R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("rgenoud-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('rgenoud')
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "genoud"
> 
> ### * genoud
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: genoud
> ### Title: GENetic Optimization Using Derivatives
> ### Aliases: genoud
> ### Keywords: optimize nonlinear
> 
> ### ** Examples
> 
> #maximize the sin function
>  sin1 <- genoud(sin, nvars=1, max=TRUE);


Wed Jul 13 18:38:03 2005
Domains:
 -1.000000e+01   <=  X1   <=    1.000000e+01 

NOTE: Operator 6 (Multiple Point Simple Crossover) may only be started
NOTE: an even number of times.  I am increasing this operator by one.

NOTE: Operator 8 (Heuristic Crossover) may only be started
NOTE: an even number of times.  I am increasing this operator by one.

Data Type: Floating Point
Operators (code number, name, population) 
	(1) Cloning........................... 	122
	(2) Uniform Mutation.................. 	125
	(3) Boundary Mutation................. 	125
	(4) Non-Uniform Mutation.............. 	125
	(5) Polytope Crossover................ 	125
	(6) Multiple Point Simple Crossover... 	126
	(7) Whole Non-Uniform Mutation........ 	125
	(8) Heuristic Crossover............... 	126
	(9) Local-Minimum Crossover........... 	0

HARD Maximum Number of Generations: 100
Maximum Nonchanging Generations: 10
Population size       : 1000
Convergence Tolerance: 1.000000e-03

Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
Checking Gradients before Stopping
Not Using Out of Bounds Individuals and Not Allowing Trespassing.



Maximization Problem.



The 2 best initial individuals are
-4.71	
fitness = 9.999970e-01

 1.57	
fitness = 9.999937e-01


The worst fit of the population is: -1.000000e+00


GENERATION: 0 (initializing the population)
Fitness Value... 9.999970e-01
mean............ 2.104858e-02
var............. 4.765535e-01
skewness........ -4.001914e-02
kurtosis........ 1.547834e+00
#null........... 0
#unique......... 1000, #Total UniqueCount: 1000
var 1:
best............ -4.709956e+00
mean............ 1.799116e-01
var............. 3.261355e+01
skewness........ 2.603477e-03
kurtosis........ 1.823791e+00
#null........... 0

GENERATION: 1
Fitness Value... 1.000000e+00
mean............ 4.045625e-01
var............. 5.177172e-01
skewness........ -9.011320e-01
kurtosis........ 2.195615e+00
#null........... 0
#unique......... 610, #Total UniqueCount: 1610
var 1:
best............ 1.570796e+00
mean............ -3.648799e-01
var............. 2.795717e+01
skewness........ 2.436018e-01
kurtosis........ 1.891389e+00
#null........... 0

GENERATION: 2
Fitness Value... 1.000000e+00
mean............ 4.348096e-01
var............. 5.481938e-01
skewness........ -8.903893e-01
kurtosis........ 2.127496e+00
#null........... 0
#unique......... 577, #Total UniqueCount: 2187
var 1:
best............ 1.570796e+00
mean............ -2.196294e-01
var............. 2.107054e+01
skewness........ 2.008551e-01
kurtosis........ 2.015899e+00
#null........... 0

GENERATION: 3
Fitness Value... 1.000000e+00
mean............ 5.936946e-01
var............. 4.381315e-01
skewness........ -1.374060e+00
kurtosis........ 3.312485e+00
#null........... 0
#unique......... 430, #Total UniqueCount: 2617
var 1:
best............ 1.570796e+00
mean............ 5.406312e-01
var............. 1.054313e+01
skewness........ -4.822266e-01
kurtosis........ 3.341585e+00
#null........... 0

GENERATION: 4
Fitness Value... 1.000000e+00
mean............ 6.386443e-01
var............. 4.036382e-01
skewness........ -1.573947e+00
kurtosis........ 3.913175e+00
#null........... 0
#unique......... 420, #Total UniqueCount: 3037
var 1:
best............ 1.570796e+00
mean............ 1.323212e+00
var............. 6.286824e+00
skewness........ -9.594515e-01
kurtosis........ 7.699915e+00
#null........... 0

