`pygad.gann`

Module¶

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

The `pygad.gann`

module trains neural networks (for either
classification or regression) using the genetic algorithm. It makes use
of the 2 modules `pygad`

and `pygad.nn`

.

`pygad.gann.GANN`

Class¶

The `pygad.gann`

module has a class named `pygad.gann.GANN`

for
training neural networks using the genetic algorithm. The constructor,
methods, function, and attributes within the class are discussed in this
section.

`__init__()`

¶

In order to train a neural network using the genetic algorithm, the
first thing to do is to create an instance of the `pygad.gann.GANN`

class.

The `pygad.gann.GANN`

class constructor accepts the following
parameters:

`num_solutions`

: Number of neural networks (i.e. solutions) in the population. Based on the value passed to this parameter, a number of identical neural networks are created where their parameters are optimized using the genetic algorithm.`num_neurons_input`

: Number of neurons in the input layer.`num_neurons_output`

: Number of neurons in the output layer.`num_neurons_hidden_layers=[]`

: A list holding the number of neurons in the hidden layer(s). If empty`[]`

, then no hidden layers are used. For each`int`

value it holds, then a hidden layer is created with a number of hidden neurons specified by the corresponding`int`

value. For example,`num_neurons_hidden_layers=[10]`

creates a single hidden layer with**10**neurons.`num_neurons_hidden_layers=[10, 5]`

creates 2 hidden layers with 10 neurons for the first and 5 neurons for the second hidden layer.`output_activation="softmax"`

: The name of the activation function of the output layer which defaults to`"softmax"`

.`hidden_activations="relu"`

: The name(s) of the activation function(s) of the hidden layer(s). It defaults to`"relu"`

. If passed as a string, this means the specified activation function will be used across all the hidden layers. If passed as a list, then it must have the same length as the length of the`num_neurons_hidden_layers`

list. An exception is raised if their lengths are different. When`hidden_activations`

is a list, a one-to-one mapping between the`num_neurons_hidden_layers`

and`hidden_activations`

lists occurs.

In order to validate the parameters passed to the `pygad.gann.GANN`

class constructor, the `pygad.gann.validate_network_parameters()`

function is called.

## Instance Attributes¶

All the parameters in the `pygad.gann.GANN`

class constructor are used
as instance attributes. Besides such attributes, there are other
attributes added to the instances from the `pygad.gann.GANN`

class
which are:

`parameters_validated`

: If`True`

, then the parameters passed to the GANN class constructor are valid. Its initial value is`False`

.`population_networks`

: A list holding references to all the solutions (i.e. neural networks) used in the population.

## Methods in the GANN Class¶

This section discusses the methods available for instances of the
`pygad.gann.GANN`

class.

`create_population()`

¶

The `create_population()`

method creates the initial population of the
genetic algorithm as a list of neural networks (i.e. solutions). For
each network to be created, the `pygad.gann.create_network()`

function
is called.

Each element in the list holds a reference to the last (i.e. output)
layer for the network. The method does not accept any parameter and it
accesses all the required details from the `pygad.gann.GANN`

instance.

The method returns the list holding the references to the networks. This
list is later assigned to the `population_networks`

attribute of the
instance.

`update_population_trained_weights()`

¶

The `update_population_trained_weights()`

method updates the
`trained_weights`

attribute of the layers of each network (check the
documentation of the pygad.nn.DenseLayer
class for
more information) according to the weights passed in the
`population_trained_weights`

parameter.

Accepts the following parameters:

`population_trained_weights`

: A list holding the trained weights of all networks as matrices. Such matrices are to be assigned to the`trained_weights`

attribute of all layers of all networks.

# Functions in the `pygad.gann`

Module¶

This section discusses the functions in the `pygad.gann`

module.

`pygad.gann.validate_network_parameters()`

¶

Validates the parameters passed to the constructor of the
`pygad.gann.GANN`

class. If at least one an invalid parameter exists,
an exception is raised and the execution stops.

The function accepts the same parameters passed to the constructor of
the `pygad.gann.GANN`

class. Please check the documentation of such
parameters in the section discussing the class constructor.

The reason why this function sets a default value to the
`num_solutions`

parameter is differentiating whether a population of
networks or a single network is to be created. If `None`

, then a
single network will be created. If not `None`

, then a population of
networks is to be created.

If the value passed to the `hidden_activations`

parameter is a string,
not a list, then a list is created by replicating the passed name of the
activation function a number of times equal to the number of hidden
layers (i.e. the length of the `num_neurons_hidden_layers`

parameter).

Returns a list holding the name(s) of the activation function(s) of the hidden layer(s).

`pygad.gann.create_network()`

¶

Creates a neural network as a linked list between the input, hidden, and output layers where the layer at index N (which is the last/output layer) references the layer at index N-1 (which is a hidden layer) using its previous_layer attribute. The input layer does not reference any layer because it is the last layer in the linked list.

