Research On Uncertain Constraint Modeling And Searching Algorithms Of Optimal Design For Mixture Experiments

Mixture experimental design can be a powerful tool in many fields,for example,the optimal formula finding process in both industry and academic experiments.There are many methods generated by researchers in this filed.This thesis mainly considers about mathematical modeling for uncertain constraints and computational algorithm for optimal design.The thesis has three parts:The first part gives an introduction to the history of experimental design.As the thesis is mainly discussing about optimal mixture design,there are some sections intro-ducing the optimal design,mixture design,equivalence theorem.The second part will introduce our main work,i.e.innovation points,which will be illustrated with simulation data.We will give a method for modeling the complex uncertain constraints mathematically.Properties for both uncertain inequalities and the operable design region formed by constraints will be given.The method for splitting the uncertain constraints into normal inequalities is illustrated as a theorem with proof.The CONSIM algorithm will be introduced for getting the extreme vertices of the operable region.Classical computational algorithms will be introduced.As the points within the operable region can be expressed by a linear combination of vertices,this property can be used as a basic condition for constructing the modified MDRS algorithm.An example will illustrate the algorithm for its efficiency.We will propose a matrix algorithm for finding the bound of the region formed by uncertain inequalities.The matrix algorithm can overcome the disadvantage of CON-SIM algorithm for it did not rely heavily on software.The operation process of matrix algorithm is easy going without heavy computational burden.Especially,it has high efficiency in high dimension situations.Next section is mainly introducing the generalized uncertain constraint,which adds coefficient for each component.The coefficients here can be expressed as density of effective ingredient in each herb medicine.The properties of this new operable region within simplex for mixture design are given.The thesis also gives a theory for splitting the new uncertain inequalities into normal ones,then the vertices of this region can be gotten by CONSIM algorithm.A similar compress dimensionality reduction algorithm will proposed for finding the optimal design.An example will be given here for illustrat-ing the algorithm and showing its efficiency.The last part is the conclusion and future works that may be worth doing,which can be divided into two parts.The first part mainly summarized the whole works of this thesis including the process of generalizing uncertain inequalities into general ones which add coefficients on components;Second part propose some works that may worth doing in future based on the first part of this chapter.It's about more actual application situation and improving the property of robust for optimal design by bringing in the other design methods,such as,uniform design,axial design,etc.