GENERATION: 5
Fitness Value... 1.000000e+00
mean............ 6.331647e-01
var............. 3.991565e-01
skewness........ -1.542122e+00
kurtosis........ 3.853704e+00
#null........... 0
#unique......... 412, #Total UniqueCount: 3449
var 1:
best............ 1.570796e+00
mean............ 1.322168e+00
var............. 6.276976e+00
skewness........ -1.185373e+00
kurtosis........ 8.331197e+00
#null........... 0

GENERATION: 6
Fitness Value... 1.000000e+00
mean............ 6.155854e-01
var............. 4.333246e-01
skewness........ -1.505575e+00
kurtosis........ 3.679061e+00
#null........... 0
#unique......... 428, #Total UniqueCount: 3877
var 1:
best............ 1.570796e+00
mean............ 1.455080e+00
var............. 6.116136e+00
skewness........ -6.268561e-01
kurtosis........ 7.647702e+00
#null........... 0

GENERATION: 7
Fitness Value... 1.000000e+00
mean............ 6.725007e-01
var............. 3.668690e-01
skewness........ -1.708551e+00
kurtosis........ 4.407633e+00
#null........... 0
#unique......... 378, #Total UniqueCount: 4255
var 1:
best............ 1.570796e+00
mean............ 1.499447e+00
var............. 5.936244e+00
skewness........ -8.894250e-01
kurtosis........ 9.247930e+00
#null........... 0

GENERATION: 8
Fitness Value... 1.000000e+00
mean............ 6.625179e-01
var............. 3.794775e-01
skewness........ -1.676950e+00
kurtosis........ 4.304363e+00
#null........... 0
#unique......... 389, #Total UniqueCount: 4644
var 1:
best............ 1.570796e+00
mean............ 1.315104e+00
var............. 5.086661e+00
skewness........ -1.042969e+00
kurtosis........ 1.027363e+01
#null........... 0

GENERATION: 9
Fitness Value... 1.000000e+00
mean............ 6.486078e-01
var............. 3.719986e-01
skewness........ -1.617199e+00
kurtosis........ 4.159252e+00
#null........... 0
#unique......... 422, #Total UniqueCount: 5066
var 1:
best............ 1.570796e+00
mean............ 1.388363e+00
var............. 5.794821e+00
skewness........ -8.263275e-01
kurtosis........ 9.112604e+00
#null........... 0

GENERATION: 10
Fitness Value... 1.000000e+00
mean............ 6.667651e-01
var............. 3.795484e-01
skewness........ -1.713583e+00
kurtosis........ 4.389747e+00
#null........... 0
#unique......... 406, #Total UniqueCount: 5472
var 1:
best............ 1.570796e+00
mean............ 1.318991e+00
var............. 6.227260e+00
skewness........ -1.363418e+00
kurtosis........ 9.229128e+00
#null........... 0

GENERATION: 11
Fitness Value... 1.000000e+00
mean............ 6.460127e-01
var............. 3.817568e-01
skewness........ -1.601524e+00
kurtosis........ 4.063542e+00
#null........... 0
#unique......... 427, #Total UniqueCount: 5899
var 1:
best............ 1.570796e+00
mean............ 1.386317e+00
var............. 5.368094e+00
skewness........ -8.166617e-01
kurtosis........ 8.418787e+00
#null........... 0

Soft Generation Wait Limit Hit.
No Improvement in 10 Generations

Best Fit Found at Generation 1
Fit Value = 1.000000e+00


Parameters at the Solution (value, gradient):

 X[ 1] :	1.570796e+00	G[ 1] :	-1.195945e-09

Solution Found Generation 1
Number of Generations Run 11


Wed Jul 13 18:38:04 2005
Total run time : 0 hours 0 minutes and 1 seconds
> 
> #minimize the sin function
>  sin2 <- genoud(sin, nvars=1, max=FALSE);


Wed Jul 13 18:38:04 2005
Domains:
 -1.000000e+01   <=  X1   <=    1.000000e+01 

NOTE: Operator 6 (Multiple Point Simple Crossover) may only be started
NOTE: an even number of times.  I am increasing this operator by one.

NOTE: Operator 8 (Heuristic Crossover) may only be started
NOTE: an even number of times.  I am increasing this operator by one.

