Python Genetic Algorithm library

## Project description

# GeneAl

`geneal`

is a python library implementing genetic algorithms (GAs). It has functionality for both binary and continuous GA,
as well as specific use case applications such as a solver for the
Travelling Salesman Problem.

## Installation

```
$ pip install geneal
```

## Usage

`geneal`

provides 2 main GA solver classes, `BinaryGenAlgSolver`

and `ContinuousGenAlgSolver`

for binary and continuous problem formulations respectively. The library is set up in such a way that all problems
have to be a maximization, and hence, the fitness functions need to be adjusted accordingly.

### Binary GA

The binary GA class can be customized by the input variables provided on its initialization. The minimum required arguments to provide at the initialization are the number of genes on each individual's chromosome, and the fitness function to be maximized.

An example is shown below.

```
from geneal.genetic_algorithms import BinaryGenAlgSolver
from geneal.applications.fitness_functions.binary import fitness_functions_binary
solver = BinaryGenAlgSolver(
n_genes=3, # number of variables defining the problem
fitness_function=fitness_functions_binary(1), # fitness function to be maximized
)
solver.solve()
```

The above call will perform the optimization with the default parameters, which will most likely have to be adjusted for each individual problem at hand. The algorithm parameters can be customized as shown below.

```
from geneal.genetic_algorithms import BinaryGenAlgSolver
from geneal.applications.fitness_functions.binary import fitness_functions_binary
solver = BinaryGenAlgSolver(
n_genes=3,
fitness_function=fitness_functions_binary(1),
n_bits=1, # number of bits describing each gene (variable)
pop_size=10, # population size (number of individuals)
max_gen=500, # maximum number of generations
mutation_rate=0.05, # mutation rate to apply to the population
selection_rate=0.5, # percentage of the population to select for mating
selection_strategy="roulette_wheel", # strategy to use for selection. see below for more details
fitness_tolerance=(1E-4, 50) # Loop will be exited if the best fitness value does not change more than
# 1E-4 for 50 generations
)
solver.solve()
```

### Continuous GA

Following a similar pattern as the binary GA solver, the parameters of the continuous GA can be adjusted at initialization. As a bare minimum, the number of variables and the fitness function to maximize must be provided, as shown below.

```
from geneal.genetic_algorithms import ContinuousGenAlgSolver
from geneal.applications.fitness_functions.continuous import fitness_functions_continuous
solver = ContinuousGenAlgSolver(
n_genes=4, # number of variables defining the problem
fitness_function=fitness_functions_continuous(3), # fitness function to be maximized
)
solver.solve()
```

In order to customize the continuous GA solver further, more arguments can be passed at initialization.

```
from geneal.genetic_algorithms import ContinuousGenAlgSolver
from geneal.applications.fitness_functions.continuous import fitness_functions_continuous
solver = ContinuousGenAlgSolver(
n_genes=4,
fitness_function=fitness_functions_continuous(3),
pop_size=10, # population size (number of individuals)
max_gen=200, # maximum number of generations
mutation_rate=0.1, # mutation rate to apply to the population
selection_rate=0.6, # percentage of the population to select for mating
selection_strategy="roulette_wheel", # strategy to use for selection. see below for more details
fitness_tolerance=(1E-5, 20) # Loop will be exited if the best fitness value does not change more than
# 1E-5 for 20 generations
)
solver.solve()
```

A notable difference to the binary GA solver is the fact that we can customize the input space of the problem
by defining if the problem is of type `int`

or `float`

, and defining an overall minimum and maximum values for each
variable (or for all at once).

```
from geneal.genetic_algorithms import ContinuousGenAlgSolver
from geneal.applications.fitness_functions.continuous import fitness_functions_continuous
solver = ContinuousGenAlgSolver(
n_genes=4,
fitness_function=fitness_functions_continuous(3),
pop_size=10,
max_gen=200,
mutation_rate=0.1,
selection_rate=0.6,
selection_strategy="roulette_wheel",
problem_type=float, # Defines the possible values as float numbers
variables_limits=(-10, 10) # Defines the limits of all variables between -10 and 10.
# Alternatively one can pass an array of tuples defining the limits
# for each variable: [(-10, 10), (0, 5), (0, 5), (-20, 20)]
)
solver.solve()
```

### selection strategy

It is possible to choose the selection strategy that the algorithm will use to select the parents that will be used for generating new offsprings for the next generation. The options are:

`roulette_wheel`

`random`

`two_by_two`

`tournament`

**roulette wheel**

This selection strategy orders the individuals in the selection pool by probability, with the fittest individuals having higher odds of being selected.

**random**

This selection procedure selects randomly individuals from the selection pool, following in essence a similar procedure as the roulette wheel, but with the same probabilities for each individual.

**two_by_two**

This strategy groups the individuals in the mating pool 2 by 2, from top to bottom.

**tournament**

This strategy will select 3 individuals candidates for each parent position, which are then sorted by their fitness and from which the fittest one is selected.

