Design And Application Of Experiments With Mixture Bace On Particle Swarm Optimization

Research formula ratio is a problem that often meet in production, managementand scientific experiments. Mixing experiment is doing test that in differentpercentages of each component of the combination. Find the relationship betweenthe response variable and the respective components. Usually,these componentsare percentage, and their sum must be1. The purpose of mixing experimental designwas found Scheffe regression equation that have a better accuracy by experimentwith different combinations of percentages. Select the optimal combination ofmixing from the regression equation to guide the actual production. People oftenuse contour method to find the optimal solution from the regression equation.This method is subjective and often can’t get the optimal solution, and thismethod’s relatively is poor when fraction is more.Particle Swarm Optimization（PSO） algorithm that developed in recent yearsis a iterative optimization algorithm，it uses position-speed update formulato iterative. Particle swarm optimization have a wide range of applicationsin practice because of its easy implementation、fast convergence and highaccuracy. But nobody use the PSO algorithm applied to the mixing experiments.It is the first time that this paper use PSO algorithm to fount optimal solutionfrom the regression equation of mixture experiment. Consider mixing conditionsin the standard PSO algorithm, get the new PSO algorithm: Mixing Particle SwarmOptimization. And the penalty function method applied to the PSO algorithm, getanother new PSO algorithm: penalty function of Particle Swarm Optimization. Andmade some empirical analysis for algorithm parameter settings and theparameters,affecting to algorithm. Empirical evidence shows that MixingParticle Swarm Optimization will convergence when it iterations about200times.It independent from the initial particle number.The initial number of particlesis affecting the iteration times that algorithm search the optimal solution. The more the number of particles, the faster find the optimal solution.Experimental results show that two algorithms can converge to optimal solutionwell in conditions of low-dimensional, in the high-dimensional, Mixing ParticleSwarm Optimization still converge to the optimal solution well, But the penaltyfunction PSO algorithm is difficult to converge.This new Mixing Particle Swarm Optimization is easy to use. It can be appliedto almost all mixing optimization problems. It just need change the fitnessfunction and constraints matrix. Expect this new Mixing Particle SwarmOptimization problems can be a standard methods of Mixing Optimization.