Data Type: Floating Point
Operators (code number, name, population) 
	(1) Cloning........................... 	122
	(2) Uniform Mutation.................. 	125
	(3) Boundary Mutation................. 	125
	(4) Non-Uniform Mutation.............. 	125
	(5) Polytope Crossover................ 	125
	(6) Multiple Point Simple Crossover... 	126
	(7) Whole Non-Uniform Mutation........ 	125
	(8) Heuristic Crossover............... 	126
	(9) Local-Minimum Crossover........... 	0

HARD Maximum Number of Generations: 100
Maximum Nonchanging Generations: 10
Population size       : 1000
Convergence Tolerance: 1.000000e-03

Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
Checking Gradients before Stopping
Not Using Out of Bounds Individuals and Not Allowing Trespassing.



Minimization Problem.



The 2 best initial individuals are
 4.71	
fitness = -1.000000e+00

-7.85	
fitness = -9.999953e-01


The worst fit of the population is: 9.999987e-01


GENERATION: 0 (initializing the population)
Fitness Value... -1.000000e+00
mean............ -1.838334e-02
var............. 4.625091e-01
skewness........ -1.006333e-02
kurtosis........ 1.597132e+00
#null........... 0
#unique......... 1000, #Total UniqueCount: 1000
var 1:
best............ 4.712609e+00
mean............ -2.336378e-01
var............. 3.245014e+01
skewness........ 4.317284e-02
kurtosis........ 1.838354e+00
#null........... 0

GENERATION: 1
Fitness Value... -1.000000e+00
mean............ -4.918366e-01
var............. 4.487237e-01
skewness........ 1.102017e+00
kurtosis........ 2.677595e+00
#null........... 0
#unique......... 600, #Total UniqueCount: 1600
var 1:
best............ 4.712389e+00
mean............ 3.336851e-01
var............. 3.196038e+01
skewness........ -3.596601e-01
kurtosis........ 1.750551e+00
#null........... 0

GENERATION: 2
Fitness Value... -1.000000e+00
mean............ -6.570484e-01
var............. 3.787633e-01
skewness........ 1.641440e+00
kurtosis........ 4.193701e+00
#null........... 0
#unique......... 594, #Total UniqueCount: 2194
var 1:
best............ 4.712389e+00
mean............ 3.267749e+00
var............. 1.463447e+01
skewness........ -1.713306e+00
kurtosis........ 5.302080e+00
#null........... 0

GENERATION: 3
Fitness Value... -1.000000e+00
mean............ -6.291834e-01
var............. 4.171809e-01
skewness........ 1.496328e+00
kurtosis........ 3.622638e+00
#null........... 0
#unique......... 412, #Total UniqueCount: 2606
var 1:
best............ 4.712389e+00
mean............ 4.000233e+00
var............. 7.550967e+00
skewness........ -2.350905e+00
kurtosis........ 9.487240e+00
#null........... 0

GENERATION: 4
Fitness Value... -1.000000e+00
mean............ -6.770421e-01
var............. 3.477211e-01
skewness........ 1.736171e+00
kurtosis........ 4.605020e+00
#null........... 0
#unique......... 413, #Total UniqueCount: 3019
var 1:
best............ 4.712389e+00
mean............ 3.871204e+00
var............. 8.469054e+00
skewness........ -2.296966e+00
kurtosis........ 9.116166e+00
#null........... 0

GENERATION: 5
Fitness Value... -1.000000e+00
mean............ -6.438838e-01
var............. 3.881373e-01
skewness........ 1.588675e+00
kurtosis........ 3.996355e+00
#null........... 0
#unique......... 432, #Total UniqueCount: 3451
var 1:
best............ 4.712389e+00
mean............ 4.104657e+00
var............. 7.421646e+00
skewness........ -2.497797e+00
kurtosis........ 1.098258e+01
#null........... 0

GENERATION: 6
Fitness Value... -1.000000e+00
mean............ -6.550346e-01
var............. 3.650058e-01
skewness........ 1.610495e+00
kurtosis........ 4.146523e+00
#null........... 0
#unique......... 428, #Total UniqueCount: 3879
var 1:
best............ 4.712389e+00
mean............ 4.046703e+00
var............. 7.363244e+00
skewness........ -2.523771e+00
kurtosis........ 1.068327e+01
#null........... 0

GENERATION: 7
Fitness Value... -1.000000e+00
mean............ -6.724479e-01
var............. 3.491416e-01
skewness........ 1.721409e+00
kurtosis........ 4.546284e+00
#null........... 0
#unique......... 420, #Total UniqueCount: 4299
var 1:
best............ 4.712389e+00
mean............ 4.031679e+00
var............. 7.615073e+00
skewness........ -2.414285e+00
kurtosis........ 1.029078e+01
#null........... 0

