How to easily find the optimal solution without exhaustive search using Genetic Algorithms

Viacheslav Kakovskyi — Kyiv.py #16

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Me!@kakovskyiPython Developer at SoftServe

Recent projects:● Backend for instant messenger● Backend for embedded system for traffic analysis ● Software for personal nutrition planning

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Agenda● Cases from my experience● Terminology● Genetic Algorithms by example● Theoretical background● Genetic Algorithms in Python● Pros and cons● Tasks from real life● Summary● Further reading

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Software for personal nutrition planning● Find a set of suboptimal personal nutrition plans● Minimize difference between required macronutrients and energetic value for

suggested plan ● Genetic Algorithms used for generation of daily meals● The problem is similar to Knapsack problem

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Embedded system for traffic analysis (R&D)

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Data from camera (LPR), 2D Data from radar, 2D

Embedded system for traffic analysis (R&D) ● Find suboptimal transition matrix (4x4)● Challenge: surface relief● Maximize intersection of data from LPR and converted data from radar● Tried to use Genetic Algorithms for parametric optimization

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Math party● Function - a rule● Domain - a set of possible input values of a function● Codomain - a set of possible output values of a function● Extremum - maximum or minimum of a function for a given domain● Local extremum - an extremum of some neighbourhood of domain● Global extremum - an extremum of all domain

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Genetics party● Genotype - a set of genes of an instance● Phenotype - a set of features of an instance● Fitness-function - a function which describes adaptability of an instance● Generation defines a lifetime of instances● Population - a set of all instances which exist in the same area

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Genetics party● Selection - a stage of GA when instances are chosen from a population for

later breeding● Crossover - an operator used to vary chromosomes from one generation to

the next● Mutation - an operator used to maintain genetic diversity from one generation

of a population to the next

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Genetic Algorithms by example● Problem: find a solution of a linear Diophantine equation● The equation: 1027x + 712y = 1● D(x) = [-1 500; 1 500]● D(y) = [-1 500; 1 500]

Analytical solution:

● http://mathworld.wolfram.com/DiophantineEquation.html● http://math.stackexchange.com/a/20727

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Genetic Algorithms by example● Problem type: minimization● F(x,y) = |1027x+ 712y - 1| ● lambda x, y: abs(1027 * x + 712 * y - 1)● IND_SIZE = 4● NGEN = 100● Initial population:

(-432, 325) -> 212265(48, 1217) -> 915799(-660, 1473) -> 370955(22, 786) -> 582225

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Selection● Ordering: 212265, 370955, 582225, 915799● (48, 1217) -> 915799 is the worst adapted

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Crossover

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Crossover

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Mutation

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● Add a random integer from the range [-10, 10]● MUTPB = 0.25

Mutation

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● Add a random integer from the range [-10, 10]● MUTPB = 0.25

Selection 2

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Selection 2

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Last generation

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Flowchart

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Complexity● IND_SIZE - size of population● NGEN - number of generations● CXPB - crossover probability● MUTPB - mutation probability

Complexity ≈ IND_SIZE * NGEN * O(Fitness) * O(Selection) * (CXPB * O(Crossover) + MUTPB * O(Mutation))

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Guidelines● Define your fitness-function● Choose the problem type● Define the domain and NGEN● Define how the initial population should be chosen and IND_SIZE● Define the type of selection● Define the type of crossover● Define the type of mutation and MUTPB● Try it!● Define heuristics if needed

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Genetic Algorithms in Python● DEAP● Pyevolve● PyBrain● pygene● pyeasyga● pyneurgen● pyislands● inspyred● tinyevolver

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DEAP: Distributed Evolutionary Algorithms in Python● Batteries included● Parallelization● Genetic Programming● Works on Python 2, Python 3 and PyPy● Lots of scientific projects already use it

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DEAP by example● Problem: find a solution of a linear Diophantine equation.● The equation: 1027x+ 712y = 1● D(x) = [-1 500; 1 500]● D(y) = [-1 500; 1 500]

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DEAP by example"""The equation: 1027 * x + 712 * y = 1D(x) = [-1 500; 1 500]D(y) = [-1 500; 1 500]"""import randomimport operator

from deap import tools, base, creator, algorithms

MIN, MAX = -1500, 1500SOLUTION = [-165, 238]VARIABLES = len(SOLUTION)

MUT_MIN, MUT_MAX = -10, 10NGEN, IND_SIZE, CXPB, MUTPB, TRN_SIZE = 100, 50, 0.5, 0.25, 100HALL_SIZE = 10DEFAULT_MAIN_ARGS = NGEN, IND_SIZE, CXPB, MUTPB

BEST_INSTANCE_MSG = 'Best instance:'NO_SOLUTION_MSG = 'No solution in integers. Distance is:'

