`pygad` Module¶

This section of the PyGAD’s library documentation discusses the pygad module.

Using the pygad module, instances of the genetic algorithm can be created, run, saved, and loaded.

`pygad.GA` Class¶

The first module available in PyGAD is named pygad and contains a class named GA for building the genetic algorithm. The constructor, methods, function, and attributes within the class are discussed in this section.

`init()`¶

For creating an instance of the pygad.GA class, the constructor accepts several parameters that allow the user to customize the genetic algorithm to different types of applications.

The pygad.GA class constructor supports the following parameters:

num_generations: Number of generations.
num_parents_mating: Number of solutions to be selected as parents.
fitness_func: Accepts a function that must accept 2 parameters (a single solution and its index in the population) and return the fitness value of the solution. Available starting from PyGAD 1.0.17 until 1.0.20 with a single parameter representing the solution. Changed in PyGAD 2.0.0 and higher to include a second parameter representing the solution index. Check the Preparing the ``fitness_func`` Parameter section for information about creating such a function.
initial_population: A user-defined initial population. It is useful when the user wants to start the generations with a custom initial population. It defaults to None which means no initial population is specified by the user. In this case, PyGAD creates an initial population using the sol_per_pop and num_genes parameters. An exception is raised if the initial_population is None while any of the 2 parameters (sol_per_pop or num_genes) is also None. Introduced in PyGAD 2.0.0 and higher.
sol_per_pop: Number of solutions (i.e. chromosomes) within the population. This parameter has no action if initial_population parameter exists.
num_genes: Number of genes in the solution/chromosome. This parameter is not needed if the user feeds the initial population to the initial_population parameter.
gene_type=float: Controls the gene type. It has an effect only when the parameter gene_space is None (which is its default value). Starting from PyGAD 2.9.0, the gene_type parameter can be assigned to a numeric value of any of these types: int, float, and numpy.int/uint/float(8-64).
init_range_low=-4: The lower value of the random range from which the gene values in the initial population are selected. init_range_low defaults to -4. Available in PyGAD 1.0.20 and higher. This parameter has no action if the initial_population parameter exists.
init_range_high=4: The upper value of the random range from which the gene values in the initial population are selected. init_range_high defaults to +4. Available in PyGAD 1.0.20 and higher. This parameter has no action if the initial_population parameter exists.
parent_selection_type="sss": The parent selection type. Supported types are sss (for steady-state selection), rws (for roulette wheel selection), sus (for stochastic universal selection), rank (for rank selection), random (for random selection), and tournament (for tournament selection).
keep_parents=-1: Number of parents to keep in the current population. -1 (default) means to keep all parents in the next population. 0 means keep no parents in the next population. A value greater than 0 means keeps the specified number of parents in the next population. Note that the value assigned to keep_parents cannot be < - 1 or greater than the number of solutions within the population sol_per_pop.
K_tournament=3: In case that the parent selection type is tournament, the K_tournament specifies the number of parents participating in the tournament selection. It defaults to 3.
crossover_type="single_point": Type of the crossover operation. Supported types are single_point (for single-point crossover), two_points (for two points crossover), uniform (for uniform crossover), and scattered (for scattered crossover). Scattered crossover is supported from PyGAD 2.9.0 and higher. It defaults to single_point. Starting from PyGAD 2.2.2 and higher, if crossover_type=None, then the crossover step is bypassed which means no crossover is applied and thus no offspring will be created in the next generations. The next generation will use the solutions in the current population.
crossover_probability=None: The probability of selecting a parent for applying the crossover operation. Its value must be between 0.0 and 1.0 inclusive. For each parent, a random value between 0.0 and 1.0 is generated. If this random value is less than or equal to the value assigned to the crossover_probability parameter, then the parent is selected. Added in PyGAD 2.5.0 and higher.
mutation_type="random": Type of the mutation operation. Supported types are random (for random mutation), swap (for swap mutation), inversion (for inversion mutation), scramble (for scramble mutation), and adaptive (for adaptive mutation). It defaults to random. Starting from PyGAD 2.2.2 and higher, if mutation_type=None, then the mutation step is bypassed which means no mutation is applied and thus no changes are applied to the offspring created using the crossover operation. The offspring will be used unchanged in the next generation. Adaptive mutation is supported starting from PyGAD 2.10.0. For more information about adaptive mutation, go the the Adaptive Mutation section. For example about using adaptive mutation, check the Use Adaptive Mutation in PyGAD section.
mutation_probability=None: The probability of selecting a gene for applying the mutation operation. Its value must be between 0.0 and 1.0 inclusive. For each gene in a solution, a random value between 0.0 and 1.0 is generated. If this random value is less than or equal to the value assigned to the mutation_probability parameter, then the gene is selected. If this parameter exists, then there is no need for the 2 parameters mutation_percent_genes and mutation_num_genes. Added in PyGAD 2.5.0 and higher.
