/usr/share/tcltk/tcllib1.17/simulation/annealing.tcl is in tcllib 1.17-dfsg-1.
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# Package implementing simulated annealing for minimizing functions
# of one or more parameters
#
# Copyright (c) 2007 by Arjen Markus <arjenmarkus@users.sourceforge.net>
#
# See the file "license.terms" for information on usage and redistribution
# of this file, and for a DISCLAIMER OF ALL WARRANTIES.
#
# RCS: @(#) $Id: annealing.tcl,v 1.4 2008/02/22 13:34:07 arjenmarkus Exp $
#------------------------------------------------------------------------------
package require Tcl 8.4
# ::simulation::annealing --
# Create the namespace
#
namespace eval ::simulation::annealing {
}
# getOption --
# Return the value of an option
#
# Arguments:
# option Name of the option (without -)
# Result:
# The value or an error message if it does not exist
#
proc ::simulation::annealing::getOption {option} {
variable ann_option
if { [info exists ann_option(-$option)] } {
return $ann_option(-$option)
} else {
return -code error "No such option: $option"
}
}
# setOption --
# Set the value of an option
#
# Arguments:
# option Name of the option (without -)
# value Value of the option
# Result:
# None
#
proc ::simulation::annealing::setOption {option value} {
variable ann_option
set ann_option(-$option) $value
}
# hasOption --
# Return whether the given option exists or not
#
# Arguments:
# option Name of the option (without -)
# Result:
# 1 if it exists, 0 if not
#
proc ::simulation::annealing::hasOption {option} {
variable ann_option
if { [info exists ann_option(-$option)] } {
return 1
} else {
return 0
}
}
# findMinimum --
# Find the (global) minimum of a function using simulated annealing
#
# Arguments:
# args Option-value pairs:
# -parameters list - triples defining parameters and ranges
# -function expr - expression defining the function
# -code body - body of code to define the function
# (takes precedence over -function)
# should set the variable "result"
# -init code - code to be run at start up
# -final code - code to be run at the end
# -trials n - number of trials before reducing the temperature
# -reduce factor - reduce the temperature by this factor
# (between 0 and 1)
# -initial-temp t - initial temperature
# -scale s - scale of the function (order of
# magnitude of the values)
# -estimate-scale y/n - estimate the scale (only if -scale not present)
# -verbose y/n - Turn verbose printing on (1) or off (0)
# -reportfile file - Channel to write verbose output to
# Any others can be used via the getOption procedure
# in the body.
#
# Result:
# Estimated minimum and the parameters involved:
# function value param1 value param2 value ...
#
proc ::simulation::annealing::findMinimum {args} {
variable ann_option
#
# Handle the options
#
set ann_option(-parameters) {}
set ann_option(-function) {}
set ann_option(-code) {}
set ann_option(-init) {}
set ann_option(-final) {}
set ann_option(-trials) 300
set ann_option(-reduce) 0.95
set ann_option(-initial-temp) 1.0
set ann_option(-scale) {}
set ann_option(-estimate-scale) 0
set ann_option(-verbose) 0
set ann_option(-reportfile) stdout
foreach {option value} $args {
set ann_option($option) $value
}
if { $ann_option(-scale) == {} } {
if { ! $ann_option(-estimate-scale) } {
set ann_option(-scale) 1.0
}
}
if { $ann_option(-code) != {} } {
set ann_option(-function) {}
}
if { $ann_option(-code) == {} && $ann_option(-function) == {} } {
return -code error "Neither code nor function given! Nothing to optimize"
}
if { $ann_option(-parameters) == {} } {
return -code error "No parameters given! Nothing to optimize"
}
