This optimization module is an implementation of the popular Nelder-Mead Simplex Algorithm (1965) (1). The SIMPLEX method is a standard direct, deterministic optimization algorithm, which is implemented in many numerical tools (e.g. as method
fminsearch.m in the MATLAB(R) optimization toolbox or in GNU Octave). A good introduction is given by Wright (2).
The algorithm works best for a small number of design variables (1-10, sometimes 1-20). It fails, for example, on the Rosenbrock function, if more than 10 design variables are given.
|Design Variables||Written for continuous variables. Discrete or mixed variables are NOT possible.|
|Objectives||single-objective for minimization.|
|Starting at this module|| Module requires exactly one connection of type |
|Ending at this module|
|Run||starts the optimization.|
The options are currently described as "pop-up help".
The SIMPLEX algorithm is implemented using the paper of Wright (2). However, some extensions are made as e.g. the initialization is not given in the references.
First, an initial simplex is generated. Here, a simplex is a body in the N-dimensional design space that has N+1 vertices. The vertices are connected by straight lines. For two (N=2) and three (N=3) design variables, a simplex is a triangle or tetrahedron, respectively.
If the optimization problem provides an initial solution, this point is taken as first vertex of the simplex. If not, the initial simplex gets a random position obeying certain rules.
We distinguish several cases, depending on the problem properties (
initial solution, initial search region, bounds).
|Problem Properties Given?||Action|
|Yes||No||No|| option |
|Yes or No||Yes||Yes or No|| option |
|Yes or No||No||Yes|| option |
The SIMPLEX method follows a deterministic procedure. Except the initialization, always one new point is generated and evaluated. Thus, parallelization is not implemented.
ToDo:Link to SVN
1 Nelder, J. A. and Mead, R. "A Simplex Method for Function Minimization." Comput. J. 7, 308-313, 1965.
2 M. H. Wright. "Direct search methods: once scorned, now respectable". In D. F. Griffiths and G. A. Watson, editors, Numerical Analysis 1995 (Proceedings of the 1995 Dundee Biennial Conference in Numerical Analysis), pages 191–208. Addison Wesley Longman, 1996.