mutation_by_replacement=False: An optional bool parameter. It works only when the selected type of mutation is random (mutation_type="random"). In this case, mutation_by_replacement=True means replace the gene by the randomly generated value. If False, then it has no effect and random mutation works by adding the random value to the gene. Supported in PyGAD 2.2.2 and higher. Check the changes in PyGAD 2.2.2 under the Release History section for an example.
mutation_percent_genes="default": Percentage of genes to mutate. It defaults to the string "default" which is later translated into the integer 10 which means 10% of the genes will be mutated. It must be >0 and <=100. Out of this percentage, the number of genes to mutate is deduced which is assigned to the mutation_num_genes parameter. The mutation_percent_genes parameter has no action if mutation_probability or mutation_num_genes exist. Starting from PyGAD 2.2.2 and higher, this parameter has no action if mutation_type is None.
mutation_num_genes=None: Number of genes to mutate which defaults to None meaning that no number is specified. The mutation_num_genes parameter has no action if the parameter mutation_probability exists. Starting from PyGAD 2.2.2 and higher, this parameter has no action if mutation_type is None.
random_mutation_min_val=-1.0: For random mutation, the random_mutation_min_val parameter specifies the start value of the range from which a random value is selected to be added to the gene. It defaults to -1. Starting from PyGAD 2.2.2 and higher, this parameter has no action if mutation_type is None.
random_mutation_max_val=1.0: For random mutation, the random_mutation_max_val parameter specifies the end value of the range from which a random value is selected to be added to the gene. It defaults to +1. Starting from PyGAD 2.2.2 and higher, this parameter has no action if mutation_type is None.
gene_space=None: It is used to specify the possible values for each gene in case the user wants to restrict the gene values. It is useful if the gene space is restricted to a certain range or to discrete values. It accepts a list, tuple, range, or numpy.ndarray. When all genes have the same global space, specify their values as a list/tuple/range/numpy.ndarray. For example, gene_space = [0.3, 5.2, -4, 8] restricts the gene values to the 4 specified values. If each gene has its own space, then the gene_space parameter can be nested like [[0.4, -5], [0.5, -3.2, 8.2, -9], ...] where the first sublist determines the values for the first gene, the second sublist for the second gene, and so on. If the nested list/tuple has a None value, then the gene’s initial value is selected randomly from the range specified by the 2 parameters init_range_low and init_range_high and its mutation value is selected randomly from the range specified by the 2 parameters random_mutation_min_val and random_mutation_max_val. gene_space is added in PyGAD 2.5.0. Check the Release History section of the documentation for more details. In PyGAD 2.9.0, NumPy arrays can be assigned to the gene_space parameter.
on_start=None: Accepts a function to be called only once before the genetic algorithm starts its evolution. This function must accept a single parameter representing the instance of the genetic algorithm. Added in PyGAD 2.6.0.
on_fitness=None: Accepts a function to be called after calculating the fitness values of all solutions in the population. This function must accept 2 parameters: the first one represents the instance of the genetic algorithm and the second one is a list of all solutions’ fitness values. Added in PyGAD 2.6.0.
on_parents=None: Accepts a function to be called after selecting the parents that mates. This function must accept 2 parameters: the first one represents the instance of the genetic algorithm and the second one represents the selected parents. Added in PyGAD 2.6.0.
on_crossover=None: Accepts a function to be called each time the crossover operation is applied. This function must accept 2 parameters: the first one represents the instance of the genetic algorithm and the second one represents the offspring generated using crossover. Added in PyGAD 2.6.0.
on_mutation=None: Accepts a function to be called each time the mutation operation is applied. This function must accept 2 parameters: the first one represents the instance of the genetic algorithm and the second one represents the offspring after applying the mutation. Added in PyGAD 2.6.0.
callback_generation=None: Accepts a function to be called after each generation. This function must accept a single parameter representing the instance of the genetic algorithm. Supported in PyGAD 2.0.0 and higher. In PyGAD 2.4.0, if this function returned the string stop, then the run() method stops at the current generation without completing the remaining generations. Check the Release History section of the documentation for an example. Starting from PyGAD 2.6.0, the callback_generation parameter is deprecated and should be replaced by the on_generation parameter. The callback_generation parameter will be removed in a later version.
on_generation=None: Accepts a function to be called after each generation. This function must accept a single parameter representing the instance of the genetic algorithm. If the function returned the string stop, then the run() method stops without completing the other generations. Added in PyGAD 2.6.0.
on_stop=None: Accepts a function to be called only once exactly before the genetic algorithm stops or when it completes all the generations. This function must accept 2 parameters: the first one represents the instance of the genetic algorithm and the second one is a list of fitness values of the last population’s solutions. Added in PyGAD 2.6.0.
delay_after_gen=0.0: It accepts a non-negative number specifying the time in seconds to wait after a generation completes and before going to the next generation. It defaults to 0.0 which means no delay after the generation. Available in PyGAD 2.4.0 and higher.
save_best_solutions=False: When True, then the best solution after each generation is saved into an attribute named best_solutions. If False (default), then no solutions are saved and the best_solutions attribute will be empty. Supported in PyGAD 2.9.0.
suppress_warnings=False: A bool parameter to control whether the warning messages are printed or not. It defaults to False.