In addition to the `parameters_validated`

parameter, this function
accepts the same parameters passed to the constructor of the
`pygad.gann.GANN`

class except for the `num_solutions`

parameter
because only a single network is created out of the `create_network()`

function.

`parameters_validated`

: If `False`

, then the parameters are not
validated and a call to the `validate_network_parameters()`

function
is made.

Returns the reference to the last layer in the network architecture which is the output layer. Based on such a reference, all network layers can be fetched.

`pygad.gann.population_as_vectors()`

¶

Accepts the population as networks and returns a list holding all weights of the layers of each solution (i.e. network) in the population as a vector.

For example, if the population has 6 solutions (i.e. networks), this function accepts references to such networks and returns a list with 6 vectors, one for each network (i.e. solution). Each vector holds the weights for all layers for a single network.

Accepts the following parameters:

`population_networks`

: A list holding references to the output (last) layers of the neural networks used in the population.

Returns a list holding the weights vectors for all solutions (i.e. networks).

`pygad.gann.population_as_matrices()`

¶

Accepts the population as both networks and weights vectors and returns the weights of all layers of each solution (i.e. network) in the population as a matrix.

For example, if the population has 6 solutions (i.e. networks), this function returns a list with 6 matrices, one for each network holding its weights for all layers.

Accepts the following parameters:

`population_networks`

: A list holding references to the output (last) layers of the neural networks used in the population.`population_vectors`

: A list holding the weights of all networks as vectors. Such vectors are to be converted into matrices.

Returns a list holding the weights matrices for all solutions (i.e. networks).

# Steps to Build and Train Neural Networks using Genetic Algorithm¶

The steps to use this project for building and training a neural network using the genetic algorithm are as follows:

Prepare the training data.

Create an instance of the

`pygad.gann.GANN`

class.Fetch the population weights as vectors.

Prepare the fitness function.

Prepare the generation callback function.

Create an instance of the

`pygad.GA`

class.Run the created instance of the

`pygad.GA`

class.Plot the Fitness Values

Information about the best solution.

Making predictions using the trained weights.

Calculating some statistics.

Let’s start covering all of these steps.

## Prepare the Training Data¶

Before building and training neural networks, the training data (input and output) is to be prepared. The inputs and the outputs of the training data are NumPy arrays.

Here is an example of preparing the training data for the XOR problem.

For the input array, each element must be a list representing the inputs
(i.e. features) for the sample. If there are 200 samples and each sample
has 50 features, then the shape of the inputs array is `(200, 50)`

.
The variable `num_inputs`

holds the length of each sample which is 2
in this example.

```
data_inputs = numpy.array([[1, 1],
[1, 0],
[0, 1],
[0, 0]])
data_outputs = numpy.array([0,
1,
1,
0])
num_inputs = data_inputs.shape[1]
```

For the output array, each element must be a single number representing
the class label of the sample. The class labels must start at `0`

. So,
if there are 200 samples, then the shape of the output array is
`(200)`

. If there are 5 classes in the data, then the values of all
the 200 elements in the output array must range from 0 to 4 inclusive.
Generally, the class labels start from `0`

to `N-1`

where `N`

is
the number of classes.

For the XOR example, there are 2 classes and thus their labels are 0 and
1. The `num_classes`

variable is assigned to 2.

Note that the project only supports classification problems where each sample is assigned to only one class.

## Create an Instance of the `pygad.gann.GANN`

Class¶

After preparing the input data, an instance of the `pygad.gann.GANN`

class is created by passing the appropriate parameters.

Here is an example that creates a network for the XOR problem. The
`num_solutions`

parameter is set to 6 which means the genetic
algorithm population will have 6 solutions (i.e. networks). All of these
6 neural networks will have the same architectures as specified by the
other parameters.

The output layer has 2 neurons because there are only 2 classes (0 and 1).

```
import pygad.gann
import pygad.nn
num_solutions = 6
GANN_instance = pygad.gann.GANN(num_solutions=num_solutions,
num_neurons_input=num_inputs,
num_neurons_hidden_layers=[2],
num_neurons_output=2,
hidden_activations=["relu"],
output_activation="softmax")
```

The architecture of the created network has the following layers:

An input layer with 2 neurons (i.e. inputs)

A single hidden layer with 2 neurons.

An output layer with 2 neurons (i.e. classes).

The weights of the network are as follows:

Between the input and the hidden layer, there is a weights matrix of size equal to

`(number inputs x number of hidden neurons) = (2x2)`

.Between the hidden and the output layer, there is a weights matrix of size equal to

`(number of hidden neurons x number of outputs) = (2x2)`

.

The activation function used for the output layer is `softmax`

. The
`relu`

activation function is used for the hidden layer.

After creating the instance of the `pygad.gann.GANN`

class next is to
fetch the weights of the population as a list of vectors.

## Fetch the Population Weights as Vectors¶

For the genetic algorithm, the parameters (i.e. genes) of each solution are represented as a single vector.

