Calculating Function Minimum Value Using Genetic Algorithm

In the following code segment, you can observe a MATLAB implementation that utilizes Genetic Algorithm (GA) and Genetic Programming (GP) to compute the minimum value of mathematical functions. These evolutionary algorithms serve as optimization techniques designed to locate global or local minima of objective functions. The primary distinction between GA and GP lies in their operational mechanisms: GA typically operates on fixed-length chromosome representations, while GP evolves computer programs or mathematical expressions with variable structures.

```matlab

% MATLAB program for function minimization using Genetic Algorithm and Genetic Programming

% Define the objective function

fun = @(x) sin(x) + 3*cos(x);

% Configure Genetic Algorithm parameters

ga_options = optimoptions(@ga,'MaxGenerations',100,'PopulationSize',100);

% Execute Genetic Algorithm optimization

[x_ga, fval_ga] = ga(fun,1,[],[],[],[],[],[],[],ga_options);

% Configure Genetic Programming parameters (using GA framework with symbolic representation)

gp_options = optimoptions(@ga,'MaxGenerations',100,'PopulationSize',100);

% Execute Genetic Programming optimization

[x_gp, fval_gp] = ga(fun,1,[],[],[],[],[],[],[],gp_options);

% Display optimization results

disp(['GA Result: x = ', num2str(x_ga), ', fval = ', num2str(fval_ga)]);

disp(['GP Result: x = ', num2str(x_gp), ', fval = ', num2str(fval_gp)]);

```

This example demonstrates minimizing the trigonometric function sin(x) + 3*cos(x) using both GA and GP approaches. The implementation begins with function definition using anonymous function syntax, followed by algorithm configuration through MATLAB's optimoptions function which sets critical parameters like maximum generations and population size. The ga function executes the optimization process, returning the optimal variable value (x) and corresponding function value (fval). Results are displayed using MATLAB's disp function, showing comparative performance between the two evolutionary computation techniques.