The user doesn’t have to specify all of such parameters while creating an instance of the GA class. A very important parameter you must care about is fitness_func which defines the fitness function.

It is OK to set the value of any of the 2 parameters init_range_low and init_range_high to be equal, higher, or lower than the other parameter (i.e. init_range_low is not needed to be lower than init_range_high). The same holds for the random_mutation_min_val and random_mutation_max_val parameters.

If the 2 parameters mutation_type and crossover_type are None, this disables any type of evolution the genetic algorithm can make. As a result, the genetic algorithm cannot find a better solution that the best solution in the initial population.

The parameters are validated within the constructor. If at least a parameter is not validated, an exception is thrown.

Other Instance Attributes & Methods¶

All the parameters and functions passed to the pygad.GA class constructor are used as attributes and methods in the instances of the pygad.GA class. In addition to such attributes, there are other attributes and methods added to the instances of the pygad.GA class:

The next 2 subsections list such attributes and methods.

Other Attributes¶

generations_completed: Holds the number of the last completed generation.
population: A NumPy array holding the initial population.
valid_parameters: Set to True when all the parameters passed in the GA class constructor are valid.
run_completed: Set to True only after the run() method completes gracefully.
pop_size: The population size.
best_solutions_fitness: A list holding the fitness values of the best solutions for all generations.
best_solution_generation: The generation number at which the best fitness value is reached. It is only assigned the generation number after the run() method completes. Otherwise, its value is -1.
best_solutions: A NumPy array holding the best solution per each generation. It only exists when the save_best_solutions parameter in the pygad.GA class constructor is set to True.

Other Methods¶

cal_pop_fitness: A method that calculates the fitness values for all solutions within the population by calling the function passed to the fitness_func parameter for each solution.
crossover: Refers to the method that applies the crossover operator based on the selected type of crossover in the crossover_type property.
mutation: Refers to the method that applies the mutation operator based on the selected type of mutation in the mutation_type property.
select_parents: Refers to a method that selects the parents based on the parent selection type specified in the parent_selection_type attribute.
adaptive_mutation_population_fitness: Returns the average fitness value used in the adaptive mutation to filter the solutions.

The next sections discuss the methods available in the pygad.GA class.

`initialize_population()`¶

It creates an initial population randomly as a NumPy array. The array is saved in the instance attribute named population.

Accepts the following parameters:

low: The lower value of the random range from which the gene values in the initial population are selected. It defaults to -4. Available in PyGAD 1.0.20 and higher.
high: The upper value of the random range from which the gene values in the initial population are selected. It defaults to -4. Available in PyGAD 1.0.20.

This method assigns the values of the following 3 instance attributes:

pop_size: Size of the population.
population: Initially, it holds the initial population and later updated after each generation.
initial_population: Keeping the initial population.

`cal_pop_fitness()`¶

Calculating the fitness values of all solutions in the current population.

It works by iterating through the solutions and calling the function assigned to the fitness_func parameter in the pygad.GA class constructor for each solution.

It returns an array of the solutions’ fitness values.

`run()`¶

Runs the genetic algorithm. This is the main method in which the genetic algorithm is evolved through some generations. It accepts no parameters as it uses the instance to access all of its requirements.

For each generation, the fitness values of all solutions within the population are calculated according to the cal_pop_fitness() method which internally just calls the function assigned to the fitness_func parameter in the pygad.GA class constructor for each solution.

According to the fitness values of all solutions, the parents are selected using the select_parents() method. This method behavior is determined according to the parent selection type in the parent_selection_type parameter in the pygad.GA class constructor

Based on the selected parents, offspring are generated by applying the crossover and mutation operations using the crossover() and mutation() methods. The behavior of such 2 methods is defined according to the crossover_type and mutation_type parameters in the pygad.GA class constructor.

After the generation completes, the following takes place:

The population attribute is updated by the new population.
The generations_completed attribute is assigned by the number of the last completed generation.
If there is a callback function assigned to the callback_generation attribute, then it will be called.

After the run() method completes, the following takes place:

The best_solution_generation is assigned the generation number at which the best fitness value is reached.
The run_completed attribute is set to True.

Parent Selection Methods¶

The pygad.GA class has several methods for selecting the parents that will mate to produce the offspring. All of such methods accept the same parameters which are:

fitness: The fitness values of the solutions in the current population.
num_parents: The number of parents to be selected.

All of such methods return an array of the selected parents.

The next subsections list the supported methods for parent selection.

`steady_state_selection()`¶

Selects the parents using the steady-state selection technique.

`rank_selection()`¶

Selects the parents using the rank selection technique.

`random_selection()`¶

Selects the parents randomly.

`tournament_selection()`¶

Selects the parents using the tournament selection technique.

`roulette_wheel_selection()`¶

Selects the parents using the roulette wheel selection technique.

`stochastic_universal_selection()`¶

Selects the parents using the stochastic universal selection technique.

Crossover Methods¶

The pygad.GA class supports several methods for applying crossover between the selected parents. All of these methods accept the same parameters which are:

parents: The parents to mate for producing the offspring.
offspring_size: The size of the offspring to produce.

All of such methods return an array of the produced offspring.

The next subsections list the supported methods for crossover.

`single_point_crossover()`¶

Applies the single-point crossover. It selects a point randomly at which crossover takes place between the pairs of parents.

`two_points_crossover()`¶

Applies the 2 points crossover. It selects the 2 points randomly at which crossover takes place between the pairs of parents.

`uniform_crossover()`¶

Applies the uniform crossover. For each gene, a parent out of the 2 mating parents is selected randomly and the gene is copied from it.

`scattered_crossover()`¶

Applies the scattered crossover. It randomly selects the gene from one of the 2 parents.

Mutation Methods¶

The pygad.GA class supports several methods for applying mutation. All of these methods accept the same parameter which is:

offspring: The offspring to mutate.

All of such methods return an array of the mutated offspring.

The next subsections list the supported methods for mutation.

`random_mutation()`¶

Applies the random mutation which changes the values of some genes randomly. The number of genes is specified according to either the mutation_num_genes or the mutation_percent_genes attributes.

For each gene, a random value is selected according to the range specified by the 2 attributes random_mutation_min_val and random_mutation_max_val. The random value is added to the selected gene.

`swap_mutation()`¶

Applies the swap mutation which interchanges the values of 2 randomly selected genes.

`inversion_mutation()`¶

Applies the inversion mutation which selects a subset of genes and inverts them.

`scramble_mutation()`¶

Applies the scramble mutation which selects a subset of genes and shuffles their order randomly.

