Creating Types¶

This tutorial shows how types are created using the creator and initialized using the toolbox.

Fitness¶

The provided Fitness class is an abstract class that needs a weights attribute in order to be functional. A minimizing fitness is built using negatives weights, while a maximizing fitness has positive weights. For example, the following line creates, in the creator, a ready to use single objective minimizing fitness named FitnessMin.

creator.create("FitnessMin", base.Fitness, weights=(-1.0,))

The create() function takes at least two arguments, a name for the newly created class and a base class. Any subsequent argument becomes an attribute of the class. As specified in the Fitness documentation, the weights attribute must be a tuple so that multi-objective and single objective fitnesses can be treated the same way. A FitnessMulti would be created the same way but using:

creator.create("FitnessMulti", base.Fitness, weights=(-1.0, 1.0))

This code produces a fitness that minimizes the first objective and maximize the second one. The weights can also be used to vary the importance of each objective one against another. This means that the weights can be any real number and only the sign is used to determine if a maximization or minimization is done. An example of where the weights can be useful is in the crowding distance sort made in the NSGA-II selection algorithm.

Individual¶

Simply by thinking about the different flavors of evolutionary algorithms (GA, GP, ES, PSO, DE, …), we notice that an extremely large variety of individuals are possible, reinforcing the assumption that all types cannot be made available by developers. Here is a guide on how to create some of those individuals using the creator and initializing them using a Toolbox.

Warning

Before inheriting from numpy.ndarray you should absolutely read the Inheriting from Numpy tutorial and have a look at the One Max Problem: Using Numpy example!

List of Floats¶

The first individual created will be a simple list containing floats. In order to produce this kind of individual, we need to create an Individual class, using the creator, that will inherit from the standard list type and have a fitness attribute.

import random

from deap import base
from deap import creator
from deap import tools

creator.create("FitnessMax", base.Fitness, weights=(1.0,))
creator.create("Individual", list, fitness=creator.FitnessMax)

IND_SIZE=10

toolbox = base.Toolbox()
toolbox.register("attr_float", random.random)
toolbox.register("individual", tools.initRepeat, creator.Individual,
                 toolbox.attr_float, n=IND_SIZE)

The newly introduced register() method takes at least two arguments; an alias and a function assigned to this alias. Any subsequent argument is passed to the function when called (à la functools.partial()). Thus, the preceding code creates two aliases in the toolbox; attr_float and individual. The first one redirects to the random.random() function. The second one is a shortcut to the initRepeat() function, fixing its container argument to the creator.Individual class, its func argument to the toolbox.attr_float() function, and its number of repetitions argument to IND_SIZE.

Now, calling toolbox.individual() will call initRepeat() with the fixed arguments and return a complete creator.Individual composed of IND_SIZE floating point numbers with a maximizing single objective fitness attribute.

Variations of this type are possible by inheriting from array.array or numpy.ndarray as following.

creator.create("Individual", array.array, typecode="d", fitness=creator.FitnessMax)
creator.create("Individual", numpy.ndarray, fitness=creator.FitnessMax)

Type inheriting from arrays needs a typecode on initialization, just as the original class.

Permutation¶

An individual for the permutation representation is almost similar to the general list individual. In fact they both inherit from the basic list type. The only difference is that instead of filling the list with a series of floats, we need to generate a random permutation and provide that permutation to the individual.

import random

from deap import base
from deap import creator
from deap import tools

creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", list, fitness=creator.FitnessMin)

IND_SIZE=10

toolbox = base.Toolbox()
toolbox.register("indices", random.sample, range(IND_SIZE), IND_SIZE)
toolbox.register("individual", tools.initIterate, creator.Individual,
                 toolbox.indices)

The first registered function indices redirects to the random.sample() function with its arguments fixed to sample IND_SIZE numbers from the given range. The second registered function individual is a shortcut to the initIterate() function, with its container argument set to the creator.Individual class and its generator argument to the toolbox.indices() alias.

Calling toolbox.individual() will call initIterate() with the fixed arguments and return a complete creator.Individual composed of a permutation with a minimizing single objective fitness attribute.

