Minimize the dejong5 Function using Steepest Descent with 50 Particles

This animation, created using MATLAB, illustrates how the steepest descent algorithm would operate when implemented on the dejong5 function (see previous video). Because each particle's movement is determined by the negative of the gradient, the only way the algorithm is successful is if the initial conditions (which are uniformly randomly generated) place a particle close enough to "fall" into the deepest valley. For this reason, a few trials could be required before the algorithm is successful. In addition, the steepest descent method does not "scale up" very well for functions of many variables. It can be shown that the PSO algorithm performs comparably better (than steepest descent) when the objective function has high dimension (200 variables, 500 variables, etc.).