## Specific Applications

In the real world, there's usually the need to adapt a genetic algorithm implementation to each individual problem.
Thus, `geneal`

offers the user a level of customization that aims to be both versatile and relatively simple. For that,
one just has to create a class which inherits from the `BinaryGenAlgSolver`

or `ContinuousGenAlgSolver`

base classes, and on which some overriding methods are defined. This allows the user to control the main steps of a GA:

- fitness function
- population initialization
- mating between individuals (creation of offsprings)
- mutation of the population

A boilerplate template of such a class is shown below:

```
from geneal.genetic_algorithms import ContinuousGenAlgSolver, BinaryGenAlgSolver
class TemplateChildClass(ContinuousGenAlgSolver, BinaryGenAlgSolver):
def __init__(self, *args, **kwargs):
BinaryGenAlgSolver.__init__(self, *args, **kwargs)
ContinuousGenAlgSolver.__init__(self, *args, **kwargs)
def fitness_function(self, chromosome):
"""
Implements the logic that calculates the fitness
measure of an individual.
:param chromosome: chromosome of genes representing an individual
:return: the fitness of the individual
"""
pass
def initialize_population(self):
"""
Initializes the population of the problem
:param pop_size: number of individuals in the population
:param n_genes: number of genes representing the problem. In case of the binary
solver, it represents the number of genes times the number of bits per gene
:return: a numpy array with a randomized initialized population
"""
pass
def create_offspring(
self, first_parent, sec_parent, crossover_pt, offspring_number
):
"""
Creates an offspring from 2 parents. It uses the crossover point(s)
to determine how to perform the crossover
:param first_parent: first parent's chromosome
:param sec_parent: second parent's chromosome
:param crossover_pt: point(s) at which to perform the crossover
:param offspring_number: whether it's the first or second offspring from a pair of parents.
Important if there's different logic to be applied to each case.
:return: the resulting offspring.
"""
pass
def mutate_population(self, population, n_mutations):
"""
Mutates the population according to a given user defined rule.
:param population: the population at a given iteration
:param n_mutations: number of mutations to be performed. This number is
calculated according to mutation_rate, but can be adjusted as needed inside this function
:return: the mutated population
"""
pass
```

### Travelling Salesman Problem

One of the possible applications of genetic algorithms is to the Travelling Salesman Problem. This problem is NP hard, as the number of possible solutions grows with the factorial of the number of variables, and therefore, genetic algorithms are a good fit for approximating solutions to these problems.

As this particular problem has its own sets of constraints, a specific class adapted to this problem is provided
in `TravellingSalesmanProblemSolver`

, which can be used out of the box to virtually
all problems of this kind. As a minimum input, this class requires the user to provide a
networkx undirected graph containing all the nodes
representing the problem and with each node connected to every other node by edges with the respective
associated cost (weight). To build this graph, one can use the `create_graph`

method, as shown below:

```
import turf
from geneal.applications.tsp.helpers import create_graph
from geneal.applications.tsp.examples.world_capitals import world_capitals_dict
G = create_graph(
world_capitals_dict, # a python dictionary containing the nodes as keys
turf.distance, # function to use to calculate distance between nodes
lon=lambda x: x["CapitalLongitude"], # lambda function on how to retrieve the longitude
lat=lambda x: x["CapitalLatitude"], # lambda function on how to retrieve the latitude
)
```

After having a built graph, one can pass it directly to `TravellingSalesmanProblemSolver`

, and the number of genes
will be automatically retrieved from the number of nodes in the graph.

```
from geneal.applications.tsp.travelling_salesman_problem import TravellingSalesmanProblemSolver
from geneal.applications.tsp.examples.world_capitals.graph import G
tsp_solver = TravellingSalesmanProblemSolver(graph=G)
```

Again, one can control the solver parameters as before, by providing them on the initialization:

```
from geneal.applications.tsp.travelling_salesman_problem import TravellingSalesmanProblemSolver
from geneal.applications.tsp.examples.world_capitals.graph import G
tsp_solver = TravellingSalesmanProblemSolver(
graph=G,
pop_size=10, # population size (number of individuals)
max_gen=500, # maximum number of generations
mutation_rate=0.05, # mutation rate to apply to the population
selection_rate=0.5, # percentage of the population to select for mating
selection_strategy="tournament", # strategy to use for selection.
mutation_strategy="random_inversion" # strategy to use for mutation. see below for more details.
)
```

**specific TSP parameters**

Being a particular use case for genetic algorithms, the Travelling Salesman Problem has also specific settings that
allow the user to control the convergence for each use case. One of such parameters is `mutation_strategy`

, which
can be one of the following:

`2-opt`

,`random_swap`

,`random_inversion`

,`random_gene_nearest_neighbour`

,`worst_gene_random`

,`worst_gene_nearest_neighbour`

,`select_any_mutation`

,

Below some brief explanation is given on each of the options:

**2-opt**

It performs a 2-opt mutation on a tour. It selects randomly 2 edges from the tour and combines the resulting sub tours by swapping them. More details can be found here.

**random swap**

A random swap mutation will choose randomly 2 genes from a given tour and swap them around. This is the kind of mutation that most closely resembles a typical genetic algorithm mutation.

**random inversion**

A random inversion swap will choose a consecutive subset from the tour and reverse it. The size of the subset is also chosen randomly.

**random gene nearest neighbour**

This is a knowledge-based mutation, where a randomly selected gene is shifted next to its closest neighbour. More details can be found in point 4.2.7.

**worst gene random mutation**

This is again a knowledge-based mutation, where a randomly selected gene is swapped with the gene contributing most to the cost of the tour. More details can be found in point 4.2.3.

**worst gene random mutation**

This is again a knowledge-based mutation, where gene contributing most to the total cost of the tour is moved next to one of its neighbours. More details can be found in point 4.2.4

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