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Add 1D_optimization_example
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@PytLab
PytLab committed Dec 14, 2017
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Find the global minima of function $f(x) = x + 10sin(5x) + 7cos(4x)$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create individual (use binary encoding)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"from gaft.components import BinaryIndividual\n",
"indv = BinaryIndividual(ranges=[(0, 10)], eps=0.001, verbosity=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create a population with `50` individuals"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"from gaft.components import Population\n",
"population = Population(indv_template=indv, size=50).init()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create genetic operators: selection, crossover, mutation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1. Tournament selection"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"from gaft.operators import TournamentSelection\n",
"selection = TournamentSelection()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2. Uniform crossover\n",
"\n",
"- `pc` is the probabililty of crossover operation\n",
"- `pe` is the exchange probabiltiy for each possible gene bit in chromsome"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"from gaft.operators import UniformCrossover\n",
"crossover = UniformCrossover(pc=0.8, pe=0.5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3. Flip bit mutation\n",
"- `pm` is the probability of mutation"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"from gaft.operators import FlipBitMutation\n",
"mutation = FlipBitMutation(pm=0.1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Import an on-the-fly analysis plugin to output info to console"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"from gaft.analysis import ConsoleOutput"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Create an engine to run"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"from gaft import GAEngine\n",
"\n",
"engine = GAEngine(population=population, selection=selection,\n",
" crossover=crossover, mutation=mutation,\n",
" analysis=[ConsoleOutput])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Define target function to optimize\n",
"\n",
"here we try to find the global minima of $f(x) = x + 10sin(5x) + 7cos(4x)$\n",
"\n",
"***GAFT*** find the maxima of the fitness function, here we use the `engine.minimize` decorator to tell ***GAFT*** to find the minima."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"from math import sin, cos\n",
"\n",
"@engine.fitness_register\n",
"@engine.minimize\n",
"def fitness(indv):\n",
" x, = indv.solution\n",
" return x + 10*sin(5*x) + 7*cos(4*x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Run the engine"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"gaft.ConsoleOutput INFO Generation number: 50 Population number: 50\n",
"gaft.ConsoleOutput INFO Generation: 1, best fitness: 14.893, scaled fitness: 14.893\n",
"gaft.ConsoleOutput INFO Generation: 2, best fitness: 15.056, scaled fitness: 15.056\n",
"gaft.ConsoleOutput INFO Generation: 3, best fitness: 15.103, scaled fitness: 15.103\n",
"gaft.ConsoleOutput INFO Generation: 4, best fitness: 15.103, scaled fitness: 15.103\n",
"gaft.ConsoleOutput INFO Generation: 5, best fitness: 15.154, scaled fitness: 15.154\n",
"gaft.ConsoleOutput INFO Generation: 6, best fitness: 15.161, scaled fitness: 15.161\n",
"gaft.ConsoleOutput INFO Generation: 7, best fitness: 15.161, scaled fitness: 15.161\n",
"gaft.ConsoleOutput INFO Generation: 8, best fitness: 15.161, scaled fitness: 15.161\n",
"gaft.ConsoleOutput INFO Generation: 9, best fitness: 15.161, scaled fitness: 15.161\n",
"gaft.ConsoleOutput INFO Generation: 10, best fitness: 15.161, scaled fitness: 15.161\n",
"gaft.ConsoleOutput INFO Generation: 11, best fitness: 15.161, scaled fitness: 15.161\n",
"gaft.ConsoleOutput INFO Generation: 12, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 13, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 14, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 15, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 16, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 17, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 18, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 19, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 20, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 21, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 22, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 23, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 24, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 25, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 26, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 27, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 28, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 29, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 30, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 31, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 32, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 33, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 34, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 35, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 36, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 37, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 38, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 39, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 40, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 41, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 42, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 43, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 44, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 45, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 46, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 47, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 48, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 49, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Generation: 50, best fitness: 15.164, scaled fitness: 15.164\n",
"gaft.ConsoleOutput INFO Optimal solution: ([0.892333984375], 15.164338102247847)\n"
]
}
],
"source": [
"engine.run(ng=50)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## After engine running, we can something more..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Get the best individual"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"best_indv = engine.population.best_indv(engine.fitness)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Get the solution"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[0.892333984375]"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"best_indv.solution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## And the fitness value"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"15.164338102247847"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"engine.fitness(best_indv)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}

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