For the task of training the network for the XOR problem, the weights of each network in the population are not represented as a vector but 2 matrices each of size 2x2.

To create a list holding the population weights as vectors, one for each
network, the `pygad.gann.population_as_vectors()`

function is used.

```
population_vectors = pygad.gann.population_as_vectors(population_networks=GANN_instance.population_networks)
```

After preparing the population weights as a set of vectors, next is to prepare 2 functions which are:

Fitness function.

Callback function after each generation.

## Prepare the Fitness Function¶

The PyGAD library works by allowing the users to customize the genetic algorithm for their own problems. Because the problems differ in how the fitness values are calculated, then PyGAD allows the user to use a custom function as a maximization fitness function. This function must accept 2 positional parameters representing the following:

The solution.

The solution index in the population.

The fitness function must return a single number representing the fitness. The higher the fitness value, the better the solution.

Here is the implementation of the fitness function for training a neural
network. It uses the `pygad.nn.predict()`

function to predict the
class labels based on the current solution’s weights. The
`pygad.nn.predict()`

function uses the trained weights available in
the `trained_weights`

attribute of each layer of the network for
making predictions.

Based on such predictions, the classification accuracy is calculated. This accuracy is used as the fitness value of the solution. Finally, the fitness value is returned.

```
def fitness_func(ga_instance, solution, sol_idx):
global GANN_instance, data_inputs, data_outputs
predictions = pygad.nn.predict(last_layer=GANN_instance.population_networks[sol_idx],
data_inputs=data_inputs)
correct_predictions = numpy.where(predictions == data_outputs)[0].size
solution_fitness = (correct_predictions/data_outputs.size)*100
return solution_fitness
```

## Prepare the Generation Callback Function¶

After each generation of the genetic algorithm, the fitness function
will be called to calculate the fitness value of each solution. Within
the fitness function, the `pygad.nn.predict()`

function is used for
predicting the outputs based on the current solution’s
`trained_weights`

attribute. Thus, it is required that such an
attribute is updated by weights evolved by the genetic algorithm after
each generation.

PyGAD 2.0.0 and higher has a new parameter accepted by the `pygad.GA`

class constructor named `on_generation`

. It could be assigned to a
function that is called after each generation. The function must accept
a single parameter representing the instance of the `pygad.GA`

class.

This callback function can be used to update the `trained_weights`

attribute of layers of each network in the population.

Here is the implementation for a function that updates the
`trained_weights`

attribute of the layers of the population networks.

It works by converting the current population from the vector form to
the matric form using the `pygad.gann.population_as_matrices()`

function. It accepts the population as vectors and returns it as
matrices.

The population matrices are then passed to the
`update_population_trained_weights()`

method in the `pygad.gann`

module to update the `trained_weights`

attribute of all layers for all
solutions within the population.

```
def callback_generation(ga_instance):
global GANN_instance
population_matrices = pygad.gann.population_as_matrices(population_networks=GANN_instance.population_networks, population_vectors=ga_instance.population)
GANN_instance.update_population_trained_weights(population_trained_weights=population_matrices)
print(f"Generation = {ga_instance.generations_completed}")
print(f"Fitness = {ga_instance.best_solution()[1]}")
```

After preparing the fitness and callback function, next is to create an
instance of the `pygad.GA`

class.

## Create an Instance of the `pygad.GA`

Class¶

Once the parameters of the genetic algorithm are prepared, an instance
of the `pygad.GA`

class can be created.

Here is an example.

```
initial_population = population_vectors.copy()
num_parents_mating = 4
num_generations = 500
mutation_percent_genes = 5
parent_selection_type = "sss"
crossover_type = "single_point"
mutation_type = "random"
keep_parents = 1
init_range_low = -2
init_range_high = 5
ga_instance = pygad.GA(num_generations=num_generations,
num_parents_mating=num_parents_mating,
initial_population=initial_population,
fitness_func=fitness_func,
mutation_percent_genes=mutation_percent_genes,
init_range_low=init_range_low,
init_range_high=init_range_high,
parent_selection_type=parent_selection_type,
crossover_type=crossover_type,
mutation_type=mutation_type,
keep_parents=keep_parents,
on_generation=callback_generation)
```

The last step for training the neural networks using the genetic
algorithm is calling the `run()`

method.

## Run the Created Instance of the `pygad.GA`

Class¶

By calling the `run()`

method from the `pygad.GA`

instance, the
genetic algorithm will iterate through the number of generations
specified in its `num_generations`

parameter.

```
ga_instance.run()
```

## Plot the Fitness Values¶

After the `run()`

method completes, the `plot_fitness()`

method can
be called to show how the fitness values evolve by generation. A fitness
value (i.e. accuracy) of 100 is reached after around 180 generations.

```
ga_instance.plot_fitness()
```

By running the code again, a different initial population is created and thus a classification accuracy of 100 can be reached using a less number of generations. On the other hand, a different initial population might cause 100% accuracy to be reached using more generations or not reached at all.

