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==Summary== | ==Summary== | ||
| − | The module <code>ContinuousMOTestProblems</code> contains a set of multi-objective optimization | + | The module <code>ContinuousMOTestProblems</code> contains a set of multi-objective optimization problems, which can be used to test optimization algorithms. |
==Properties== | ==Properties== | ||
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|- | |- | ||
! Design Variables | ! Design Variables | ||
| − | | | + | | continuous design variables only |
|- | |- | ||
! Objectives | ! Objectives | ||
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|- | |- | ||
! Typical X | ! Typical X | ||
| − | | not set | + | | not set |
|- | |- | ||
|} | |} | ||
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==Module Description== | ==Module Description== | ||
| − | === | + | === Multi-Objective Sphere === |
| − | The | + | The multi-objective sphere function '''f''' is a set of quadratic functions. More precisely, each ''f<sub>i'' is computed as the square of all continuous variables. |
| − | ''f''('''x''') = sum<sub>i</sub>(x<sub> | + | ''f<sub>i</sub>''('''x''') = (''x<sub>i</sub>'' - 1)<sup>2</sup> + sum<sub>''j, j~=i''</sub> (x<sub>''j''</sub><sup>2</sup>) |
| − | + | For example | |
| + | |||
| + | ''f<sub>1</sub>''('''x''') = (''x<sub>1</sub>'' - 1)<sup>2</sup> + ''x''<sub>2</sub><sup>2</sup> + ''x''<sub>3</sub><sup>2 + ... | ||
| + | |||
| + | ''f<sub>2</sub>''('''x''') = ''x<sub>1</sub>''<sup>2</sup> + (''x<sub>2</sub>'' - 1)<sup>2</sup> + ''x''<sub>3</sub><sup>2 + ... | ||
| + | |||
| + | ... | ||
| + | |||
| + | The Pareto front for the two-objective case is given in the following picture: | ||
| + | |||
| + | {| | ||
| + | | [[Image:moo_sphere_ds.png|100x100px|center|thumb|300x300px|Design space]] | ||
| + | | [[Image:moo_sphere.png|100x100px|center|thumb|300x300px|Objective space]] | ||
| + | |} | ||
==Usage== | ==Usage== | ||
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==Source Code== | ==Source Code== | ||
| − | https://sourceforge.net/p/opendino/code/HEAD/tree/trunk/src/org/opendino/modules/problems/ | + | https://sourceforge.net/p/opendino/code/HEAD/tree/trunk/src/org/opendino/modules/problems/ContinuousMOTestProblems.java |
==References== | ==References== | ||
- | - | ||
Aktuelle Version vom 7. April 2019, 17:29 Uhr
Inhaltsverzeichnis
Summary
The module ContinuousMOTestProblems contains a set of multi-objective optimization problems, which can be used to test optimization algorithms.
Properties
General
| Algorithm | deterministic test function |
|---|---|
| Design Variables | continuous design variables only |
| Objectives | multi-objective for minimization |
| Constraints | none |
| Boundaries | problem dependent |
| Initial Search Region | problem dependent |
| Typical X | not set |
Connections
| Starting at his module | none |
|---|---|
| Ending at this module | Connections of type optimization
|
Actions
| Name | Description |
|---|---|
| - | - |
Options
The options are the number of discrete and continuous variables and an optional time delay for per evaluation.
Module Description
Multi-Objective Sphere
The multi-objective sphere function f is a set of quadratic functions. More precisely, each fi is computed as the square of all continuous variables.
fi(x) = (xi - 1)2 + sumj, j~=i (xj2)
For example
f1(x) = (x1 - 1)2 + x22 + x32 + ...
f2(x) = x12 + (x2 - 1)2 + x32 + ...
...
The Pareto front for the two-objective case is given in the following picture:
Usage
-
Source Code
References
-
