setCrossoverRate(1.0) ga.setMutationRate(0.25) ga.setPopulationSize(800) ga.evolve(freq_stats=10) best = ga.bestIndividual() print best

Interactive Mode ga.setInteractiveGeneration(50) >>> it.plotHistPopScore(population) >>> it.plotPopScore(population) >>> popScores = it.getPopScores(population)

GP Tree Graphs Gtree.GTreeGP.writePopulationDot(gp, filename, "png", 0, 1) best = ga.bestIndividual() best.writeDotImage("best.png")

Callbacks def step_callback(gp_engine): gen = gp_engine.getCurrentGeneration() if gen % 10 == 0: filename = "best_{gen}.png".format(gen=gen) GTree.GTreeGP.writePopulationDot(gp_engine, filename, "png", 0, 1) ga.stepCallback.set(step_callback)

Database Adapters csv_adapter = DBAdapters.DBFileCSV(identify="run1", filename="stats.csv") ga.setDBAdapter(csv_adapter) ga.evolve(freq_stats=10) print ga.getStatistics() - Statistics Minimum raw score = 7.35 Fitness average = 16.43 Minimum fitness = 16.32 Raw scores variance = 1352.22 Standard deviation of raw scores = 36.77 Average of raw scores = 16.43 Maximum fitness = 19.72 Maximum raw score = 295.57

Real-Time Plots adapter = DBAdapters.DBVPythonGraph(identify="run_01", frequency = 1) ga.setDBAdapter(adapter)

Genetic Programming in Python

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