One strategy for improving the efficiency of a searching algorithm is to change more than one factor at a time. A convenient way to accomplish this when there are two factors is to begin with three sets of initial factor levels, which form the vertices of a triangle. After measuring the response for each set of factor levels, we identify the combination giving the worst response and replace it with a new set of factor levels obtained by reflecting the worst vertex through the midpoint of the remaining two vertices, as illustrated here.
This process continues until we reach the global optimum or until no further optimization is possible. The set of factor levels is called a simplex. In general, for k factors a simplex is a k + 1 dimensional geometric figure.
An example showing the progress of a simplex optimization is shown here.
The green dot marks the optimum response of (3, 7). Optimization ends when the simplexes begin to circle around a single vertex.