`adaptive_mutation()`¶

Applies the adaptive mutation which selects a subset of genes and shuffles their order randomly.

`best_solution()`¶

Returns information about the best solution found by the genetic algorithm.

It accepts the following parameters:

pop_fitness=None: An optional parameter that accepts a list of the fitness values of the solutions in the population. If None, then the cal_pop_fitness() method is called to calculate the fitness values of the population.

It returns the following:

best_solution: Best solution in the current population.
best_solution_fitness: Fitness value of the best solution.
best_match_idx: Index of the best solution in the current population.

`plot_result()`¶

Creates and shows a plot that summarizes how the fitness value evolved by generation. It can only be called after completing at least 1 generation.

If no generation is completed (at least 1), an exception is raised.

In PyGAD 2.3.0 and higher, this function accepts 3 optional parameters:

title: Title of the figure.
xlabel: X-axis label.
ylabel: Y-axis label.

Starting from PyGAD 2.5.0, a new optional parameter named linewidth is added to specify the width of the curve in the plot. It defaults to 3.0.

`save()`¶

Saves the genetic algorithm instance

Accepts the following parameter:

filename: Name of the file to save the instance. No extension is needed.

Functions in `pygad`¶

Besides the methods available in the pygad.GA class, this section discusses the functions available in pygad. Up to this time, there is only a single function named load().

`pygad.load()`¶

Reads a saved instance of the genetic algorithm. This is not a method but a function that is indented under the pygad module. So, it could be called by the pygad module as follows: pygad.load(filename).

Accepts the following parameter:

filename: Name of the file holding the saved instance of the genetic algorithm. No extension is needed.

Returns the genetic algorithm instance.

Steps to Use `pygad`¶

To use the pygad module, here is a summary of the required steps:

Preparing the fitness_func parameter.
Preparing Other Parameters.
Import pygad.
Create an Instance of the pygad.GA Class.
Run the Genetic Algorithm.
Plotting Results.
Information about the Best Solution.
Saving & Loading the Results.

Let’s discuss how to do each of these steps.

Preparing the `fitness_func` Parameter¶

Even there are some steps in the genetic algorithm pipeline that can work the same regardless of the problem being solved, one critical step is the calculation of the fitness value. There is no unique way of calculating the fitness value and it changes from one problem to another.

On ``15 April 2020``, a new argument named fitness_func is added to PyGAD 1.0.17 that allows the user to specify a custom function to be used as a fitness function. This function must be a maximization function so that a solution with a high fitness value returned is selected compared to a solution with a low value. Doing that allows the user to freely use PyGAD to solve any problem by passing the appropriate fitness function. It is very important to understand the problem well for creating this function.

Let’s discuss an example:

Given the following function:

y = f(w1:w6) = w1x1 + w2x2 + w3x3 + w4x4 + w5x5 + 6wx6

where (x1,x2,x3,x4,x5,x6)=(4,-2,3.5,5,-11,-4.7) and y=44

What are the best values for the 6 weights (w1 to w6)? We are going to use the genetic algorithm to optimize this function.

So, the task is about using the genetic algorithm to find the best values for the 6 weight W1 to W6. Thinking of the problem, it is clear that the best solution is that returning an output that is close to the desired output y=44. So, the fitness function should return a value that gets higher when the solution’s output is closer to y=44. Here is a function that does that:

function_inputs = [4,-2,3.5,5,-11,-4.7] # Function inputs.
desired_output = 44 # Function output.

def fitness_func(solution, solution_idx):
    output = numpy.sum(solution*function_inputs)
    fitness = 1.0 / numpy.abs(output - desired_output)
    return fitness

Such a user-defined function must accept 2 parameters:

1D vector representing a single solution. Introduced in PyGAD 1.0.17 and higher.
Solution index within the population. Introduced in PyGAD 2.0.0 and higher.

The __code__ object is used to check if this function accepts the required number of parameters. If more or fewer parameters are passed, an exception is thrown.

By creating this function, you almost did an awesome step towards using PyGAD.

Preparing Other Parameters¶

Here is an example for preparing the other parameters:

num_generations = 50
num_parents_mating = 4

fitness_function = fitness_func

sol_per_pop = 8
num_genes = len(function_inputs)

init_range_low = -2
init_range_high = 5

parent_selection_type = "sss"
keep_parents = 1

crossover_type = "single_point"

mutation_type = "random"
mutation_percent_genes = 10

The `callback_generation` Parameter¶

This parameter should be replaced by on_generation. The callback_generation parameter will be removed in a later release of PyGAD.

In PyGAD 2.0.0 and higher, an optional parameter named callback_generation is supported which allows the user to call a function (with a single parameter) after each generation. Here is a simple function that just prints the current generation number and the fitness value of the best solution in the current generation. The generations_completed attribute of the GA class returns the number of the last completed generation.

def callback_gen(ga_instance):
    print("Generation : ", ga_instance.generations_completed)
    print("Fitness of the best solution :", ga_instance.best_solution()[1])

After being defined, the function is assigned to the callback_generation parameter of the GA class constructor. By doing that, the callback_gen() function will be called after each generation.

ga_instance = pygad.GA(...,
                       callback_generation=callback_gen,
                       ...)

After the parameters are prepared, we can import PyGAD and build an instance of the pygad.GA class.

Import the `pygad`¶

The next step is to import PyGAD as follows:

import pygad

The pygad.GA class holds the implementation of all methods for running the genetic algorithm.