Arithmetic Expression¶

The next individual that is commonly used is a prefix tree of mathematical expressions. This time, a PrimitiveSet must be defined containing all possible mathematical operators that our individual can use. Here, the set is called MAIN and has a single variable defined by the arity. Operators add(), sub(), and mul() are added to the primitive set with each an arity of 2. Next, the Individual class is created as before with the addition of a static attribute pset to remember the global primitive set. This time, the content of the individuals will be generated by the genHalfAndHalf() function that generates trees in a list format based on a ramped procedure. Once again, the individual is initialized using the initIterate() function to give the complete generated iterable to the individual class.

import operator

from deap import base
from deap import creator
from deap import gp
from deap import tools

pset = gp.PrimitiveSet("MAIN", arity=1)
pset.addPrimitive(operator.add, 2)
pset.addPrimitive(operator.sub, 2)
pset.addPrimitive(operator.mul, 2)

creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", gp.PrimitiveTree, fitness=creator.FitnessMin,
               pset=pset)

toolbox = base.Toolbox()
toolbox.register("expr", gp.genHalfAndHalf, pset=pset, min_=1, max_=2)
toolbox.register("individual", tools.initIterate, creator.Individual,
                 toolbox.expr)

Calling toolbox.individual() will readily return a complete individual that is an arithmetic expression in the form of a prefix tree with a minimizing single objective fitness attribute.

Evolution Strategy¶

Evolution strategies individuals are slightly different as they contain generally two lists, one for the actual individual and one for its mutation parameters. This time, instead of using the list base class, we will inherit from an array.array for both the individual and the strategy. Since there is no helper function to generate two different vectors in a single object, we must define this function ourselves. The initES() function receives two classes and instantiates them generating itself the random numbers in the ranges provided for individuals of a given size.

import array
import random

from deap import base
from deap import creator
from deap import tools

creator.create("FitnessMin", base.Fitness, weights=(-1.0,))
creator.create("Individual", array.array, typecode="d",
               fitness=creator.FitnessMin, strategy=None)
creator.create("Strategy", array.array, typecode="d")

def initES(icls, scls, size, imin, imax, smin, smax):
    ind = icls(random.uniform(imin, imax) for _ in range(size))
    ind.strategy = scls(random.uniform(smin, smax) for _ in range(size))
    return ind

IND_SIZE = 10
MIN_VALUE, MAX_VALUE = -5., 5.
MIN_STRAT, MAX_STRAT = -1., 1. 

toolbox = base.Toolbox()
toolbox.register("individual", initES, creator.Individual,
                 creator.Strategy, IND_SIZE, MIN_VALUE, MAX_VALUE, MIN_STRAT, 
                 MAX_STRAT)

Calling toolbox.individual() will readily return a complete evolution strategy with a strategy vector and a minimizing single objective fitness attribute.

Particle¶

A particle is another special type of individual as it usually has a speed and generally remembers its best position. This type of individual is created (once again) the same way as inheriting from a list. This time, speed, best and speed limits (smin, smax) attributes are added to the object. Again, an initialization function initParticle() is also registered to produce the individual receiving the particle class, size, domain, and speed limits as arguments.

import random

from deap import base
from deap import creator
from deap import tools

creator.create("FitnessMax", base.Fitness, weights=(1.0, 1.0))
creator.create("Particle", list, fitness=creator.FitnessMax, speed=None,
               smin=None, smax=None, best=None)

def initParticle(pcls, size, pmin, pmax, smin, smax):
    part = pcls(random.uniform(pmin, pmax) for _ in range(size))
    part.speed = [random.uniform(smin, smax) for _ in range(size)]
    part.smin = smin
    part.smax = smax
    return part

toolbox = base.Toolbox()
toolbox.register("particle", initParticle, creator.Particle, size=2,
                 pmin=-6, pmax=6, smin=-3, smax=3)

Calling toolbox.particle() will readily return a complete particle with a speed vector and a fitness attribute for maximizing two objectives.

