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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. | 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<sub>i</sub>''('''x''') = ''x<sub>i</sub>''<sup>2</sup> + sum<sub>''j, j~=i''</sub> (x<sub>''j''</sub><sup>2</sup>) | + | ''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== | ||
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
-
