**7. Search optimization**

The optimization of a single answer or the simultaneous optimization of several responses from the thus chosen models must be carried out graphically, numerically, with artificial neural networks (ANNs), and/or by extrapolation outside the domain.

#### **7.1 Graphical optimization**

The goal of graphical optimization is to choose the optimum formulation from a feasible factor space region. To do this, the factor values are screened in accordance with the desired limits of the response variables. A combination of the following approaches can be used to optimize graphics: ANNs, canonical analysis, overlay plots, brute-force searches, and mathematical optimization are further methods for optimizing numerous replies.

#### *7.1.1 Brute-force search*

The simplest and most precise optimization search technique is brute-force search, commonly referred to as exhaustive search because it involves looking at every single point in the function space. Here, the response variables of the formulations that can be created by practically every feasible arrangement of independent factors are

#### *Formulation by Design: An Overview DOI: http://dx.doi.org/10.5772/intechopen.109702*

filtered [24]. Then, by further reducing the possible region, the acceptable boundaries are established for these responses, and a thorough search is once more carried out. The final viable space (also known as the grid search), which satisfies the most requirements established during experimentation, is searched for the optimum formulation. The benefit of using this thorough approach is that there is very little risk of missing the actual best formulation.

## *7.1.2 Overlay plots*

To visually find the optimal compromise, the bi-dimensional response contour plots are stacked over one another. An overlay plot or integrated contour plot is what this is known as. The permissible range of objective values is defined with minimum and maximum values. The area that contains all acceptable responses is highlighted. By balancing several reactions, an optimum is found within this region.
