A Modified Particle Swarm Optimization Technique for Finding Optimal Designs for Mixture Models

Particle Swarm Optimization (PSO) is a meta-heuristic algorithm that has been shown to be successful in solving a wide variety of real and complicated optimization problems in engineering and computer science. This paper introduces a projection based PSO technique, named ProjPSO, to efficiently find different types of optimal designs, or nearly optimal designs, for mixture models with and without constraints on the components, and also for related models, like the log contrast models. We also compare the modified PSO performance with Fedorov's algorithm, a popular algorithm used to generate optimal designs, Cocktail algorithm, and the recent algorithm proposed by [1].

[1]  Mong-Na Lo Huang,et al.  MODEL-ROBUST D- AND A-OPTIMAL DESIGNS FOR MIXTURE EXPERIMENTS , 2009 .

[2]  N. Becker,et al.  MODELS AND DESIGNS FOR EXPERIMENTS WITH MIXTURES , 1978 .

[3]  Andries Petrus Engelbrecht,et al.  Fundamentals of Computational Swarm Intelligence , 2005 .

[4]  André I. Khuri,et al.  Linear Model Methodology , 2009 .

[5]  H. Wynn.  Results in the Theory and Construction of D‐Optimum Experimental Designs , 1972 .

[6]  Weichung Wang,et al.  Using animal instincts to design efficient biomedical studies via particle swarm optimization , 2014, Swarm Evol. Comput..

[7]  J. Aitchison,et al.  Log contrast models for experiments with mixtures , 1984 .

[8]  Yaming Yu,et al.  D-optimal designs via a cocktail algorithm , 2009, Stat. Comput..

[9]  Tushar Nahata,et al.  Formulation optimization of long-acting depot injection of aripiprazole by using D-optimal mixture design. , 2009, PDA journal of pharmaceutical science and technology.

[10]  Ralf-Dieter Hilgers,et al.  Optimal designs for mixture amount experiments , 1995 .

[11]  Muriel Bigan,et al.  Efficient size control of amphiphilic cyclodextrin nanoparticles through a statistical mixture design methodology. , 2005, Journal of pharmacy & pharmaceutical sciences : a publication of the Canadian Society for Pharmaceutical Sciences, Societe canadienne des sciences pharmaceutiques.

[12]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[13]  Weng Kee Wong,et al.  Optimal designs for mixture models with amount constraints , 2013 .

[14]  James M Whitacre,et al.  Survival of the flexible: explaining the recent dominance of nature-inspired optimization within a rapidly evolving world , 2009, 0907.0332.

[15]  James M. Whitacre,et al.  Survival of the flexible: explaining the recent popularity of nature-inspired optimization within a rapidly evolving world , 2011, Computing.

[16]  B. M. Fulk.  MATH , 1992 .

[17]  Ling-Yau Chan,et al.  Optimal design for a linear log contrast model for experiments with mixtures , 1988 .

[18]  R. D. Cook,et al.  A Comparison of Algorithms for Constructing Exact D-Optimal Designs , 1980 .

[19]  J. Kiefer.  General Equivalence Theory for Optimum Designs (Approximate Theory) , 1974 .

[20]  Lynne B. Hare,et al.  Experiments with Mixtures: Designs, Models and the Analysis of Mixture Data, 2nd Ed. , 1991 .

[21]  O. Dykstra.  The Augmentation of Experimental Data to Maximize [X′X] , 1971 .

[22]  Shuangzhe Liu,et al.  A V-optimal design for Scheffé's polynomial model , 1995 .

[23]  Manisha Pal,et al.  Optimum Mixture Design Using Deficiency Criterion , 2008 .

[24]  Z. Galil,et al.  Comparison of Simplex Designs for Quadratic Mixture Models , 1977 .

[25]  M. Agha,et al.  Experiments with Mixtures , 1992 .

[26]  James M. Whitacre.  Recent trends indicate rapid growth of nature-inspired optimization in academia and industry , 2011, Computing.

[27]  Fattah Mikaeili,et al.  D-optimum design for cubic without 3-way effect on the simplex , 1989 .

[28]  Sami Nazzal,et al.  D-Optimal Mixture Design: Optimization of Ternary Matrix Blends for Controlled Zero-Order Drug Release From Oral Dosage Forms , 2006, Drug development and industrial pharmacy.

[29]  N. G. Becker.  Models for the Response of a Mixture , 1968 .

[30]  Fattah Mikaeili,et al.  D-optimum design for full cubic on q-simplex , 1993 .

[31]  J. Cornell.  Experiments with Mixtures: Designs, Models and the Analysis of Mixture Data , 1982 .

[32]  S Furlanetto,et al.  Mixture experiment methods in the development and optimization of microemulsion formulations. , 2011, Journal of pharmaceutical and biomedical analysis.

[33]  Heng Peng,et al.  DUAL-OBJECTIVE OPTIMAL MIXTURE DESIGNS: DUAL-OBJECTIVE OPTIMAL MIXTURE DESIGNS , 2012 .

[34]  Manisha Pal,et al.  Minimax designs for optimum mixtures , 2008 .

[35]  Otto Dykstra,et al.  The Augmentation of Experimental Data to Maximize |X′X|@@@The Augmentation of Experimental Data to Maximize |X prime X| , 1971 .

[36]  Ling-yau. Chan,et al.  Optimal design for experiments with mixtures , 1986 .

[37]  Andrej Pázman,et al.  Foundations of Optimum Experimental Design , 1986 .

[38]  Zhenyu Zhao,et al.  optimization of extended zero-order release gliclazide tablets using D-optimal mixture design. , 2008, Yakugaku zasshi : Journal of the Pharmaceutical Society of Japan.

[39]  Weichung Wang,et al.  Minimax optimal designs via particle swarm optimization methods , 2015, Stat. Comput..

[40]  ウラニシ.  Optimum design for the special cubic regression on the q-simplex , 1964 .

[41]  Tushar Nahata,et al.  D-optimal designing and optimization of long acting microsphere-based injectable formulation of aripiprazole. , 2008, Drug development and industrial pharmacy.

[42]  Miao-Kuan Huang,et al.  D s -Optimal Designs for Quadratic Log Contrast Model for Experiments with Mixtures , 2009 .

[43]  Miao-Kuan Huang,et al.  $${\phi_p}$$-optimal designs for a linear log contrast model for experiments with mixtures , 2009 .

[44]  R. Eberhart,et al.  Comparing inertia weights and constriction factors in particle swarm optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[45]  Toby J. Mitchell,et al.  An Algorithm for the Construction of “D-Optimal” Experimental Designs , 2000, Technometrics.

[46]  Stefanie Biedermann,et al.  On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm , 2013 .