Documentation/Modules/OptAlgSimplex - Versionsgeschichte

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Dirk: /* References */

2013-02-15T20:17:15Z

‎References

Dirk am 15. Februar 2013 um 20:16 Uhr

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Dirk: /* References */

2013-02-15T20:16:12Z

‎References

Dirk: /* General */

2013-02-15T20:15:14Z

‎General

Dirk: Created page with " « back to module overview ==Summary== This optimization module is an implementation of the popular Nelder-Mead Simplex Algorithm (1965) [[#NelMead ..."

2013-02-04T14:38:18Z

Created page with " « back to module overview ==Summary== This optimization module is an implementation of the popular Nelder-Mead Simplex Algorithm (1965) [[#NelMead ..."

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[[Documentation/Modules | « back to module overview]]

==Summary==

This optimization module is an implementation of the popular Nelder-Mead Simplex Algorithm (1965) [[#NelMead | (1)]]. The SIMPLEX method is a standard direct, deterministic optimization algorithm, which is implemented in many numerical tools (e.g. as method <code>fminsearch.m</code> in the MATLAB(R) optimization toolbox or in [http://www.gnu.org/software/octave/ GNU Octave]). A good introduction is given by Wright [[#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.

==Properties==

===General===

{| class="wikitable" style="text-align:left" border="2" cellpadding="5" cellspacing="5"
|-
! Algorithm
| deterministic
|-
! Design Variables
| Written for continuous variables. Discrete or mixed variables are NOT possible.
|-
! Objectives
| single-objective for minimization. No constraint handling.
|-
! Constraint handling
| no
|-
! Boundary handling
| no
|-
! Initialization
| Requires at least one of the following: initial solution, initial search region, or bounds. |-
|}

===Connections===

{| class="wikitable" style="text-align:left" border="1" cellpadding="5" cellspacing="0"
|-
! Starting at this module
| Module requires exactly one connection of type <code>optimization</code>.
|-
! Ending at this module
|-
|}

===Actions===

{| class="wikitable" style="text-align:left" border="1" cellpadding="5" cellspacing="0"
|-
! Name !! Description
|-
! '''Run'''
| starts the optimization.
|-
|}

===Options===

The options are currently described as "pop-up help".

==Module Description==

The SIMPLEX algorithm is implemented using the paper of Wright [[#Wright | (2)]].
However, some extensions are made as e.g. the initialization is not given in the references.

=== Initialization ===

First, an initial simplex is generated. Here, a [http://en.wikipedia.org/wiki/Simplex 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 (<code>initial solution, initial search region, bounds</code>).

{| border="1" cellspacing="0"
! colspan="3" | Problem Properties Given? || Action
|-
| <code>initial solution</code> || <code>initial search region</code> || <code>bounds</code> ||
|-
|Yes || No || No || option <code>Initial Size of the Simplex</code> defines the absolute length of the simplex in each design variable direction. I.e. a simplex is constructed, such that the distance between each vertex and the plane generated by the remaining points has this length.
|-
|Yes or No || Yes || Yes or No || option <code>Initial Size of the Simplex</code> defines the relative length of the simplex in each design variable direction compared to the size of the initial search region (i.e. difference upper to lower limit). Bounds are ignored.
|-
|Yes or No || No || Yes || option <code>Initial Size of the Simplex</code> defines the relative length of the simplex in each design variable direction compared to the size of the bounds (i.e. difference upper to lower limit).
|}

=== Optimization ===

The SIMPLEX method follows a deterministic procedure. Except the initialization, always one new point is generated and evaluated. Thus, parallelization is not implemented.

==Usage==

... todo

==Source Code==

ToDo:Link to SVN

==References==

<span id="NelMead">1</span> Nelder, J. A. and Mead, R. "A Simplex Method for Function Minimization." Comput. J. 7, 308-313, 1965.
<span id="Wright">2</span> 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.

[[Documentation/Modules | « back to module overview]],[[Documentation/Modules | « back to module overview]]

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	pages 191–208. Addison Wesley Longman, 1996.		pages 191–208. Addison Wesley Longman, 1996.

−	~~[[Documentation/Modules \| « back to module overview]],~~[[Documentation/Modules \| « back to module overview]]	+	[[Documentation/Modules \| « back to module overview]]

← Nächstältere Version	Version vom 24. April 2019, 21:03 Uhr
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@@ Zeile 96: / Zeile 96: @@
 <span id="NelMead">1</span> Nelder, J. A. and Mead, R. "A Simplex Method for Function Minimization." Comput. J. 7, 308-313, 1965.
 <span id="Wright">2</span> 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.

@@ Zeile 1: / Zeile 1: @@
 ==Summary==
@@ Zeile 100: / Zeile 98: @@
 <span id="Wright">2</span> 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.

@@ Zeile 20: / Zeile 20: @@
 |-
 ! Objectives
-| single-objective for minimization. No constraint handling.
+| single-objective for minimization.
 |-
 ! Constraint handling