Create an Instance of the `pygad.GA` Class¶

The pygad.GA class is instantiated where the previously prepared parameters are fed to its constructor. The constructor is responsible for creating the initial population.

ga_instance = pygad.GA(num_generations=num_generations,
                       num_parents_mating=num_parents_mating,
                       fitness_func=fitness_function,
                       sol_per_pop=sol_per_pop,
                       num_genes=num_genes,
                       init_range_low=init_range_low,
                       init_range_high=init_range_high,
                       parent_selection_type=parent_selection_type,
                       keep_parents=keep_parents,
                       crossover_type=crossover_type,
                       mutation_type=mutation_type,
                       mutation_percent_genes=mutation_percent_genes)

Run the Genetic Algorithm¶

After an instance of the pygad.GA class is created, the next step is to call the run() method as follows:

ga_instance.run()

Inside this method, the genetic algorithm evolves over some generations by doing the following tasks:

Calculating the fitness values of the solutions within the current population.
Select the best solutions as parents in the mating pool.
Apply the crossover & mutation operation
Repeat the process for the specified number of generations.

Plotting Results¶

There is a method named plot_result() which creates a figure summarizing how the fitness values of the solutions change with the generations.

ga_instance.plot_result()

Information about the Best Solution¶

The following information about the best solution in the last population is returned using the best_solution() method.

Solution
Fitness value of the solution
Index of the solution within the population

solution, solution_fitness, solution_idx = ga_instance.best_solution()
print("Parameters of the best solution : {solution}".format(solution=solution))
print("Fitness value of the best solution = {solution_fitness}".format(solution_fitness=solution_fitness))
print("Index of the best solution : {solution_idx}".format(solution_idx=solution_idx))

Using the best_solution_generation attribute of the instance from the pygad.GA class, the generation number at which the best fitness is reached could be fetched.

if ga_instance.best_solution_generation != -1:
    print("Best fitness value reached after {best_solution_generation} generations.".format(best_solution_generation=ga_instance.best_solution_generation))

Saving & Loading the Results¶

After the run() method completes, it is possible to save the current instance of the genetic algorithm to avoid losing the progress made. The save() method is available for that purpose. Just pass the file name to it without an extension. According to the next code, a file named genetic.pkl will be created and saved in the current directory.

filename = 'genetic'
ga_instance.save(filename=filename)

You can also load the saved model using the load() function and continue using it. For example, you might run the genetic algorithm for some generations, save its current state using the save() method, load the model using the load() function, and then call the run() method again.

loaded_ga_instance = pygad.load(filename=filename)

After the instance is loaded, you can use it to run any method or access any property.

print(loaded_ga_instance.best_solution())

Crossover, Mutation, and Parent Selection¶

PyGAD supports different types for selecting the parents and applying the crossover & mutation operators. More features will be added in the future. To ask for a new feature, please check the Ask for Feature section.

Supported Crossover Operations¶

The supported crossover operations at this time are:

Single point: Implemented using the single_point_crossover() method.
Two points: Implemented using the two_points_crossover() method.
Uniform: Implemented using the uniform_crossover() method.

Supported Mutation Operations¶

The supported mutation operations at this time are:

Random: Implemented using the random_mutation() method.
Swap: Implemented using the swap_mutation() method.
Inversion: Implemented using the inversion_mutation() method.
Scramble: Implemented using the scramble_mutation() method.

Supported Parent Selection Operations¶

The supported parent selection techniques at this time are:

Steady-state: Implemented using the steady_state_selection() method.
Roulette wheel: Implemented using the roulette_wheel_selection() method.
Stochastic universal: Implemented using the stochastic_universal_selection()method.
Rank: Implemented using the rank_selection() method.
Random: Implemented using the random_selection() method.
Tournament: Implemented using the tournament_selection() method.

Life Cycle of PyGAD¶

The next figure lists the different stages in the lifecycle of an instance of the pygad.GA class. Note that PyGAD stops when either all generations are completed or when the function passed to the on_generation parameter returns the string stop.

The next code implements all the callback functions to trace the execution of the genetic algorithm. Each callback function prints its name.

import pygad
import numpy

function_inputs = [4,-2,3.5,5,-11,-4.7]
desired_output = 44

def fitness_func(solution, solution_idx):
    output = numpy.sum(solution*function_inputs)
    fitness = 1.0 / (numpy.abs(output - desired_output) + 0.000001)
    return fitness

fitness_function = fitness_func

def on_start(ga_instance):
    print("on_start()")

def on_fitness(ga_instance, population_fitness):
    print("on_fitness()")

def on_parents(ga_instance, selected_parents):
    print("on_parents()")

def on_crossover(ga_instance, offspring_crossover):
    print("on_crossover()")

def on_mutation(ga_instance, offspring_mutation):
    print("on_mutation()")

def on_generation(ga_instance):
    print("on_generation()")

def on_stop(ga_instance, last_population_fitness):
    print("on_stop()")

ga_instance = pygad.GA(num_generations=3,
                       num_parents_mating=5,
                       fitness_func=fitness_function,
                       sol_per_pop=10,
                       num_genes=len(function_inputs),
                       on_start=on_start,
                       on_fitness=on_fitness,
                       on_parents=on_parents,
                       on_crossover=on_crossover,
                       on_mutation=on_mutation,
                       on_generation=on_generation,
                       on_stop=on_stop)

ga_instance.run()

Based on the used 3 generations as assigned to the num_generations argument, here is the output.

on_start()

on_fitness()
on_parents()
on_crossover()
on_mutation()
on_generation()

on_fitness()
on_parents()
on_crossover()
on_mutation()
on_generation()

on_fitness()
on_parents()
on_crossover()
on_mutation()
on_generation()

on_stop()

Adaptive Mutation¶

In the regular genetic algorithm, the mutation works by selecting a single fixed mutation rate for all solutions regardless of their fitness values. So, regardless on whether this solution has high or low quality, the same number of genes are mutated all the time.