## Information about the Best Solution¶

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

method in the `pygad.GA`

class.

Solution

Fitness value of the solution

Index of the solution within the population

Here is how such information is returned. The fitness value (i.e. accuracy) is 100.

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

```
Parameters of the best solution : [3.55081391 -3.21562011 -14.2617784 0.68044231 -1.41258145 -3.2979315 1.58136006 -7.83726169]
Fitness value of the best solution = 100.0
Index of the best solution : 0
```

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. According to the result, the best
fitness value is reached after 182 generations.

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

```
Best solution reached after 182 generations.
```

## Making Predictions using the Trained Weights¶

The `pygad.nn.predict()`

function can be used to make predictions
using the trained network. As printed, the network is able to predict
the labels correctly.

```
predictions = pygad.nn.predict(last_layer=GANN_instance.population_networks[solution_idx], data_inputs=data_inputs)
print(f"Predictions of the trained network : {predictions}")
```

```
Predictions of the trained network : [0. 1. 1. 0.]
```

## Calculating Some Statistics¶

Based on the predictions the network made, some statistics can be calculated such as the number of correct and wrong predictions in addition to the classification accuracy.

```
num_wrong = numpy.where(predictions != data_outputs)[0]
num_correct = data_outputs.size - num_wrong.size
accuracy = 100 * (num_correct/data_outputs.size)
print(f"Number of correct classifications : {num_correct}.")
print(f"Number of wrong classifications : {num_wrong.size}.")
print(f"Classification accuracy : {accuracy}.")
```

```
Number of correct classifications : 4
print("Number of wrong classifications : 0
Classification accuracy : 100
```

# Examples¶

This section gives the complete code of some examples that build and train neural networks using the genetic algorithm. Each subsection builds a different network.

## XOR Classification¶

This example is discussed in the **Steps to Build and Train Neural
Networks using Genetic Algorithm** section that builds the XOR gate and
its complete code is listed below.

```
import numpy
import pygad
import pygad.nn
import pygad.gann
def fitness_func(ga_instance, solution, sol_idx):
global GANN_instance, data_inputs, data_outputs
# If adaptive mutation is used, sometimes sol_idx is None.
if sol_idx == None:
sol_idx = 1
predictions = pygad.nn.predict(last_layer=GANN_instance.population_networks[sol_idx],
data_inputs=data_inputs)
correct_predictions = numpy.where(predictions == data_outputs)[0].size
solution_fitness = (correct_predictions/data_outputs.size)*100
return solution_fitness
def callback_generation(ga_instance):
global GANN_instance, last_fitness
population_matrices = pygad.gann.population_as_matrices(population_networks=GANN_instance.population_networks,
population_vectors=ga_instance.population)
GANN_instance.update_population_trained_weights(population_trained_weights=population_matrices)
print(f"Generation = {ga_instance.generations_completed}")
print(f"Fitness = {ga_instance.best_solution()[1]}")
print(f"Change = {ga_instance.best_solution()[1] - last_fitness}")
last_fitness = ga_instance.best_solution()[1].copy()
# Holds the fitness value of the previous generation.
last_fitness = 0
# Preparing the NumPy array of the inputs.
data_inputs = numpy.array([[1, 1],
[1, 0],
[0, 1],
[0, 0]])
# Preparing the NumPy array of the outputs.
data_outputs = numpy.array([0,
1,
1,
0])
# The length of the input vector for each sample (i.e. number of neurons in the input layer).
num_inputs = data_inputs.shape[1]
# The number of neurons in the output layer (i.e. number of classes).
num_classes = 2
# Creating an initial population of neural networks. The return of the initial_population() function holds references to the networks, not their weights. Using such references, the weights of all networks can be fetched.
num_solutions = 6 # A solution or a network can be used interchangeably.
GANN_instance = pygad.gann.GANN(num_solutions=num_solutions,
num_neurons_input=num_inputs,
num_neurons_hidden_layers=[2],
num_neurons_output=num_classes,
hidden_activations=["relu"],
output_activation="softmax")
# population does not hold the numerical weights of the network instead it holds a list of references to each last layer of each network (i.e. solution) in the population. A solution or a network can be used interchangeably.
# If there is a population with 3 solutions (i.e. networks), then the population is a list with 3 elements. Each element is a reference to the last layer of each network. Using such a reference, all details of the network can be accessed.
population_vectors = pygad.gann.population_as_vectors(population_networks=GANN_instance.population_networks)
# 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.
initial_population = population_vectors.copy()
num_parents_mating = 4 # Number of solutions to be selected as parents in the mating pool.
num_generations = 500 # Number of generations.
mutation_percent_genes = [5, 10] # Percentage of genes to mutate. This parameter has no action if the parameter mutation_num_genes exists.
parent_selection_type = "sss" # Type of parent selection.
crossover_type = "single_point" # Type of the crossover operator.
mutation_type = "adaptive" # Type of the mutation operator.
keep_parents = 1 # Number of parents to keep in the next population. -1 means keep all parents and 0 means keep nothing.
init_range_low = -2
init_range_high = 5
ga_instance = pygad.GA(num_generations=num_generations,
num_parents_mating=num_parents_mating,
initial_population=initial_population,
fitness_func=fitness_func,
mutation_percent_genes=mutation_percent_genes,
init_range_low=init_range_low,
init_range_high=init_range_high,
parent_selection_type=parent_selection_type,
crossover_type=crossover_type,
mutation_type=mutation_type,
keep_parents=keep_parents,
suppress_warnings=True,
on_generation=callback_generation)
ga_instance.run()
# After the generations complete, some plots are showed that summarize how the outputs/fitness values evolve over generations.
ga_instance.plot_fitness()
# Returning the details of the best solution.
solution, solution_fitness, solution_idx = ga_instance.best_solution()
print(f"Parameters of the best solution : {solution}")
print(f"Fitness value of the best solution = {solution_fitness}")
print(f"Index of the best solution : {solution_idx}")
if ga_instance.best_solution_generation != -1:
print(f"Best fitness value reached after {ga_instance.best_solution_generation} generations.")
# Predicting the outputs of the data using the best solution.
predictions = pygad.nn.predict(last_layer=GANN_instance.population_networks[solution_idx],
data_inputs=data_inputs)
print(f"Predictions of the trained network : {predictions}")
# Calculating some statistics
num_wrong = numpy.where(predictions != data_outputs)[0]
num_correct = data_outputs.size - num_wrong.size
accuracy = 100 * (num_correct/data_outputs.size)
print(f"Number of correct classifications : {num_correct}.")
print(f"Number of wrong classifications : {num_wrong.size}.")
print(f"Classification accuracy : {accuracy}.")
```

