Genetic Algorithm for Optimization in MATLAB

This MATLAB script implements a basic Genetic Algorithm (GA) to solve basic optimization problem (single objective). The GA operates by creating a population of potential solutions, represented as binary strings, and iteratively improving them through genetic operations like crossover and mutation.

Key Features

• Binary Representation: The script uses a binary string to represent each candidate solution.
• Population Size Adjustment: Ensures the population size (N) is even for pairwise crossover.
• Selection: Implements tournament selection to choose parents for the next generation.
• Crossover: Employs single-point crossover with a defined crossover rate (pc).
• Mutation: Applies mutation with a specified mutation probability (pm).
• Cost Evaluation: Evaluates each candidate using a CostFunction, which needs to be defined separately.
• Convergence Tracking: Tracks and plots the best cost value across generations.

Usage

1. Define the Cost Function: Implement the CostFunction that evaluates the fitness of a candidate solution. The function should take a binary string as input and return a cost value.

2. Configure GA Parameters: Set the GA parameters such as the number of variables (nVar), population size (N), maximum generations (maxGen), crossover rate (pc), and mutation rate (pm).

3. Run the Script: Execute the script in MATLAB. It initializes a population, applies genetic operations, and evolves the population for a specified number of generations.

4. View Results: The script displays the best cost value at each iteration and plots the convergence of the best cost over time.

Script Structure

• Initialization: Sets up the GA by initializing the population and evaluating the initial candidates.
• Main Loop: Runs the GA operations for a set number of generations. Each iteration involves selection, crossover, mutation, and the generation of a new population.
• Results: At the end of the GA run, the script plots the best cost found in each iteration, showing the algorithm's progress.

Note

• The script assumes that a CostFunction is defined elsewhere in the environment. This function should be tailored to the specific optimization problem you're addressing.
• The script includes a visualization (plot) of the algorithm's performance over iterations, which helps in assessing the convergence.

Conclusion

This MATLAB script provides a foundational implementation of a Genetic Algorithm for optimization problems. Users can adapt the script to their specific problems by modifying the cost function and tuning the GA parameters.