Optimization Applications Of Multi-Objective Drug Mixture Data Based On Hyperspherical Transformation And Partial Least Squares

Objective:The regression model of mixture data is recommended with applying the methods of dimension-reduction approach through a hyperspherical transformation and partial least squares regression. After establishing the unconstrained model of mixture data, the genetic algorithm is proposed for solving the problem of multi-objective optimization of mixture formulation. The optimization results of mixture data using genetic algorithm and response surface diagram are compared, with studies from the literature. The research offers a reasonable method for modeling and optimizing of mixture data. Methods:An exploratory study using the two types of mixture data which embedded with zero components and which without zero components was conducted. The experiment was designed using the mixture components as independent variables, the properties of drug as dependent variables. We use a dimension-reduction approach through a hyperspherical transformation that is capable of resolving the unit-sum in mixture data and use partial least squares regression that is capable of resolving the multiple correlation among variables for establishing the unconstrained model of mixture data. A global optimum genetic algorithm is using for multi-objective optimization of mixture formulation. The optimization results of mixture data using genetic algorithm and response surface diagram are compared, with studies from the literature. Results:(1)The evaluation to the effectiveness of genetic algorithm based on hyperspherical transformation: choose test functions of mixture design for simulation test of software packages, then evaluating the feasibility of the strategy, which use a dimension-reduction approach through a hyperspherical transformation that is capable of resolving the unit-sum in mixture data and use genetic algorithm to optimize the mixture formulation. It is concluded that the genetic algorithm based on hyperspherical transformation can be substantially consistent with the contour plot method optimal solution with Pareto solutions. And the strategy is a practical optimization application to mixture problem.(2)A case of mixture data which embedded with zero components: Using a D-optimal mixture design to select the optimal combination of nano composite precursor, nondominated sorting genetic algorithm is a better choice to seek a optimal solution, one of recipes is predicted levels of CH, PVA and HA are 25.20, 1.14 and 73.66% respectively. The predicted values of TGA and density are 739.02℃ and 2.03 g/cm3 respectively. Compared with the solution by response surface diagram method in original literature, the TGA was increased 12.6℃, which increased 1.73% and the density was decreased 0.4 g/cm3, which decreased 16.46%.(3)A case of mixture data which without zero components: Using a d-optimal design for optimizing a microemulsion having desirable formulation characteristics, whose optimal solutions were obtained by nondominated sorting genetic algorithm. The microemulsion with oil, Smix and water in content of 5.01%, 17.70% and 77.29% was obtained as the optimized microemulsion with the globule size of 46.94 nm, percent transmittance value of 99.64%, skin retention value of 42.062m/ cmg, Perm6 h value of 16.952m/ cmg.Compared with the original solution by response surface diagram method, the globule size was decreased 7.46 nm, which decreased 13.71%, percent transmittance value increased 0.49%, which increased 0.49%, skin retention value increased 1.72m/ cmg, which increased 4.21%, Perm6 h value increased 0.66 m/ cmg2,which increased 4.05%. Both of Skin retention value and Perm6 h value are greatly improved as important evaluation index. Genetic algorithm can not only give a good optimal solution, but also provides a wealth of non-inferior pareto solutions. Conclusions:The dimension-reduction approach through a hyperspherical transformation can resolve the unit-sum in mixture data. And the partial least squares regression can resolve the multiple correlation among variables. The two approaches are applied to structure models in analysis of mixture data. The multi-objective genetic algorithm is proposed for solving the problem of optimization. The optimal formulation can be obtained though inverse transform of hyperspherical transformation. The entire solution for the analysis of mixture data is reasonable and practicable. The methods can effectively solve the multi-objective optimization problem in drug mixture data, and it also can be extended to similar optimization applications of other sectors.