## Image Classification¶

In the documentation of the `pygad.nn`

module, a neural network is
created for classifying images from the Fruits360 dataset without being
trained using an optimization algorithm. This section discusses how to
train such a classifier using the genetic algorithm with the help of the
`pygad.gann`

module.

Please make sure that the training data files dataset_features.npy and outputs.npy are available. For downloading them, use these links:

dataset_features.npy: The features https://github.com/ahmedfgad/NumPyANN/blob/master/dataset_features.npy

outputs.npy: The class labels https://github.com/ahmedfgad/NumPyANN/blob/master/outputs.npy

After the data is available, here is the complete code that builds and trains a neural network using the genetic algorithm for classifying images from 4 classes of the Fruits360 dataset.

Because there are 4 classes, the output layer is assigned has 4 neurons
according to the `num_neurons_output`

parameter of the
`pygad.gann.GANN`

class constructor.

```
import numpy
import pygad
import pygad.nn
import pygad.gann
def fitness_func(ga_instance, solution, sol_idx):
global GANN_instance, data_inputs, data_outputs
predictions = pygad.nn.predict(last_layer=GANN_instance.population_networks[sol_idx],
data_inputs=data_inputs)
correct_predictions = numpy.where(predictions == data_outputs)[0].size
solution_fitness = (correct_predictions/data_outputs.size)*100
return solution_fitness
def callback_generation(ga_instance):
global GANN_instance, last_fitness
population_matrices = pygad.gann.population_as_matrices(population_networks=GANN_instance.population_networks,
population_vectors=ga_instance.population)
GANN_instance.update_population_trained_weights(population_trained_weights=population_matrices)
print(f"Generation = {ga_instance.generations_completed}")
print(f"Fitness = {ga_instance.best_solution()[1]}")
print(f"Change = {ga_instance.best_solution()[1] - last_fitness}")
last_fitness = ga_instance.best_solution()[1].copy()
# Holds the fitness value of the previous generation.
last_fitness = 0
# Reading the input data.
data_inputs = numpy.load("dataset_features.npy") # Download from https://github.com/ahmedfgad/NumPyANN/blob/master/dataset_features.npy
# Optional step of filtering the input data using the standard deviation.
features_STDs = numpy.std(a=data_inputs, axis=0)
data_inputs = data_inputs[:, features_STDs>50]
# Reading the output data.
data_outputs = numpy.load("outputs.npy") # Download from https://github.com/ahmedfgad/NumPyANN/blob/master/outputs.npy
# The length of the input vector for each sample (i.e. number of neurons in the input layer).
num_inputs = data_inputs.shape[1]
# The number of neurons in the output layer (i.e. number of classes).
num_classes = 4
# Creating an initial population of neural networks. The return of the initial_population() function holds references to the networks, not their weights. Using such references, the weights of all networks can be fetched.
num_solutions = 8 # A solution or a network can be used interchangeably.
GANN_instance = pygad.gann.GANN(num_solutions=num_solutions,
num_neurons_input=num_inputs,
num_neurons_hidden_layers=[150, 50],
num_neurons_output=num_classes,
hidden_activations=["relu", "relu"],
output_activation="softmax")
# population does not hold the numerical weights of the network instead it holds a list of references to each last layer of each network (i.e. solution) in the population. A solution or a network can be used interchangeably.
# If there is a population with 3 solutions (i.e. networks), then the population is a list with 3 elements. Each element is a reference to the last layer of each network. Using such a reference, all details of the network can be accessed.
population_vectors = pygad.gann.population_as_vectors(population_networks=GANN_instance.population_networks)