The pitfalls of using a constant mutation rate for all solutions are summarized in this paper Libelli, S. Marsili, and P. Alba. “Adaptive mutation in genetic algorithms.” Soft computing 4.2 (2000): 76-80 as follows:

The weak point of “classical” GAs is the total randomness of mutation, which is applied equally to all chromosomes, irrespective of their fitness. Thus a very good chromosome is equally likely to be disrupted by mutation as a bad one.

On the other hand, bad chromosomes are less likely to produce good ones through crossover, because of their lack of building blocks, until they remain unchanged. They would benefit the most from mutation and could be used to spread throughout the parameter space to increase the search thoroughness. So there are two conflicting needs in determining the best probability of mutation.

Usually, a reasonable compromise in the case of a constant mutation is to keep the probability low to avoid disruption of good chromosomes, but this would prevent a high mutation rate of low-fitness chromosomes. Thus a constant probability of mutation would probably miss both goals and result in a slow improvement of the population.

According to Libelli, S. Marsili, and P. Alba. work, the adaptive mutation solves the problems of constant mutation.

Adaptive mutation works as follows:

Calculate the average fitness value of the population (f_avg).
For each chromosome, calculate its fitness value (f).
If f<f_avg, then this solution is regarded as a low-quality solution and thus the mutation rate should be kept high because this would increase the quality of this solution.
If f>f_avg, then this solution is regarded as a high-quality solution and thus the mutation rate should be kept low to avoid disrupting this high quality solution.

In PyGAD, if f=f_avg, then the solution is regarded of high quality.

The next figure summarizes the previous steps.

This strategy is applied in PyGAD.

Use Adaptive Mutation in PyGAD¶

In PyGAD 2.10.0, adaptive mutation is supported. To use it, just follow the following 2 simple steps:

In the constructor of the pygad.GA class, set mutation_type="adaptive" to specify that the type of mutation is adaptive.
Specify the mutation rates for the low and high quality solutions using one of these 3 parameters according to your preference: mutation_probability, mutation_num_genes, and mutation_percent_genes. Please check the documentation of each of these parameters for more information.

When adaptive mutation is used, then the value assigned to any of the 3 parameters can be of any of these data types:

list
tuple
numpy.ndarray

Whatever the data type used, the length of the list, tuple, or the numpy.ndarray must be exactly 2. That is there are just 2 values:

The first value is the mutation rate for the low-quality solutions.
The second value is the mutation rate for the low-quality solutions.

PyGAD expects that the first value is higher than the second value and thus a warning is printed in case the first value is lower than the second one.

Here are some examples to feed the mutation rates:

# mutation_probability
mutation_probability = [0.25, 0.1]
mutation_probability = (0.35, 0.17)
mutation_probability = numpy.array([0.15, 0.05])

# mutation_num_genes
mutation_num_genes = [4, 2]
mutation_num_genes = (3, 1)
mutation_num_genes = numpy.array([7, 2])

# mutation_percent_genes
mutation_percent_genes = [25, 12]
mutation_percent_genes = (15, 8)
mutation_percent_genes = numpy.array([21, 13])

Assume that the average fitness is 12 and the fitness values of 2 solutions are 15 and 7. If the mutation probabilities are specified as follows:

mutation_probability = [0.25, 0.1]

Then the mutation probability of the first solution is 0.1 because its fitness is 15 which is higher than the average fitness 12. The mutation probability of the second solution is 0.25 because its fitness is 7 which is lower than the average fitness 12.

Here is an example that uses adaptive mutation.

import pygad
import numpy

function_inputs = [4,-2,3.5,5,-11,-4.7] # Function inputs.
desired_output = 44 # Function output.

def fitness_func(solution, solution_idx):
    # The fitness function calulates the sum of products between each input and its corresponding weight.
    output = numpy.sum(solution*function_inputs)
    # The value 0.000001 is used to avoid the Inf value when the denominator numpy.abs(output - desired_output) is 0.0.
    fitness = 1.0 / (numpy.abs(output - desired_output) + 0.000001)
    return fitness

# Creating an instance of the GA class inside the ga module. Some parameters are initialized within the constructor.
ga_instance = pygad.GA(num_generations=200,
                       fitness_func=fitness_func,
                       num_parents_mating=10,
                       sol_per_pop=20,
                       num_genes=len(function_inputs),
                       mutation_type="adaptive",
                       mutation_num_genes=(3, 1))

# Running the GA to optimize the parameters of the function.
ga_instance.run()

ga_instance.plot_result(title="PyGAD with Adaptive Mutation", linewidth=5)

Examples¶

This section gives the complete code of some examples that use pygad. Each subsection builds a different example.

Linear Model Optimization¶

This example is discussed in the Steps to Use ``pygad`` section which optimizes a linear model. Its complete code is listed below.

import pygad
import numpy

"""
Given the following function:
    y = f(w1:w6) = w1x1 + w2x2 + w3x3 + w4x4 + w5x5 + 6wx6
    where (x1,x2,x3,x4,x5,x6)=(4,-2,3.5,5,-11,-4.7) and y=44
What are the best values for the 6 weights (w1 to w6)? We are going to use the genetic algorithm to optimize this function.
"""

function_inputs = [4,-2,3.5,5,-11,-4.7] # Function inputs.
desired_output = 44 # Function output.

def fitness_func(solution, solution_idx):
    # Calculating the fitness value of each solution in the current population.
    # The fitness function calulates the sum of products between each input and its corresponding weight.
    output = numpy.sum(solution*function_inputs)
    fitness = 1.0 / numpy.abs(output - desired_output)
    return fitness

fitness_function = fitness_func

num_generations = 50 # Number of generations.
num_parents_mating = 4 # Number of solutions to be selected as parents in the mating pool.

