Evolution and Optimum Seeking

Multidimensional Strategies 63
(If necessary repeat this process until Gj(x (0 ) ) 0 for all j =1(1)m.)
Set k =0.
Step 1: (Re ection)
Determine the index w (worst vertex) such that
F (x (kw) ) = maxfF (x (k ) ) =1(1)Ng:
Construct x = 1
N;1
NP
=1
6=w
(k ) x
and x 0 = x + (x ; x (kw) ) (over-re ection factor =1:3):
Step 2: (Check for constraints)
If m = 0, go to step 7 otherwise set j =1.
If m 1 = 0 , go to step 5.
Step 3: (Set vertex back into bounds for explicit constraints)
Obtain g = Gj(x0 )=Gj(x0 `j).
If g 0, go to step 4
otherwise replace x0 `j x0 `j + g + " (backwards length " =10 ;6 ).
If Gj(x0 ) < 0, replace x0 `j x0`j ; 2(g + ").
Step 4: (Explicit constraints loop)
Increase j j +1.
If
8
><
>:
j m 1 go to step 3
m 1 m go to step 7:
Step 5: (Check implicit constraints)
If Gj(x 0 ) 0, go to step 6
otherwise go to step 8, unless the same constraint caused a failure ve times
in a row without its function value Gj(x 0 ) being changed. In this case go to
step 9.
Step 6: (Implicit constraints loop)
If j < m, increase j j +1 and go to step 5.
Step 7: (Check for improvement)
If F (x0 )