# 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.
initial_population = population_vectors.copy()
num_parents_mating = 4 # Number of solutions to be selected as parents in the mating pool.
num_generations = 500 # Number of generations.
mutation_percent_genes = 10 # Percentage of genes to mutate. This parameter has no action if the parameter mutation_num_genes exists.
parent_selection_type = "sss" # Type of parent selection.
crossover_type = "single_point" # Type of the crossover operator.
mutation_type = "random" # Type of the mutation operator.
keep_parents = -1 # Number of parents to keep in the next population. -1 means keep all parents and 0 means keep nothing.
ga_instance = pygad.GA(num_generations=num_generations,
num_parents_mating=num_parents_mating,
initial_population=initial_population,
fitness_func=fitness_func,
mutation_percent_genes=mutation_percent_genes,
parent_selection_type=parent_selection_type,
crossover_type=crossover_type,
mutation_type=mutation_type,
keep_parents=keep_parents,
on_generation=callback_generation)
ga_instance.run()
# After the generations complete, some plots are showed that summarize how the outputs/fitness values evolve over generations.
ga_instance.plot_fitness()
# Returning the details of the best solution.
solution, solution_fitness, solution_idx = ga_instance.best_solution()
print(f"Parameters of the best solution : {solution}")
print(f"Fitness value of the best solution = {solution_fitness}")
print(f"Index of the best solution : {solution_idx}")
if ga_instance.best_solution_generation != -1:
print(f"Best fitness value reached after {ga_instance.best_solution_generation} generations.")
# Predicting the outputs of the data using the best solution.
predictions = pygad.nn.predict(last_layer=GANN_instance.population_networks[solution_idx],
data_inputs=data_inputs)
print(f"Predictions of the trained network : {predictions}")
# Calculating some statistics
num_wrong = numpy.where(predictions != data_outputs)[0]
num_correct = data_outputs.size - num_wrong.size
accuracy = 100 * (num_correct/data_outputs.size)
print(f"Number of correct classifications : {num_correct}.")
print(f"Number of wrong classifications : {num_wrong.size}.")
print(f"Classification accuracy : {accuracy}.")
```

After training completes, here are the outputs of the print statements. The number of wrong classifications is only 1 and the accuracy is 99.949%. This accuracy is reached after 482 generations.

```
Fitness value of the best solution = 99.94903160040775
Index of the best solution : 0
Best fitness value reached after 482 generations.
Number of correct classifications : 1961.
Number of wrong classifications : 1.
Classification accuracy : 99.94903160040775.
```

The next figure shows how fitness value evolves by generation.

## Regression Example 1¶

To train a neural network for regression, follow these instructions:

Set the

`output_activation`

parameter in the constructor of the`pygad.gann.GANN`

class to`"None"`

. It is possible to use the ReLU function if all outputs are nonnegative.

```
GANN_instance = pygad.gann.GANN(...
output_activation="None")
```

Wherever the

`pygad.nn.predict()`

function is used, set the`problem_type`

parameter to`"regression"`

.

```
predictions = pygad.nn.predict(...,
problem_type="regression")
```

Design the fitness function to calculate the error (e.g. mean absolute error).

```
def fitness_func(ga_instance, solution, sol_idx):
...
predictions = pygad.nn.predict(...,
problem_type="regression")
solution_fitness = 1.0/numpy.mean(numpy.abs(predictions - data_outputs))
return solution_fitness
```

