The optimal region to run a process is usually determined after a sequence of experiments is conducted and a series of empirical models are obtained. In many engineering and science applications, experiments are conducted and empirical models are developed with the objective of improving the responses of interest. From a mathematical point of view, the objective is to find the operating conditions (or factor levels) X₁, X₂, ...,X_k that maximize or minimize the r system response variables Y₁, Y₂, ...,Y_r. In experimental optimization, different optimization techniques are applied to the fitted response equations . Provided that the fitted equations approximate adequately the true (unknown) system responses, the optimal operating conditions of the model will be "close'' to the optimal operating conditions of the true system.

Randomness (sampling variability) effects the final answers and should be taken into account

1. Experimental optimization is an iterative process, that is, experiments conducted in one set of experiments result in fitted models that indicate where to search for improved operating conditions in the next set of experiments. Thus the coefficients of the fitted equations (or the form of the fitted equations) may change during the optimization process. This is in contrast to classical optimization where the functions to optimize are supposed to be fixed and given. 

 
2. The response models are fitted from experimental data that usually contains random variability due to uncontrollable or unknown causes. This implies that an experiment, if repeated, will result in a different fitted response surface model that might lead to different optimal operating conditions. Therefore, sampling variability should be considered in experimental optimization. 


In contrast, in classical optimization techniques the functions are deterministic and given.
 

3. The fitted responses are local approximations, implying that the optimization process requires the input of the experimenter (a person familiar with the process). This is in contrast with classical optimization which is always automated in the form of some computer algorithm.