Including Upper And Lower Bound Constraints Based On Genetic Algorithm Optimization Of Mixture Experiments Prescription

The mixing problem with respect to formula and their proportion are commonly involved in many real-world fields such as industrial and agricultural production, the drug synthesis and some other scientific researches. The blend is made of several components according to specific proportions, and some characteristics of the several components are not related to absolute value of product, but the corresponding percentage of ingredients. In the field of medicine, there is a growing need to find the optimal formulation in some drug experiments, which is, the responses, some significant indicators, are required to be maximized or minimized in some specific conditions. It makes a foundation for the following steps:model a suitable mathematical model, determine a approach obtaining the optimal formula and its proportion based on the mixture design, in order that some goals can be reached such as improve the effectiveness, enhance the production and lower relevant cost, all these difficult obstacles remain to be solved in the mixing problems.Aimed at the mixture experiments issues involving lower and upper constraints, national and international scholars come up with extreme vertices mixture design and D-optimal mixture design on the basis of optimal design principle. Classical methods are often adopted in a single objective optimization problem designed by the above two types of design, the several strategies of the direct method, contour plots method belong to traditional scope, However, these approaches exist some shortcomings in the application such as a great deal of subjectivity and local optimum to some extent. In order to avoid those weaknesses, it is necessary to find out the alternative methods which can find out the entire solutions in the mixture experiment having upper and lower boundary constrains, while genetic algorithms (GA) developed in recent years is a stochastic optimization search method of simulating biological evolutionary process. The method, suitable for multi-variable nonlinear optimization, shows its outstanding advantages in solving global optimization problems due to its high efficiency, robustness as well as not subject to optimization function which must be continuous; another reason is that its search process can effectively avoid the local optimization.The two types of mixture design, the extreme vertices mixture design and D-optimal mixture design containing upper and lower boundary, will be discussed in this paper. After the insight into the principle of the single objective genetic algorithms, a further study will be carried out on the pharmaceutical optimization application of a single-objective mixture formulation by means of the GA performed by the Genetic algorithm platforms vl.0software. The main content in this paper:Section1The key content is a summary of mixing experimental design containing the upper and lower bounds constraints. This part introduces the concept of mixture experiments, the structure of model and the principle of the mixture experiments with upper and lower bounds constraints containing extreme vertices mixture design and D-optimal mixture design; the scope where the above designs should be applied and how to determine the experiment program will also be involved.Section2The main idea is an overview of a single-objective optimization by the GA. The principle of genetic algorithm, the randomized search process and the outstanding advantages compared with the traditional single-objective optimization method will be reviewed in section2.Section3This part will present the evaluation to the effectiveness of the mixing formulation with upper and lower bounds constraints by the single objective genetic algorithm. It is conducted that the single-objective genetic algorithm will be simulated by the mixing test functions, the results show that in the measurable range of the independent variable, the genetic algorithm can be substantially consistent with the contour plot method optimal solution; The optimal solutions obtained by derivation method are beyond the experiment range of the independent variables so that they do not have practical significance; The approach has a certain subjectivity when it determines the solutions while the GA is able to find the acceptable ones which meet the function constraints. Both the more accurate combinations of independent variables and the stable search results are capable of being guaranteed through the GA, these findings demonstrate that this approach and its program are satisfactory and feasible when optimizing a single objective mixing experiment results, which actually is a practical optimization application on mixture problem.Section4An exploratory study to the mixture optimal formulation based on genetic algorithm will be discussed. The literature results designed by the extreme vertices mixture design and D-optimal mixture design will be optimized using the genetic algorithm to select the best formulations, which will be compared with ones optimized by the conventional methods of the original text.In the optimal formula study of a self-nanoemulsifying drug delivery system of persimmon leaf extract (PLE), the formulation was optimized by an extreme vertices experimental design and genetic algorithms; it was showed that the search results stabilized after an evolution of30generations, when proportion of three components of oil, surfactant and co-surfactant derived from micro-emulsion delivery system, was33.0%,10.0%,57.0%, respectively, the objective function y can be maximized to0.9558, which outperforms0.0048than the maxima0.9510obtained by the contour diagram method. In the optimized nanoemulsion formulation, the total flavonoids solubility in the delivery system was49.12mg/g more1.32mg/g than one using the contour diagram strategy and the smaller droplet size reached22.92nm lowering1.32nm than the contour diagram value.D-optimal mixture design and the genetic algorithm was employed to select acceptable formulation of the antibacterial agent against Staphylococcus aurous, and its solutions were stable when evolution generations were up to10. The ratio of three formulations, Nisin, chitosan, rosemary extract in natural antibacterial agent, was13.7:60.9:25.4, where the maxima of inhibition rate, the evaluating indicator, could be obtained up to81.768which were superior to the result by the contour map.In summary, the single objective genetic algorithm is reliable in the optimization for the formula and individual ratio designed by mixture experiments with upper and lower boundary constrains, additionally, its search effectiveness were satisfactory, hence it is worthwhile promoting this technology in solving the optimization problem of the practical mixture experiments.