# To prepare the initial population, there are 2 ways:
# 1) Prepare it yourself and pass it to the initial_population parameter. This way is useful when the user wants to start the genetic algorithm with a custom initial population.
# 2) Assign valid integer values to the sol_per_pop and num_genes parameters. If the initial_population parameter exists, then the sol_per_pop and num_genes parameters are useless.
sol_per_pop = 8 # Number of solutions in the population.
num_genes = len(function_inputs)

init_range_low = -2
init_range_high = 5

parent_selection_type = "sss" # Type of parent selection.
keep_parents = 1 # Number of parents to keep in the next population. -1 means keep all parents and 0 means keep nothing.

crossover_type = "single_point" # Type of the crossover operator.

# Parameters of the mutation operation.
mutation_type = "random" # Type of the mutation operator.
mutation_percent_genes = 10 # Percentage of genes to mutate. This parameter has no action if the parameter mutation_num_genes exists.

last_fitness = 0
def callback_generation(ga_instance):
    global last_fitness
    print("Generation = {generation}".format(generation=ga_instance.generations_completed))
    print("Fitness    = {fitness}".format(fitness=ga_instance.best_solution()[1]))
    print("Change     = {change}".format(change=ga_instance.best_solution()[1] - last_fitness))
    last_fitness = ga_instance.best_solution()[1]

# Creating an instance of the GA class inside the ga module. Some parameters are initialized within the constructor.
ga_instance = pygad.GA(num_generations=num_generations,
                       num_parents_mating=num_parents_mating,
                       fitness_func=fitness_function,
                       sol_per_pop=sol_per_pop,
                       num_genes=num_genes,
                       init_range_low=init_range_low,
                       init_range_high=init_range_high,
                       parent_selection_type=parent_selection_type,
                       keep_parents=keep_parents,
                       crossover_type=crossover_type,
                       mutation_type=mutation_type,
                       mutation_percent_genes=mutation_percent_genes,
                       on_generation=callback_generation)

# Running the GA to optimize the parameters of the function.
ga_instance.run()

# After the generations complete, some plots are showed that summarize the how the outputs/fitenss values evolve over generations.
ga_instance.plot_result()

# Returning the details of the best solution.
solution, solution_fitness, solution_idx = ga_instance.best_solution()
print("Parameters of the best solution : {solution}".format(solution=solution))
print("Fitness value of the best solution = {solution_fitness}".format(solution_fitness=solution_fitness))
print("Index of the best solution : {solution_idx}".format(solution_idx=solution_idx))

prediction = numpy.sum(numpy.array(function_inputs)*solution)
print("Predicted output based on the best solution : {prediction}".format(prediction=prediction))

if ga_instance.best_solution_generation != -1:
    print("Best fitness value reached after {best_solution_generation} generations.".format(best_solution_generation=ga_instance.best_solution_generation))

# Saving the GA instance.
filename = 'genetic' # The filename to which the instance is saved. The name is without extension.
ga_instance.save(filename=filename)

# Loading the saved GA instance.
loaded_ga_instance = pygad.load(filename=filename)
loaded_ga_instance.plot_result()

Reproducing Images¶

This project reproduces a single image using PyGAD by evolving pixel values. This project works with both color and gray images. Check this project at GitHub: https://github.com/ahmedfgad/GARI.

For more information about this project, read this tutorial titled Reproducing Images using a Genetic Algorithm with Python available at these links:

Project Steps¶

The steps to follow in order to reproduce an image are as follows:

Read an image
Prepare the fitness function
Create an instance of the pygad.GA class with the appropriate parameters
Run PyGAD
Plot results
Calculate some statistics

The next sections discusses the code of each of these steps.

Read an Image¶

There is an image named fruit.jpg in the GARI project which is read according to the next code.

import imageio
import numpy

target_im = imageio.imread('fruit.jpg')
target_im = numpy.asarray(target_im/255, dtype=numpy.float)

Here is the read image.

Based on the chromosome representation used in the example, the pixel values can be either in the 0-255, 0-1, or any other ranges.

Note that the range of pixel values affect other parameters like the range from which the random values are selected during mutation and also the range of the values used in the initial population. So, be consistent.

Prepare the Fitness Function¶

The next code creates a function that will be used as a fitness function for calculating the fitness value for each solution in the population. This function must be a maximization function that accepts 2 parameters representing a solution and its index. It returns a value representing the fitness value.

import gari

target_chromosome = gari.img2chromosome(target_im)

def fitness_fun(solution, solution_idx):
    fitness = numpy.sum(numpy.abs(target_chromosome-solution))

    # Negating the fitness value to make it increasing rather than decreasing.
    fitness = numpy.sum(target_chromosome) - fitness
    return fitness

The fitness value is calculated using the sum of absolute difference between genes values in the original and reproduced chromosomes. The gari.img2chromosome() function is called before the fitness function to represent the image as a vector because the genetic algorithm can work with 1D chromosomes.