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def fitness(instance): x, y = instance return abs(1027 * x + 712 * y - 1),

def spawn_instance(): return random.randint(MIN, MAX), random.randint(MIN, MAX)

def mutate(instance, mutpb): if random.random() <= mutpb: index = random.randint(0, len(instance) - 1) instance[index] += random.randint(MUT_MIN, MUT_MAX) return instance, return instance,

def get_best_result(population): if isinstance(population[0], list): fitness_values = list(map(fitness, population)) index = fitness_values.index(min(fitness_values)) return population[index] else: return min(population, key=operator.attrgetter('fitness'))

DEAP by example

def terminate(population): if fitness(get_best_result(population)) == (0, ): raise StopIteration return False

def distance_from_best_result(population): result = get_best_result(population) return fitness(result)[0]

def output(best_instance): print(BEST_INSTANCE_MSG, best_instance) distance = fitness(best_instance) if distance: print(NO_SOLUTION_MSG, distance)

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def setup(mutpb): creator.create("FitnessMin", base.Fitness, weights=(-1,)) creator.create("Individual", list, fitness=creator.FitnessMin) toolbox = base.Toolbox() toolbox.register("attribute", random.randint, MIN, MAX) toolbox.register("individual", tools.initRepeat, creator.Individual, toolbox.attribute, n=VARIABLES) toolbox.register("population", tools.initRepeat, list, toolbox.individual) toolbox.register("mate", tools.cxOnePoint) toolbox.register("mutate", mutate, mutpb=mutpb) toolbox.register("select", tools.selBest) toolbox.register("evaluate", fitness) return toolbox

DEAP by exampledef main(ngen, ind_size, cxpb, mutpb): toolbox = setup(ind_size) population = toolbox.population(n=ind_size) stats = tools.Statistics() stats.register("best_instance_of_population", get_best_result) stats.register("distance", distance_from_best_result) stats.register("terminate", terminate) halloffame = tools.HallOfFame(HALL_SIZE) try: algorithms.eaSimple(population, toolbox, cxpb, mutpb, ngen, stats=stats, halloffame=halloffame) except StopIteration: pass finally: best_instance = halloffame[0] output(best_instance) return best_instance

if __name__ == '__main__': main(*DEFAULT_MAIN_ARGS)

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github.com/viachk/ga-example-diophantine

Crossover types

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● cxOnePoint● cxTwoPoint● cxUniform● cxPartialyMatched● cxUniformPartialyMatched● cxOrdered● cxBlend● cxESBlend● cxESTwoPoint● cxSimulatedBinary● cxSimulatedBinaryBounded● cxMessyOnePoint

Mutation types● mutGaussian● mutShuffleIndexes● mutFlipBit● mutPolynomialBounded● mutUniformInt● mutESLogNormal

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Selection types● selTournament● selRoulette● selNSGA2● selSPEA2● selRandom● selBest● selWorst● selTournamentDCD● selDoubleTournament

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Pros of Genetic Algorithms● easy in use ● lots lots of options for heuristics● can solve majority of problems (somehow)

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Cons of Genetic Algorithms

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Local vs Global extrema

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Cons of Genetic Algorithms● can't find the optimal solution● terminates after the first local extremum● computationally expensive

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Right tasks for Genetic Algorithms● parametric optimization● NP-complete problems● machine learning● bioinformatics● when you need to design a prototype, looks like a proper solution for a

hackaton

https://en.wikipedia.org/wiki/List_of_genetic_algorithm_applications (78 items)

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Wrong tasks for Genetic Algorithms● real-time processing● an accurate method of solving the problem already exists● huge amount of local extrema

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Summaries about Genetic Algorithms● easy to start● stochastic● have lots of options for heuristics● but the task should be formalized● we have batteries for them in Python● applicable in variety of real-life tasks● terminate after the first local extremum● computationally expensive● for 99% of tasks find suboptimal solution

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Next steps● Video: Genetic Algorithms by example (Eng)● Video: Genetic Algorithms by example (Ru)● Video: MIT AI class - Genetic Algorithms (Eng)● Video: Kyiv AI 2012 - Evolutionary Algorithms (Ru)● Video: Implementation of Genetic Algorithms (Ru)● Video: A Framework for Genetic Algorithms Based on Hadoop (Eng)

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Next steps● Pretty awesome book about Genetic Algorithms by Panchenko (Ru)● Articles about Genetic Algorithms (Ru)● Q&A about Genetic Algorithms (Ru)● A Framework for Genetic Algorithms Based on Hadoop (Eng)

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Next steps

Try DEAP

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Thank you!

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Viacheslav Kakovskyiviach.kakovskyi@gmail.com@kakovskyi

Evolved antenna

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