Particle Swarm Optimization Techniques for Finding Optimal Mixture Designs

Particle Swarm Optimization (PSO) is a meta-heuristic algorithm that has been shown to be successful in finding the optimum solution or close to the optimum for a wide variety of real and complicated optimization problems in engineering and computer science. This paper adapts PSO methodology by first solving an optimization problem on the hypercube and then projecting the solution onto the q-simplex optimization space to find different optimal designs for mixture models commonly used in agronomy, food science and pharmaceutical science. We show that PSO is also flexible in that it can be modified straightforwardly to find optimal designs for log contrast models and constrained mixture models. We conclude with a list of advantages of this simple and novel way for finding optimal mixture designs over current methods.