Dr. John Borkowski (Dept. of Mathematical Sciences, MSU)

09/18/2023

Abstract:

In Particle Swarm Optimization (PSO), a particle represents a candidate solution to an optimization problem. The objective function $F$ measures a particle's fitness as a solution. That is, $F$ takes a particle as input and outputs a fitness value. With PSO, an initial population of particles is generated, and at each iteration, $F$ is evaluated for each particle. The “global” (or, historically best) particle and the “local” (or best particle for that iteration) particle are stored. Each particle then moves within the solution space utilizing the global best and local best, plus a random directional velocity component. The global and local best particles are then updated. The PSO process continues producing a more fit solution until an acceptable solution has evolved.

 

In this talk, an introduction to Particle Swarm Optimization (PSO) will be given followed by applications that include simple linear regression, maximum Likelihood estimation for the two-parameter Weibull and three-parameter Lognormal distributions, nonlinear models, the rastrigin function, generation of optimal response surface designs, and finding minimum volume ellipses bootstrap confidence regions.