GENERATION: 8
Fitness Value... -1.000000e+00
mean............ -6.588988e-01
var............. 3.648928e-01
skewness........ 1.643437e+00
kurtosis........ 4.242591e+00
#null........... 0
#unique......... 426, #Total UniqueCount: 4725
var 1:
best............ 4.712389e+00
mean............ 4.049616e+00
var............. 7.932597e+00
skewness........ -2.321234e+00
kurtosis........ 9.978718e+00
#null........... 0

GENERATION: 9
Fitness Value... -1.000000e+00
mean............ -6.582979e-01
var............. 3.600642e-01
skewness........ 1.646802e+00
kurtosis........ 4.289559e+00
#null........... 0
#unique......... 440, #Total UniqueCount: 5165
var 1:
best............ 4.712389e+00
mean............ 4.012773e+00
var............. 6.995505e+00
skewness........ -2.404531e+00
kurtosis........ 1.084269e+01
#null........... 0

GENERATION: 10
Fitness Value... -1.000000e+00
mean............ -6.399800e-01
var............. 3.950623e-01
skewness........ 1.567133e+00
kurtosis........ 3.903356e+00
#null........... 0
#unique......... 432, #Total UniqueCount: 5597
var 1:
best............ 4.712389e+00
mean............ 4.136187e+00
var............. 6.074372e+00
skewness........ -2.418790e+00
kurtosis........ 1.138057e+01
#null........... 0

GENERATION: 11
Fitness Value... -1.000000e+00
mean............ -6.833527e-01
var............. 3.378190e-01
skewness........ 1.754963e+00
kurtosis........ 4.655640e+00
#null........... 0
#unique......... 411, #Total UniqueCount: 6008
var 1:
best............ 4.712389e+00
mean............ 4.124047e+00
var............. 6.529164e+00
skewness........ -2.519309e+00
kurtosis........ 1.135629e+01
#null........... 0

Soft Generation Wait Limit Hit.
No Improvement in 10 Generations

Best Fit Found at Generation 1
Fit Value = -1.000000e+00


Parameters at the Solution (value, gradient):

 X[ 1] :	4.712389e+00	G[ 1] :	-3.847042e-11

Solution Found Generation 1
Number of Generations Run 11


Wed Jul 13 18:38:06 2005
Total run time : 0 hours 0 minutes and 2 seconds
> 
> #maximize a univariate normal mixture which looks like a claw and
> #plot it
> claw <- function(xx) {
+   Nd <- function(x, mu, sigma) {
+     w <- (1.0/sqrt(2.0*pi*sigma*sigma)) ;
+     z <- (x-mu)/sigma;
+     w <- w*exp(-0.5*z*z) ;
+     as.double(w);
+   }
+   x <- xx[1];
+   y <- (0.46*(Nd(x,-1.0,2.0/3.0) + Nd(x,1.0,2.0/3.0)) +
+            (1.0/300.0)*(Nd(x,-0.5,.01) + Nd(x,-1.0,.01) + Nd(x,-1.5,.01)) +
+            (7.0/300.0)*(Nd(x,0.5,.07) + Nd(x,1.0,.07) + Nd(x,1.5,.07))) ;
+   as.double(y);
+ }
>  claw1   <- genoud(claw, nvars=1,P9=100,max=TRUE);


Wed Jul 13 18:38:06 2005
Domains:
 -1.000000e+01   <=  X1   <=    1.000000e+01 

Data Type: Floating Point
Operators (code number, name, population) 
	(1) Cloning........................... 	99
	(2) Uniform Mutation.................. 	100
	(3) Boundary Mutation................. 	100
	(4) Non-Uniform Mutation.............. 	100
	(5) Polytope Crossover................ 	100
	(6) Multiple Point Simple Crossover... 	100
	(7) Whole Non-Uniform Mutation........ 	100
	(8) Heuristic Crossover............... 	100
	(9) Local-Minimum Crossover........... 	200

HARD Maximum Number of Generations: 100
Maximum Nonchanging Generations: 10
Population size       : 1000
Convergence Tolerance: 1.000000e-03

Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
Checking Gradients before Stopping
Not Using Out of Bounds Individuals and Not Allowing Trespassing.



