Difference between revisions of "Reflection/Expansion"

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(Created page with "TO COMPLETE == Basic selection (s0) == Select $D+1$ agents at random<br /> Be sure that the current one is in this list. If not, replace the last of the list by the current o...")
 
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TO COMPLETE
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== Basic expansion (e0) ==
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We combine four individuals, $x_{best}$, $x_{worst2}$, $w_{worst}$, and the current $x_i$ that has to be moved. The idea is that a move from $w_{worst}$ to $w_{worst2}$ is probably a good one, so, on the contrary, the same move applied to $x_{best}$ is probably a bad one, i.e. it tends to deteriorate the position.  But on the other hand, it also gives a chance to escape from the attraction basin of $x_{best}$.
  
== Basic selection (s0) ==
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Of course, for a unimodal landscape, this is a waste of time, but for multimodal ones, it may be useful. Moreover, this move is not applied on all dimensions, but only on some of them, according to the probability estimated at the end of the selection phase. So, finally, the formulae to define the new point $x_e$ are, for each dimension $d$:<br />
Select $D+1$ agents at random<br />
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Be sure that the current one is in this list. If not, replace the last of the list by the current one.<br />
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Compute the volume $V_s$ of the simplex defined by these points.
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if $rand(0,1)<p) x_{e,d}=x_{best,d}+(w_{worst2,d}-w_{worst,d})<br />
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else x_{e,d}=x_{i,d}
  
Take the three first ones, and sort them by increasing order of fitness.
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Revision as of 17:34, 28 June 2013

Basic expansion (e0)

We combine four individuals, $x_{best}$, $x_{worst2}$, $w_{worst}$, and the current $x_i$ that has to be moved. The idea is that a move from $w_{worst}$ to $w_{worst2}$ is probably a good one, so, on the contrary, the same move applied to $x_{best}$ is probably a bad one, i.e. it tends to deteriorate the position. But on the other hand, it also gives a chance to escape from the attraction basin of $x_{best}$.

Of course, for a unimodal landscape, this is a waste of time, but for multimodal ones, it may be useful. Moreover, this move is not applied on all dimensions, but only on some of them, according to the probability estimated at the end of the selection phase. So, finally, the formulae to define the new point $x_e$ are, for each dimension $d$:

if $rand(0,1)<p) x_{e,d}=x_{best,d}+(w_{worst2,d}-w_{worst,d})
else x_{e,d}=x_{i,d}


.