Abstract

A new method is presented for determining the reflection point (centroid) which automatically varies the polyhedron (simplex or complex) moves to favor, in the early stages, a weighted move, and as the algorithm progresses, evolve to a more geometric move. Based on numerical experience to date, these attributes seem to be desirable for rapid progress throughout the algorithm stages. Introduction In a previous paper, a modification of the simplex-type direct search technique for constrained nonlinear minimization was presented While recent algorithm development has largely focused on gradient-based algorithms-e.g., generalized variable metric, conjugate directions, reduced gradient-and successive quadratic programming algorithms, there still remains a substantial place for direct search techniques. In particular, the multipoint hill-climbing/descending techniques such as the algorithms considered here enjoy the usually cited advantages of direct-search methods (simpler problem preparation, no problems with numerical derivatives, etc.), plus they can often handle difficult terrains (e.g., corrugated), functions which are not continuous or differentiable or which have rapidly exponentially increasing terms (locally or globally, especially near an optimum) with minimal tuning resetting, problem preparation or other special treatment. This is because of their admittedly conservative mode of negotiating the design space contours -a strategy which may be slow on many conventional (or test) problems, but which can solve problems which are highly complex or interactive or have the aforementioned traits. Accordingly, such algorithms may be quite problem dependent (most algorithms are), and simplex/complex algorithms may well fall in the realm of