Maximization Problem.



The 2 best initial individuals are
 1.00	
fitness = 4.112697e-01

 0.99	
fitness = 4.096164e-01


The worst fit of the population is: 7.571275e-41


GENERATION: 0 (initializing the population)
Fitness Value... 4.112697e-01
mean............ 5.196359e-02
var............. 9.814944e-03
skewness........ 1.725390e+00
kurtosis........ 4.562012e+00
#null........... 0
#unique......... 1000, #Total UniqueCount: 1000
var 1:
best............ 1.001257e+00
mean............ -1.207810e-01
var............. 3.394398e+01
skewness........ 7.421800e-03
kurtosis........ 1.813354e+00
#null........... 0

GENERATION: 1
Fitness Value... 4.113123e-01
mean............ 2.696166e-01
var............. 2.493123e-02
skewness........ -6.775300e-01
kurtosis........ 1.946391e+00
#null........... 0
#unique......... 688, #Total UniqueCount: 1688
var 1:
best............ 9.995032e-01
mean............ 7.045994e-01
var............. 6.600127e+00
skewness........ -2.659099e-01
kurtosis........ 6.997625e+00
#null........... 0

GENERATION: 2
Fitness Value... 4.113123e-01
mean............ 3.077875e-01
var............. 2.651643e-02
skewness........ -1.128458e+00
kurtosis........ 2.488235e+00
#null........... 0
#unique......... 592, #Total UniqueCount: 2280
var 1:
best............ 9.995032e-01
mean............ 8.853374e-01
var............. 5.653928e+00
skewness........ -7.059805e-01
kurtosis........ 8.723113e+00
#null........... 0

GENERATION: 3
Fitness Value... 4.113123e-01
mean............ 3.106247e-01
var............. 2.485199e-02
skewness........ -1.169796e+00
kurtosis........ 2.651480e+00
#null........... 0
#unique......... 346, #Total UniqueCount: 2626
var 1:
best............ 9.995032e-01
mean............ 8.351425e-01
var............. 4.949041e+00
skewness........ -7.442519e-01
kurtosis........ 9.446446e+00
#null........... 0

GENERATION: 4
Fitness Value... 4.113123e-01
mean............ 3.100857e-01
var............. 2.588955e-02
skewness........ -1.179983e+00
kurtosis........ 2.620789e+00
#null........... 0
#unique......... 339, #Total UniqueCount: 2965
var 1:
best............ 9.995032e-01
mean............ 8.634655e-01
var............. 5.394732e+00
skewness........ -7.367818e-01
kurtosis........ 8.752588e+00
#null........... 0

GENERATION: 5
Fitness Value... 4.113123e-01
mean............ 3.024078e-01
var............. 2.668232e-02
skewness........ -1.070367e+00
kurtosis........ 2.386006e+00
#null........... 0
#unique......... 368, #Total UniqueCount: 3333
var 1:
best............ 9.995032e-01
mean............ 8.797546e-01
var............. 4.559391e+00
skewness........ -7.545391e-01
kurtosis........ 8.716749e+00
#null........... 0

GENERATION: 6
Fitness Value... 4.113123e-01
mean............ 3.023385e-01
var............. 2.686175e-02
skewness........ -1.056334e+00
kurtosis........ 2.352736e+00
#null........... 0
#unique......... 363, #Total UniqueCount: 3696
var 1:
best............ 9.995032e-01
mean............ 8.965979e-01
var............. 5.571501e+00
skewness........ -7.160336e-01
kurtosis........ 8.784038e+00
#null........... 0

GENERATION: 7
Fitness Value... 4.113123e-01
mean............ 3.134529e-01
var............. 2.444592e-02
skewness........ -1.221791e+00
kurtosis........ 2.775723e+00
#null........... 0
#unique......... 340, #Total UniqueCount: 4036
var 1:
best............ 9.995032e-01
mean............ 8.911587e-01
var............. 4.573122e+00
skewness........ -7.269539e-01
kurtosis........ 9.600617e+00
#null........... 0

