fmga 0.1.8

Genetic algorithms for 2-dimensional function maximization.

## fmga
**fmga** (**f**unction **m**aximization through **g**enetic **a**lgorithms) is a package that takes a genetic algorithm approach to maximization problem of non-convex objective functions in two dimensions.

The idea is to sample an evolving population of points converging to the function maximum over many iterations.

Given a function on two variables x and y, say:
```python
def f(x, y):
return x - math.sin(y) + 28
```
Pass this function as the *objective_function* argument to the **population2D** constructor (lambdas work too!):
```python
population = population2D(objective_function=f, population_size=60)
```
The population can be set to breed and iterate by using the **.converge()** method.
```python
population.converge(iterations=20)
```
To perform only one iteration of breeding and mutating, do:
```python
population.iterate()
```
Access population mean fitness and mean L1 diversity stats through the _.mean_fitness_ and _.mean_diversity_ attributes:
```python
print(population.mean_fitness, population.mean_diversity)
```

The **.best_estimate()** method returns the point closest to the function point of maxima in the population, as a **Point2D** object.
```python
best_point = population.best_estimate()
```
Every **Point2D** object has attributes 'x' and 'y', signifying the coordinates of the maxima point.
```python
print(best_point.x, " ", best_point.y)
```
To find the value of the function at this point, use:
```python
print(best_point.fitness)
```

The objective function doesn't have to be differentiable, or even continuous in the specified domain!
The population of 2-dimensional points undergoes random mutations - and is selected through elitism along with breeding with selection weights inversely proportional to fitness and diversity ranks.

## population2D Class Methods
The population2D constructor takes the following arguments:

**population_size** (default = 60) Number of points in the population.
**objective_function** The function to maximize!
**elite_fraction** (default = 0.1) Fraction of the population's points to be kept as elite during breeding. Must be between 0 and 1, inclusive.
**x_min, x_max, y_min, y_max** (default = 0, 100, 0, and 100 respectively) The domain where the points are spread.
**mutation_probability** (default = 0.05) How likely is is for a single point to mutate - this probability is the same for all points in the population.
Must be between 0 and 1, inclusive.
**mutation_range** (default = 5) The range of the mutation when it does occur. Note that the point will never mutate out of the domain defined!
**verbose** (default = 2) How much output to be displayed when iterating population after population. Must take values 0, 1 or 2 - 2 representing the most output, and 0 representing none.