A Funky One¶

Supposing your problem has very specific needs, it is also possible to build custom individuals very easily. The next individual created is a list of alternating integers and floating point numbers, using the initCycle() function.

import random

from deap import base
from deap import creator
from deap import tools

creator.create("FitnessMax", base.Fitness, weights=(1.0, 1.0))
creator.create("Individual", list, fitness=creator.FitnessMax)

toolbox = base.Toolbox()

INT_MIN, INT_MAX = 5, 10
FLT_MIN, FLT_MAX = -0.2, 0.8
N_CYCLES = 4

toolbox.register("attr_int", random.randint, INT_MIN, INT_MAX)
toolbox.register("attr_flt", random.uniform, FLT_MIN, FLT_MAX)
toolbox.register("individual", tools.initCycle, creator.Individual,
                 (toolbox.attr_int, toolbox.attr_flt), n=N_CYCLES)

Calling toolbox.individual() will readily return a complete individual of the form [int float int float ... int float] with a maximizing two objectives fitness attribute.

Population¶

Populations are much like individuals. Instead of being initialized with attributes, they are filled with individuals, strategies or particles.

Bag¶

A bag population is the most commonly used type. It has no particular ordering although it is generally implemented using a list. Since the bag has no particular attribute, it does not need any special class. The population is initialized using the toolbox and the initRepeat() function directly.

toolbox.register("population", tools.initRepeat, list, toolbox.individual)

Calling toolbox.population() will readily return a complete population in a list, providing a number of times the repeat helper must be repeated as an argument of the population function. The following example produces a population with 100 individuals.

toolbox.population(n=100)

Grid¶

A grid population is a special case of structured population where neighbouring individuals have a direct effect on each other. The individuals are distributed in the grid where each cell contains a single individual. However, its implementation only differs from the list of the bag population, in that it is composed of lists of individuals.

toolbox.register("row", tools.initRepeat, list, toolbox.individual, n=N_COL)
toolbox.register("population", tools.initRepeat, list, toolbox.row, n=N_ROW)

Calling toolbox.population() will readily return a complete population where the individuals are accessible using two indices, for example pop[r][c]. For the moment, there is no algorithm specialized for structured populations, we are awaiting your submissions.

Swarm¶

A swarm is used in particle swarm optimization. It is different in the sense that it contains a communication network. The simplest network is the completely connected one, where each particle knows the best position that has ever been visited by any particle. This is generally implemented by copying that global best position to a gbest attribute and the global best fitness to a gbestfit attribute.

creator.create("Swarm", list, gbest=None, gbestfit=creator.FitnessMax)
toolbox.register("swarm", tools.initRepeat, creator.Swarm, toolbox.particle)

Calling toolbox.swarm() will readily return a complete swarm. After each evaluation the gbest and gbestfit should be set by the algorithm to reflect the best found position and fitness.

Demes¶

A deme is a sub-population that is contained in a population. It is similar to an island in the island model. Demes, being only sub-populations, are in fact not different from populations, aside from their names. Here, we create a population containing 3 demes, each having a different number of individuals using the n argument of the initRepeat() function.

toolbox.register("deme", tools.initRepeat, list, toolbox.individual)

DEME_SIZES = 10, 50, 100
population = [toolbox.deme(n=i) for i in DEME_SIZES]

Seeding a Population¶

Sometimes, a first guess population can be used to initialize an evolutionary algorithm. The key idea to initialize a population with non-random individuals is to have an individual initializer that takes a content as argument.

import json

from deap import base
from deap import creator

creator.create("FitnessMax", base.Fitness, weights=(1.0, 1.0))
creator.create("Individual", list, fitness=creator.FitnessMax)

def initIndividual(icls, content):
    return icls(content)

def initPopulation(pcls, ind_init, filename):
    with open(filename, "r") as pop_file:
        contents = json.load(pop_file)
    return pcls(ind_init(c) for c in contents)

toolbox = base.Toolbox()

toolbox.register("individual_guess", initIndividual, creator.Individual)
toolbox.register("population_guess", initPopulation, list, toolbox.individual_guess, "my_guess.json")

population = toolbox.population_guess()

The population will be initialized from the file my_guess.json that shall contain a list of first guess individuals. This initialization can be combined with a regular initialization to have part random and part non-random individuals. Note that the definition of initIndividual() and the registration of individual_guess() are optional as the default constructor of a list is similar. Removing those lines leads to the following:

toolbox.register("population_guess", initPopulation, list, creator.Individual, "my_guess.json")