GENERATION: 8
Fitness Value... 4.113123e-01
mean............ 3.148287e-01
var............. 2.350548e-02
skewness........ -1.233458e+00
kurtosis........ 2.851291e+00
#null........... 0
#unique......... 347, #Total UniqueCount: 4383
var 1:
best............ 9.995032e-01
mean............ 9.322415e-01
var............. 4.684608e+00
skewness........ -7.500470e-01
kurtosis........ 1.058310e+01
#null........... 0

GENERATION: 9
Fitness Value... 4.113123e-01
mean............ 3.168641e-01
var............. 2.395290e-02
skewness........ -1.277222e+00
kurtosis........ 2.916427e+00
#null........... 0
#unique......... 330, #Total UniqueCount: 4713
var 1:
best............ 9.995032e-01
mean............ 9.214294e-01
var............. 4.486820e+00
skewness........ -1.600141e-01
kurtosis........ 9.595010e+00
#null........... 0

GENERATION: 10
Fitness Value... 4.113123e-01
mean............ 3.128205e-01
var............. 2.395193e-02
skewness........ -1.222200e+00
kurtosis........ 2.813939e+00
#null........... 0
#unique......... 356, #Total UniqueCount: 5069
var 1:
best............ 9.995032e-01
mean............ 9.618829e-01
var............. 5.070343e+00
skewness........ -6.330780e-01
kurtosis........ 1.092658e+01
#null........... 0

GENERATION: 11
Fitness Value... 4.113123e-01
mean............ 3.172821e-01
var............. 2.414669e-02
skewness........ -1.284013e+00
kurtosis........ 2.907764e+00
#null........... 0
#unique......... 332, #Total UniqueCount: 5401
var 1:
best............ 9.995032e-01
mean............ 9.398430e-01
var............. 4.699622e+00
skewness........ -8.025722e-01
kurtosis........ 1.056258e+01
#null........... 0

Soft Generation Wait Limit Hit.
No Improvement in 10 Generations

Best Fit Found at Generation 1
Fit Value = 4.113123e-01


Parameters at the Solution (value, gradient):

 X[ 1] :	9.995032e-01	G[ 1] :	-7.354527e-07

Solution Found Generation 1
Number of Generations Run 11


Wed Jul 13 18:38:23 2005
Total run time : 0 hours 0 minutes and 17 seconds
>  xx <- seq(-3,3,.05);
>  plot(xx,lapply(xx,claw),type="l",xlab="Parameter",ylab="Fit",main="RGENOUD: Maximize the Claw Density");
>  points(claw1$par,claw1$value,col="red");
> 
> #maximize a bivariate normal mixture which looks like a claw
> biclaw <- function(xx) {
+   mNd2 <- function(x1, x2, mu1, mu2, sigma1, sigma2, rho)
+     {
+       z1 <- (x1-mu1)/sigma1;
+       z2 <- (x2-mu2)/sigma2;
+       w <- (1.0/(2.0*pi*sigma1*sigma2*sqrt(1-rho*rho))) ;
+       w <- w*exp(-0.5*(z1*z1 - 2*rho*z1*z2 + z2*z2)/(1-rho*rho)) ;
+       as.double(w);
+     }
+   x1 <- xx[1]+1;
+   x2 <- xx[2]+1;
+   
+   y <- (0.5*mNd2(x1,x2,0.0,0.0,1.0,1.0,0.0) +
+             0.1*(mNd2(x1,x2,-1.0,-1.0,0.1,0.1,0.0) +
+                  mNd2(x1,x2,-0.5,-0.5,0.1,0.1,0.0) +
+                  mNd2(x1,x2,0.0,0.0,0.1,0.1,0.0) +
+                  mNd2(x1,x2,0.5,0.5,0.1,0.1,0.0) +
+                  mNd2(x1,x2,1.0,1.0,0.1,0.1,0.0)));
+ 
+   as.double(y);
+ }
>  biclaw1 <- genoud(biclaw, nvars=2,P9=100,max=TRUE);


Wed Jul 13 18:38:23 2005
Domains:
 -1.000000e+01   <=  X1   <=    1.000000e+01 
 -1.000000e+01   <=  X2   <=    1.000000e+01 

Data Type: Floating Point
Operators (code number, name, population) 
	(1) Cloning........................... 	99
	(2) Uniform Mutation.................. 	100
	(3) Boundary Mutation................. 	100
	(4) Non-Uniform Mutation.............. 	100
	(5) Polytope Crossover................ 	100
	(6) Multiple Point Simple Crossover... 	100
	(7) Whole Non-Uniform Mutation........ 	100
	(8) Heuristic Crossover............... 	100
	(9) Local-Minimum Crossover........... 	200

HARD Maximum Number of Generations: 100
Maximum Nonchanging Generations: 10
Population size       : 1000
Convergence Tolerance: 1.000000e-03

Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.
Checking Gradients before Stopping
Not Using Out of Bounds Individuals and Not Allowing Trespassing.