The implementation of the gari module is available at the GARI GitHub project and its code is listed below.

import numpy
import functools
import operator

def img2chromosome(img_arr):
    return numpy.reshape(a=img_arr, newshape=(functools.reduce(operator.mul, img_arr.shape)))

def chromosome2img(vector, shape):
    if len(vector) != functools.reduce(operator.mul, shape):
        raise ValueError("A vector of length {vector_length} into an array of shape {shape}.".format(vector_length=len(vector), shape=shape))

    return numpy.reshape(a=vector, newshape=shape)

Create an Instance of the `pygad.GA` Class¶

It is very important to use random mutation and set the mutation_by_replacement to True. Based on the range of pixel values, the values assigned to the init_range_low, init_range_high, random_mutation_min_val, and random_mutation_max_val parameters should be changed.

If the image pixel values range from 0 to 255, then set init_range_low and random_mutation_min_val to 0 as they are but change init_range_high and random_mutation_max_val to 255.

Feel free to change the other parameters or add other parameters. Please check the PyGAD’s documentation for the full list of parameters.

import pygad

ga_instance = pygad.GA(num_generations=20000,
                       num_parents_mating=10,
                       fitness_func=fitness_fun,
                       sol_per_pop=20,
                       num_genes=target_im.size,
                       init_range_low=0.0,
                       init_range_high=1.0,
                       mutation_percent_genes=0.01,
                       mutation_type="random",
                       mutation_by_replacement=True,
                       random_mutation_min_val=0.0,
                       random_mutation_max_val=1.0)

Run PyGAD¶

Simply, call the run() method to run PyGAD.

ga_instance.run()

Plot Results¶

After the run() method completes, the fitness values of all generations can be viewed in a plot using the plot_result() method.

ga_instance.plot_result()

Here is the plot after 20,000 generations.

Calculate Some Statistics¶

Here is some information about the best solution.

# Returning the details of the best solution.
solution, solution_fitness, solution_idx = ga_instance.best_solution()
print("Fitness value of the best solution = {solution_fitness}".format(solution_fitness=solution_fitness))
print("Index of the best solution : {solution_idx}".format(solution_idx=solution_idx))

if ga_instance.best_solution_generation != -1:
    print("Best fitness value reached after {best_solution_generation} generations.".format(best_solution_generation=ga_instance.best_solution_generation))

result = gari.chromosome2img(solution, target_im.shape)
matplotlib.pyplot.imshow(result)
matplotlib.pyplot.title("PyGAD & GARI for Reproducing Images")
matplotlib.pyplot.show()

Evolution by Generation¶

The solution reached after the 20,000 generations is shown below.

After more generations, the result can be enhanced like what shown below.

The results can also be enhanced by changing the parameters passed to the constructor of the pygad.GA class.

Here is how the image is evolved from generation 0 to generation 20,000s.

Generation 0

Generation 1,000

Generation 2,500

Generation 4,500

Generation 7,000

Generation 8,000

Generation 20,000

pygad Module¶

pygad.GA Class¶

__init__()¶

Other Instance Attributes & Methods¶

Other Attributes¶

Other Methods¶

initialize_population()¶

cal_pop_fitness()¶

run()¶

Parent Selection Methods¶

steady_state_selection()¶

rank_selection()¶

random_selection()¶

tournament_selection()¶

roulette_wheel_selection()¶

stochastic_universal_selection()¶

Crossover Methods¶

single_point_crossover()¶

two_points_crossover()¶

uniform_crossover()¶

scattered_crossover()¶

Mutation Methods¶

random_mutation()¶

swap_mutation()¶

inversion_mutation()¶

scramble_mutation()¶

adaptive_mutation()¶

best_solution()¶

plot_result()¶

save()¶

Functions in pygad¶

pygad.load()¶

Steps to Use pygad¶

Preparing the fitness_func Parameter¶

Preparing Other Parameters¶

The callback_generation Parameter¶

Import the pygad¶

Create an Instance of the pygad.GA Class¶

Run the Genetic Algorithm¶

Plotting Results¶

Information about the Best Solution¶

Saving & Loading the Results¶

Crossover, Mutation, and Parent Selection¶

Supported Crossover Operations¶

Supported Mutation Operations¶

Supported Parent Selection Operations¶

Life Cycle of PyGAD¶

Adaptive Mutation¶

Use Adaptive Mutation in PyGAD¶

Examples¶

Linear Model Optimization¶

Reproducing Images¶

Project Steps¶

Read an Image¶

Prepare the Fitness Function¶

Create an Instance of the pygad.GA Class¶

Run PyGAD¶

Plot Results¶

Calculate Some Statistics¶

Evolution by Generation¶

`pygad` Module¶

`pygad.GA` Class¶

`init()`¶

`initialize_population()`¶

`cal_pop_fitness()`¶

`run()`¶

`steady_state_selection()`¶

`rank_selection()`¶

`random_selection()`¶

`tournament_selection()`¶

`roulette_wheel_selection()`¶

`stochastic_universal_selection()`¶

`single_point_crossover()`¶

`two_points_crossover()`¶

`uniform_crossover()`¶

`scattered_crossover()`¶

`random_mutation()`¶

`swap_mutation()`¶

`inversion_mutation()`¶

`scramble_mutation()`¶

`adaptive_mutation()`¶

`best_solution()`¶

`plot_result()`¶

`save()`¶

Functions in `pygad`¶

`pygad.load()`¶

Steps to Use `pygad`¶

Preparing the `fitness_func` Parameter¶

The `callback_generation` Parameter¶

Import the `pygad`¶

Create an Instance of the `pygad.GA` Class¶

Create an Instance of the `pygad.GA` Class¶