Reflection/Expansion - Revision history

Admin: Admin moved page Reflection to Reflection/Expansion

2015-09-22T07:39:23Z

2015-09-22T07:35:01Z

2015-09-22T07:34:14Z

typos

2013-10-17T12:03:05Z

Admin moved page Expansion to Reflection

2013-10-17T11:58:05Z

e0 => r0

2013-10-17T10:16:49Z

2013-10-17T10:15:54Z

Expansion to Reflection

2013-06-28T16:49:46Z

‎Basic expansion (e0)

2013-06-28T16:38:21Z

‎Basic expansion (e0)

2013-06-28T16:36:58Z

‎Basic expansion (e0)

← Older revision		Revision as of 07:35, 22 September 2015
Line 1:		Line 1:
−	== Basic expansion (r0) ==	+	== Basic reflection/expansion (r0) ==
	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 $x_{worst}$ to $x_{worst2}$ 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 $x_{best}$.		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 $x_{worst}$ to $x_{worst2}$ 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 $x_{best}$.

@@ Line 1: / Line 1: @@
-== Basic reflection (r0) ==
+== Basic expansion (r0) ==
-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 $x_{best}$.
+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 $x_{worst}$ to $x_{worst2}$ 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 $d$:<br />
 if ($rand(0,1)<p)$ <br />
-$  x_{r,d}=x_{best,d}+(w_{worst2,d}-w_{worst,d})$<br />
+$  x_{r,d}=x_{best,d}+(x_{worst2,d}-x_{worst,d})$<br />
 else <br />
 $  x_{r,d}=x_{i,d}$

← Older revision		Revision as of 11:58, 17 October 2013
Line 1:		Line 1:
−	== Basic reflection (e0) ==	+	== Basic reflection (r0) ==
	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 $x_{best}$.		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 $x_{best}$.

@@ Line 4: / Line 4: @@
 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 />
-if $rand(0,1)<p)$ <br />
+if ($rand(0,1)<p)$ <br />
 $  x_{r,d}=x_{best,d}+(w_{worst2,d}-w_{worst,d})$<br />
 else <br />

@@ Line 1: / Line 1: @@
-== Basic expansion (e0) ==
+== Basic reflection (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 $x_{best}$.
@@ Line 5: / Line 5: @@
 if $rand(0,1)<p)$ <br />
-$  x_{e,d}=x_{best,d}+(w_{worst2,d}-w_{worst,d})$<br />
+$  x_{r,d}=x_{best,d}+(w_{worst2,d}-w_{worst,d})$<br />
 else <br />
-$  x_{e,d}=x_{i,d}$
+$  x_{r,d}=x_{i,d}$
-If $x_{e}$ is better than $x_i$, decrease the population cost
+If $x_{r}$ is better than $x_i$, decrease the population cost
-$$ C\leftarrow C-f(x_i)+f(x_e)$$
+$$ C\leftarrow C-f(x_i)+f(x_r)$$
-If $x_{e}$ is better than the best ever found (i.e. $Best$), set $Best=x_{e}$.
+If $x_{r}$ is better than the best ever found (i.e. $Best$), set $Best=x_{r}$.

← Older revision	Revision as of 07:39, 22 September 2015
(No difference)

← Older revision	Revision as of 12:03, 17 October 2013
(No difference)

@@ Line 5: / Line 5: @@
 if $rand(0,1)<p)$ <br />
- $x_{e,d}=x_{best,d}+(w_{worst2,d}-w_{worst,d})$<br />
+:Indented line
-else $x_{e,d}=x_{i,d}$
+$x_{e,d}=x_{best,d}+(w_{worst2,d}-w_{worst,d})$<br />
+.