Figure 5.10 offers some insight as to why fixed-size simplexes can become stranded on ridges. Thus, all gradients point toward the central vertex. The information from the vertexes is not dense enough to detect the presence of the ridge. This is clearly the case in Figure 5.8 as well, and the simplexes converge on the ridge some distance from the actual optimum. Figure 5.10 A fixed-size simplex stranded on a ridge.
All gradients point toward the central vertex.
The information is not dense enough to detect the presence of the ridge. Premature convergence of the fixed-size simplex can be a problem. Authors, Frederick H. Walters, Lloyd R. Parker, Jr., Stephen L. Morgan and Stanley N. Deming.