The next code builds a complete example for building a neural network for regression.

```
import numpy
import pygad
import pygad.nn
import pygad.gann
def fitness_func(ga_instance, solution, sol_idx):
global GANN_instance, data_inputs, data_outputs
predictions = pygad.nn.predict(last_layer=GANN_instance.population_networks[sol_idx],
data_inputs=data_inputs, problem_type="regression")
solution_fitness = 1.0/numpy.mean(numpy.abs(predictions - data_outputs))
return solution_fitness
def callback_generation(ga_instance):
global GANN_instance, last_fitness
population_matrices = pygad.gann.population_as_matrices(population_networks=GANN_instance.population_networks,
population_vectors=ga_instance.population)
GANN_instance.update_population_trained_weights(population_trained_weights=population_matrices)
print(f"Generation = {ga_instance.generations_completed}")
print(f"Fitness = {ga_instance.best_solution(pop_fitness=ga_instance.last_generation_fitness)[1]}")
print(f"Change = {ga_instance.best_solution(pop_fitness=ga_instance.last_generation_fitness)[1] - last_fitness}")
last_fitness = ga_instance.best_solution(pop_fitness=ga_instance.last_generation_fitness)[1].copy()
# Holds the fitness value of the previous generation.
last_fitness = 0
# Preparing the NumPy array of the inputs.
data_inputs = numpy.array([[2, 5, -3, 0.1],
[8, 15, 20, 13]])
# Preparing the NumPy array of the outputs.
data_outputs = numpy.array([[0.1, 0.2],
[1.8, 1.5]])
# The length of the input vector for each sample (i.e. number of neurons in the input layer).
num_inputs = data_inputs.shape[1]
# Creating an initial population of neural networks. The return of the initial_population() function holds references to the networks, not their weights. Using such references, the weights of all networks can be fetched.
num_solutions = 6 # A solution or a network can be used interchangeably.
GANN_instance = pygad.gann.GANN(num_solutions=num_solutions,
num_neurons_input=num_inputs,
num_neurons_hidden_layers=[2],
num_neurons_output=2,
hidden_activations=["relu"],
output_activation="None")
# population does not hold the numerical weights of the network instead it holds a list of references to each last layer of each network (i.e. solution) in the population. A solution or a network can be used interchangeably.
# If there is a population with 3 solutions (i.e. networks), then the population is a list with 3 elements. Each element is a reference to the last layer of each network. Using such a reference, all details of the network can be accessed.
population_vectors = pygad.gann.population_as_vectors(population_networks=GANN_instance.population_networks)
# 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.
initial_population = population_vectors.copy()
num_parents_mating = 4 # Number of solutions to be selected as parents in the mating pool.
num_generations = 500 # Number of generations.
mutation_percent_genes = 5 # Percentage of genes to mutate. This parameter has no action if the parameter mutation_num_genes exists.
parent_selection_type = "sss" # Type of parent selection.
crossover_type = "single_point" # Type of the crossover operator.
mutation_type = "random" # Type of the mutation operator.
keep_parents = 1 # Number of parents to keep in the next population. -1 means keep all parents and 0 means keep nothing.
init_range_low = -1
init_range_high = 1
ga_instance = pygad.GA(num_generations=num_generations,
num_parents_mating=num_parents_mating,
initial_population=initial_population,
fitness_func=fitness_func,
mutation_percent_genes=mutation_percent_genes,
init_range_low=init_range_low,
init_range_high=init_range_high,
parent_selection_type=parent_selection_type,
crossover_type=crossover_type,
mutation_type=mutation_type,
keep_parents=keep_parents,
on_generation=callback_generation)
ga_instance.run()
# After the generations complete, some plots are showed that summarize how the outputs/fitness values evolve over generations.
ga_instance.plot_fitness()
# Returning the details of the best solution.
solution, solution_fitness, solution_idx = ga_instance.best_solution(pop_fitness=ga_instance.last_generation_fitness)
print(f"Parameters of the best solution : {solution}")
print(f"Fitness value of the best solution = {solution_fitness}")
print(f"Index of the best solution : {solution_idx}")
if ga_instance.best_solution_generation != -1:
print(f"Best fitness value reached after {ga_instance.best_solution_generation} generations.")
# Predicting the outputs of the data using the best solution.
predictions = pygad.nn.predict(last_layer=GANN_instance.population_networks[solution_idx],
data_inputs=data_inputs,
problem_type="regression")
print(f"Predictions of the trained network : {predictions}")
# Calculating some statistics
abs_error = numpy.mean(numpy.abs(predictions - data_outputs))
print(f"Absolute error : {abs_error}.")
```

The next figure shows how the fitness value changes for the generations used.

## Regression Example 2 - Fish Weight Prediction¶

This example uses the Fish Market Dataset available at Kaggle (https://www.kaggle.com/aungpyaeap/fish-market). Simply download the CSV dataset from this link (https://www.kaggle.com/aungpyaeap/fish-market/download). The dataset is also available at the GitHub project of the pygad.gann module: https://github.com/ahmedfgad/NeuralGenetic

Using the Pandas library, the dataset is read using the `read_csv()`

function.

```
data = numpy.array(pandas.read_csv("Fish.csv"))
```

The last 5 columns in the dataset are used as inputs and the **Weight**
column is used as output.

```
# Preparing the NumPy array of the inputs.
data_inputs = numpy.asarray(data[:, 2:], dtype=numpy.float32)
# Preparing the NumPy array of the outputs.
data_outputs = numpy.asarray(data[:, 1], dtype=numpy.float32) # Fish Weight
```

Note how the activation function at the last layer is set to `"None"`

.
Moreover, the `problem_type`

parameter in the `pygad.nn.train()`

and
`pygad.nn.predict()`

functions is set to `"regression"`

. Remember to
design an appropriate fitness function for the regression problem. In
this example, the fitness value is calculated based on the mean absolute
error.

```
solution_fitness = 1.0/numpy.mean(numpy.abs(predictions - data_outputs))
```

