## Overview

This vignette demonstrates how to use the
`genetic.algo.optimizeR`

package to optimize the function
\(f(x) = x^2 - 4x + 4\) using a genetic
algorithm.

## Aim

Optimize the function \(f(x) = x^2 - 4x + 4\) to find the value of \(x\) that minimizes the function.

## Method

### Initial Population

We start with a population of three individuals: \(x_1 = 1\), \(x_2 = 3\), and \(x_3 = 0\).

```
# devtools::install_github("danymukesha/genetic.algo.optimizeR", upgrade = c("never"),)
library(genetic.algo.optimizeR)
```

```
# Initialize population
population <- initialize_population(population_size = 3, min = 0, max = 3)
population
#> [1] 0 1 2
```

### Evaluation

We evaluate the fitness of each individual by calculating \(f(x)\) for each \(x\) value:

```
# Evaluate fitness
fitness <- evaluate_fitness(population)
fitness
#> [1] 4 1 0
```

### Selection

We select individuals \(x_1\) and \(x_2\) as parents for crossover because they have higher fitness.

```
# Perform selection
selected_parents <- selection(population, fitness, num_parents = 2)
selected_parents
#> [1] 2 1
```

### Crossover and Mutation

We perform crossover and mutation on the selected parents to generate offspring: \(x_1' = 1\), \(x_2' = 3\).

### Replacement

We replace individual \(x_3\) with offspring \(x_1'\), maintaining the population size.

```
# Replace individuals in the population
new_population <- replacement(population, mutated_offspring, num_to_replace = 1)
new_population
#> [1] 2 1 2
```

```
# Termination
# Repeat the above steps(from Evaluation) for multiple generations or until a termination condition is met.
```