Maximization Problem.



The 2 best initial individuals are
-0.04	-0.09	
fitness = 9.925422e-01

 0.07	 0.23	
fitness = 1.039715e-01


The worst fit of the population is: 1.416772e-50


GENERATION: 0 (initializing the population)
Fitness Value... 9.925422e-01
mean............ 2.412852e-03
var............. 1.050447e-03
skewness........ 2.864293e+01
kurtosis........ 8.713217e+02
#null........... 0
#unique......... 1000, #Total UniqueCount: 1000
var 1:
best............ -3.708312e-02
mean............ -1.095175e-01
var............. 3.415207e+01
skewness........ 7.285067e-02
kurtosis........ 1.787978e+00
#null........... 0
var 2:
best............ -9.353593e-02
mean............ 2.070009e-01
var............. 3.473768e+01
skewness........ -4.624598e-02
kurtosis........ 1.746463e+00
#null........... 0

GENERATION: 1
Fitness Value... 1.653530e+00
mean............ 3.174482e-01
var............. 2.684450e-01
skewness........ 1.444069e+00
kurtosis........ 3.510299e+00
#null........... 0
#unique......... 723, #Total UniqueCount: 1723
var 1:
best............ -1.499805e+00
mean............ -2.302861e-01
var............. 5.027632e+00
skewness........ -9.545901e-02
kurtosis........ 8.753016e+00
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -2.719070e-01
var............. 5.752401e+00
skewness........ 1.697083e-02
kurtosis........ 6.708634e+00
#null........... 0

GENERATION: 2
Fitness Value... 1.653530e+00
mean............ 8.447312e-01
var............. 5.679671e-01
skewness........ -8.674109e-02
kurtosis........ 1.122370e+00
#null........... 0
#unique......... 723, #Total UniqueCount: 2446
var 1:
best............ -1.499805e+00
mean............ -7.376452e-01
var............. 4.077810e+00
skewness........ 7.026804e-01
kurtosis........ 1.127414e+01
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -6.590804e-01
var............. 4.261916e+00
skewness........ 9.098941e-01
kurtosis........ 1.015934e+01
#null........... 0

GENERATION: 3
Fitness Value... 1.653530e+00
mean............ 1.081301e+00
var............. 6.033277e-01
skewness........ -6.336438e-01
kurtosis........ 1.411306e+00
#null........... 0
#unique......... 692, #Total UniqueCount: 3138
var 1:
best............ -1.499805e+00
mean............ -1.415448e+00
var............. 3.524990e+00
skewness........ 1.181762e+00
kurtosis........ 1.445328e+01
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -1.391298e+00
var............. 3.310899e+00
skewness........ 1.413483e+00
kurtosis........ 1.493229e+01
#null........... 0

GENERATION: 4
Fitness Value... 1.653530e+00
mean............ 1.081847e+00
var............. 5.993792e-01
skewness........ -6.337258e-01
kurtosis........ 1.418050e+00
#null........... 0
#unique......... 586, #Total UniqueCount: 3724
var 1:
best............ -1.499805e+00
mean............ -1.445415e+00
var............. 2.878014e+00
skewness........ 1.271471e+00
kurtosis........ 1.574456e+01
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -1.459978e+00
var............. 3.215938e+00
skewness........ 8.919321e-01
kurtosis........ 1.388835e+01
#null........... 0

GENERATION: 5
Fitness Value... 1.653530e+00
mean............ 1.100240e+00
var............. 5.861284e-01
skewness........ -6.844310e-01
kurtosis........ 1.489036e+00
#null........... 0
#unique......... 658, #Total UniqueCount: 4382
var 1:
best............ -1.499805e+00
mean............ -1.295737e+00
var............. 3.722713e+00
skewness........ 2.144333e+00
kurtosis........ 1.615788e+01
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -1.390284e+00
var............. 3.309234e+00
skewness........ 1.602472e+00
kurtosis........ 1.709494e+01
#null........... 0

