Implementation of Genetic Algorithm Using MATLAB Code

Genetic Algorithm is an optimization method that simulates natural selection and genetic mechanisms, particularly suitable for solving complex nonlinear integer programming problems. MATLAB provides powerful tools to implement this algorithm, with flexibility that enables handling various constraints and objective functions.

Implementing genetic algorithms in MATLAB typically utilizes the `ga` function from the Global Optimization Toolbox, which can handle nonlinear, mixed-integer programming problems. The core algorithmic steps include:

Encoding and Initialization: Variables are encoded into chromosome forms (binary or real-valued encoding), with random generation of initial population using functions like `rand` or `randi`. Fitness Evaluation: Individual fitness values are calculated through the objective function, distinguishing between superior and inferior solutions. This is implemented via a custom fitness function that returns scalar values. Selection Operation: Employing roulette wheel or tournament selection mechanisms to preserve high-fitness individuals, implemented using MATLAB's selection operators with probability distributions. Crossover and Mutation: Generating new solutions through crossover recombination, while mutation operations increase diversity to prevent premature convergence. These are controlled by parameters like `CrossoverFraction` and `MutationFcn`. Termination Conditions: Algorithm stops when reaching maximum iterations (`MaxGenerations`) or when fitness stabilizes (`StallGenLimit`).

For nonlinear integer programming, integer variable constraints need to be set in `ga` using the `IntCon` parameter, while adjusting crossover rate, mutation rate, and other parameters to balance exploration and exploitation. MATLAB's vectorized operations significantly enhance computational efficiency, particularly suitable for large-scale problems through matrix-based computations.

The advantage of this method lies in its gradient-free nature, ability to escape local optima, and suitability for non-differentiable or discrete optimization scenarios such as resource allocation, path planning, and engineering design optimization. The algorithm's implementation benefits from MATLAB's built-in visualization tools like `gaplot` functions for monitoring convergence behavior.