Here is the complete code.

```
import numpy
import pygad
import pygad.nn
import pygad.gann
import pandas
def fitness_func(ga_instance, solution, sol_idx):
global GANN_instance, data_inputs, data_outputs
predictions = pygad.nn.predict(last_layer=GANN_instance.population_networks[sol_idx],
data_inputs=data_inputs, problem_type="regression")
solution_fitness = 1.0/numpy.mean(numpy.abs(predictions - data_outputs))
return solution_fitness
def callback_generation(ga_instance):
global GANN_instance, last_fitness
population_matrices = pygad.gann.population_as_matrices(population_networks=GANN_instance.population_networks,
population_vectors=ga_instance.population)
GANN_instance.update_population_trained_weights(population_trained_weights=population_matrices)
print(f"Generation = {ga_instance.generations_completed}")
print(f"Fitness = {ga_instance.best_solution(pop_fitness=ga_instance.last_generation_fitness)[1]}")
print(f"Change = {ga_instance.best_solution(pop_fitness=ga_instance.last_generation_fitness)[1] - last_fitness}")
last_fitness = ga_instance.best_solution(pop_fitness=ga_instance.last_generation_fitness)[1].copy()
# Holds the fitness value of the previous generation.
last_fitness = 0
data = numpy.array(pandas.read_csv("../data/Fish.csv"))
# Preparing the NumPy array of the inputs.
data_inputs = numpy.asarray(data[:, 2:], dtype=numpy.float32)
# Preparing the NumPy array of the outputs.
data_outputs = numpy.asarray(data[:, 1], dtype=numpy.float32)
# The length of the input vector for each sample (i.e. number of neurons in the input layer).
num_inputs = data_inputs.shape[1]
# Creating an initial population of neural networks. The return of the initial_population() function holds references to the networks, not their weights. Using such references, the weights of all networks can be fetched.
num_solutions = 6 # A solution or a network can be used interchangeably.
GANN_instance = pygad.gann.GANN(num_solutions=num_solutions,
num_neurons_input=num_inputs,
num_neurons_hidden_layers=[2],
num_neurons_output=1,
hidden_activations=["relu"],
output_activation="None")
# population does not hold the numerical weights of the network instead it holds a list of references to each last layer of each network (i.e. solution) in the population. A solution or a network can be used interchangeably.
# If there is a population with 3 solutions (i.e. networks), then the population is a list with 3 elements. Each element is a reference to the last layer of each network. Using such a reference, all details of the network can be accessed.
population_vectors = pygad.gann.population_as_vectors(population_networks=GANN_instance.population_networks)
# 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.
initial_population = population_vectors.copy()
num_parents_mating = 4 # Number of solutions to be selected as parents in the mating pool.
num_generations = 500 # Number of generations.
mutation_percent_genes = 5 # Percentage of genes to mutate. This parameter has no action if the parameter mutation_num_genes exists.
parent_selection_type = "sss" # Type of parent selection.
crossover_type = "single_point" # Type of the crossover operator.
mutation_type = "random" # Type of the mutation operator.
keep_parents = 1 # Number of parents to keep in the next population. -1 means keep all parents and 0 means keep nothing.
init_range_low = -1
init_range_high = 1
ga_instance = pygad.GA(num_generations=num_generations,
num_parents_mating=num_parents_mating,
initial_population=initial_population,
fitness_func=fitness_func,
mutation_percent_genes=mutation_percent_genes,
init_range_low=init_range_low,
init_range_high=init_range_high,
parent_selection_type=parent_selection_type,
crossover_type=crossover_type,
mutation_type=mutation_type,
keep_parents=keep_parents,
on_generation=callback_generation)
ga_instance.run()
# After the generations complete, some plots are showed that summarize how the outputs/fitness values evolve over generations.
ga_instance.plot_fitness()
# Returning the details of the best solution.
solution, solution_fitness, solution_idx = ga_instance.best_solution(pop_fitness=ga_instance.last_generation_fitness)
print(f"Parameters of the best solution : {solution}")
print(f"Fitness value of the best solution = {solution_fitness}")
print(f"Index of the best solution : {solution_idx}")
if ga_instance.best_solution_generation != -1:
print(f"Best fitness value reached after {ga_instance.best_solution_generation} generations.")
# Predicting the outputs of the data using the best solution.
predictions = pygad.nn.predict(last_layer=GANN_instance.population_networks[solution_idx],
data_inputs=data_inputs,
problem_type="regression")
print(f"Predictions of the trained network : {predictions}")
# Calculating some statistics
abs_error = numpy.mean(numpy.abs(predictions - data_outputs))
print(f"Absolute error : {abs_error}.")
```

The next figure shows how the fitness value changes for the 500 generations used.