GENERATION: 6
Fitness Value... 1.653530e+00
mean............ 1.133999e+00
var............. 5.738856e-01
skewness........ -7.856685e-01
kurtosis........ 1.626993e+00
#null........... 0
#unique......... 549, #Total UniqueCount: 4931
var 1:
best............ -1.499805e+00
mean............ -1.313593e+00
var............. 2.962008e+00
skewness........ 2.130707e+00
kurtosis........ 1.673027e+01
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -1.409912e+00
var............. 2.844190e+00
skewness........ 1.619571e+00
kurtosis........ 2.011661e+01
#null........... 0

GENERATION: 7
Fitness Value... 1.653530e+00
mean............ 1.103879e+00
var............. 5.829955e-01
skewness........ -6.956137e-01
kurtosis........ 1.504795e+00
#null........... 0
#unique......... 571, #Total UniqueCount: 5502
var 1:
best............ -1.499805e+00
mean............ -1.338938e+00
var............. 2.717643e+00
skewness........ 2.053667e+00
kurtosis........ 1.628919e+01
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -1.316340e+00
var............. 2.757645e+00
skewness........ 2.944927e+00
kurtosis........ 2.088150e+01
#null........... 0

GENERATION: 8
Fitness Value... 1.653530e+00
mean............ 1.127176e+00
var............. 5.722982e-01
skewness........ -7.624317e-01
kurtosis........ 1.600428e+00
#null........... 0
#unique......... 527, #Total UniqueCount: 6029
var 1:
best............ -1.499805e+00
mean............ -1.409122e+00
var............. 1.817824e+00
skewness........ 1.632175e+00
kurtosis........ 2.160476e+01
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -1.316026e+00
var............. 3.273460e+00
skewness........ 1.516643e+00
kurtosis........ 1.413415e+01
#null........... 0

GENERATION: 9
Fitness Value... 1.653530e+00
mean............ 1.119872e+00
var............. 5.729727e-01
skewness........ -7.424285e-01
kurtosis........ 1.576286e+00
#null........... 0
#unique......... 362, #Total UniqueCount: 6391
var 1:
best............ -1.499805e+00
mean............ -1.377003e+00
var............. 2.674903e+00
skewness........ 2.993767e+00
kurtosis........ 2.562608e+01
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -1.266454e+00
var............. 3.865792e+00
skewness........ 2.175041e+00
kurtosis........ 1.557521e+01
#null........... 0

GENERATION: 10
Fitness Value... 1.653530e+00
mean............ 1.131102e+00
var............. 5.724345e-01
skewness........ -7.716536e-01
kurtosis........ 1.608475e+00
#null........... 0
#unique......... 337, #Total UniqueCount: 6728
var 1:
best............ -1.499805e+00
mean............ -1.411657e+00
var............. 2.361724e+00
skewness........ 1.902220e+00
kurtosis........ 2.265128e+01
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -1.421756e+00
var............. 2.607812e+00
skewness........ 1.604477e+00
kurtosis........ 1.852527e+01
#null........... 0

GENERATION: 11
Fitness Value... 1.653530e+00
mean............ 1.095734e+00
var............. 5.824138e-01
skewness........ -6.727468e-01
kurtosis........ 1.481408e+00
#null........... 0
#unique......... 374, #Total UniqueCount: 7102
var 1:
best............ -1.499805e+00
mean............ -1.413112e+00
var............. 2.969382e+00
skewness........ 1.292388e+00
kurtosis........ 1.770412e+01
#null........... 0
var 2:
best............ -1.499805e+00
mean............ -1.393019e+00
var............. 2.977014e+00
skewness........ 1.505656e+00
kurtosis........ 1.839001e+01
#null........... 0

Soft Generation Wait Limit Hit.
No Improvement in 10 Generations

Best Fit Found at Generation 2
Fit Value = 1.653530e+00


Parameters at the Solution (value, gradient):

 X[ 1] :	-1.499805e+00	G[ 1] :	1.660889e-06
 X[ 2] :	-1.499805e+00	G[ 2] :	1.163506e-06

Solution Found Generation 2
Number of Generations Run 11


Wed Jul 13 18:38:46 2005
Total run time : 0 hours 0 minutes and 23 seconds
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  41.88 0.12 42.75 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')