http://opendino.org/wiki/index.php?feed=atom&namespace=0&title=Spezial%3ANeue_Seiten 2026-04-17T13:21:00Z Aus OpenDino MediaWiki 1.28.0 http://opendino.org/wiki/index.php?title=Documentation/Modules/ContinuousMOTestProblems 2019-04-07T13:06:16Z

<p>Admin: /* Module Description */</p> <hr /> <div>==Summary==<br /> <br /> The module &lt;code&gt;ContinuousMOTestProblems&lt;/code&gt; contains a set of multi-objective optimization problems, which can be used to test optimization algorithms.<br /> <br /> ==Properties==<br /> <br /> ===General===<br /> <br /> {| class=&quot;wikitable&quot; style=&quot;text-align:left&quot; border=&quot;2&quot; cellpadding=&quot;5&quot; cellspacing=&quot;5&quot;<br /> |-<br /> ! Algorithm<br /> | deterministic test function<br /> |-<br /> ! Design Variables<br /> | continuous design variables only<br /> |-<br /> ! Objectives<br /> | multi-objective for minimization<br /> |-<br /> ! Constraints <br /> | none<br /> |-<br /> ! Boundaries <br /> | problem dependent<br /> |-<br /> ! Initial Search Region <br /> | problem dependent<br /> |-<br /> ! Typical X <br /> | not set<br /> |-<br /> |}<br /> <br /> ===Connections===<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:left&quot; border=&quot;1&quot; cellpadding=&quot;5&quot; cellspacing=&quot;0&quot;<br /> |-<br /> ! Starting at his module <br /> | none<br /> |-<br /> ! Ending at this module <br /> | Connections of type &lt;code&gt;optimization&lt;/code&gt;<br /> |-<br /> |}<br /> <br /> ===Actions===<br /> {| class=&quot;wikitable&quot; style=&quot;text-align:left&quot; border=&quot;1&quot; cellpadding=&quot;5&quot; cellspacing=&quot;0&quot;<br /> |-<br /> ! Name !! Description <br /> |-<br /> ! -<br /> | -<br /> |-<br /> |}<br /> <br /> ===Options===<br /> The options are the number of discrete and continuous variables and an optional time delay for per evaluation.<br /> <br /> ==Module Description== <br /> <br /> === Multi-Objective Sphere === <br /> <br /> The multi-objective sphere function '''f''' is a set of quadratic functions. More precisely, each ''f&lt;sub&gt;i'' is computed as the square of all continuous variables.<br /> <br /> ''f&lt;sub&gt;i&lt;/sub&gt;''('''x''') = (''x&lt;sub&gt;i&lt;/sub&gt;'' - 1)&lt;sup&gt;2&lt;/sup&gt; + sum&lt;sub&gt;''j, j~=i''&lt;/sub&gt; (x&lt;sub&gt;''j''&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;)<br /> <br /> For example<br /> <br /> ''f&lt;sub&gt;1&lt;/sub&gt;''('''x''') = (''x&lt;sub&gt;1&lt;/sub&gt;'' - 1)&lt;sup&gt;2&lt;/sup&gt; + ''x''&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt; + ''x''&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;2 + ...<br /> <br /> ''f&lt;sub&gt;2&lt;/sub&gt;''('''x''') = ''x&lt;sub&gt;1&lt;/sub&gt;''&lt;sup&gt;2&lt;/sup&gt; + (''x&lt;sub&gt;2&lt;/sub&gt;'' - 1)&lt;sup&gt;2&lt;/sup&gt; + ''x''&lt;sub&gt;3&lt;/sub&gt;&lt;sup&gt;2 + ...<br /> <br /> ...<br /> <br /> The Pareto front for the two-objective case is given in the following picture:<br /> <br /> {|<br /> | [[Image:moo_sphere_ds.png|100x100px|center|thumb|300x300px|Design space]]<br /> | [[Image:moo_sphere.png|100x100px|center|thumb|300x300px|Objective space]]<br /> |}<br /> <br /> ==Usage==<br /> -<br /> ==Source Code==<br /> <br /> https://sourceforge.net/p/opendino/code/HEAD/tree/trunk/src/org/opendino/modules/problems/ContinuousMOTestProblems.java<br /> <br /> ==References==<br /> <br /> -</div>

Admin