if { $ann_option(-function) != {} } {
set ann_option(-code) "set result \[expr {$ann_option(-function)}\]"
}
#
# Create the procedure
#
proc FindMin {} [string map \
[list PARAMETERS $ann_option(-parameters) \
CODE $ann_option(-code) \
INIT $ann_option(-init) \
FINAL $ann_option(-final)] {
#
# Give all parameters a value
#
foreach {_param_ _min_ _max_} {PARAMETERS} {
set $_param_ $_min_
}
set _trials_ [getOption trials]
set _temperature_ [getOption initial-temp]
set _reduce_ [getOption reduce]
set _noparams_ [expr {[llength {PARAMETERS}]/3}]
set _verbose_ [getOption verbose]
set _reportfile_ [getOption reportfile]
INIT
#
# Estimate the scale
#
if { [getOption estimate-scale] == 1 } {
set _sum_ 0.0
for { set _trial_ 0 } { $_trial_ < $_trials_/3 } { incr _trial_ } {
set _randp_ [expr {3*int($_noparams_*rand())}]
set _param_ [lindex {PARAMETERS} $_randp_]
set _min_ [lindex {PARAMETERS} [expr {$_randp_+1}]]
set _max_ [lindex {PARAMETERS} [expr {$_randp_+2}]]
set _old_param_ [set $_param_]
set $_param_ [expr {$_min_ + rand()*($_max_-$_min_)}]
CODE
set _sum_ [expr {$_sum_ + abs($result)}]
}
set _scale_ [expr {3.0*$_sum_/$_trials_}]
} else {
set _scale_ [getOption scale]
}
if { $_verbose_ } {
puts $_reportfile_ "Scale value: $_scale_"
}
#
# Start the outer loop
#
set _changes_ 1
#
# Get the initial value of the function
#
CODE
set _old_result_ $result
if { $_verbose_ } {
puts $_reportfile_ "Result -- Mean of accepted values -- % accepted"
}
while {1} {
set _sum_ $_old_result_
set _accepted_ 1
for { set _trial_ 0 } { $_trial_ < $_trials_} { incr _trial_ } {
set _randp_ [expr {3*int($_noparams_*rand())}]
set _param_ [lindex {PARAMETERS} $_randp_]
set _min_ [lindex {PARAMETERS} [expr {$_randp_+1}]]
set _max_ [lindex {PARAMETERS} [expr {$_randp_+2}]]
set _old_param_ [set $_param_]
set $_param_ [expr {$_min_ + rand()*($_max_-$_min_)}]
CODE
#
# Accept the new solution?
#
set _rand_ [expr {rand()}]
if { log($_rand_) < -($result-$_old_result_)/($_scale_*$_temperature_) } {
incr _changes_
set _old_result_ $result
set _sum_ [expr {$_sum_ + $result}]
incr _accepted_
} else {
set $_param_ $_old_param_
}
}
if { $_verbose_ } {
puts $_reportfile_ \
[format "%.5g -- %.5g -- %.2f %%" $_old_result_ \
[expr {$_sum_/$_accepted_}] [expr {100.0*double($_changes_)/$_trials_}]]
}
set _temperature_ [expr {$_reduce_ * $_temperature_}]
if { $_changes_ == 0 } {
break
} else {
set _changes_ 0
}
}
set result [list result $_old_result_] ;# Note: we need the last accepted result!
foreach {_param_ _min_ _max_} {PARAMETERS} {
lappend result $_param_ [set $_param_]
}
FINAL
return $result
}]
#
# Do the actual computation and return the result
#
return [FindMin]
}
# findCombinatorialMinimum --
# Find the (global) minimum of a combinatorial function using simulated annealing
#
# Arguments:
# args Option-value pairs:
# -number-params n - number of (binary) parameters
# -initial-values list - list of parameter values to start with
# -function expr - expression defining the function
# -code body - body of code to define the function
# (takes precedence over -function)
# should set the variable "result"
# The values of the solutions
# are stored as a list in the
# variable params
# -init code - code to be run at start up
# -final code - code to be run at the end
# -trials n - number of trials before reducing the temperature
# -reduce factor - reduce the temperature by this factor
# (between 0 and 1)
# -initial-temp t - initial temperature
# -scale s - scale of the function (order of
# magnitude of the values)
# -estimate-scale y/n - estimate the scale (only if -scale not present)
# -verbose y/n - Turn verbose printing on (1) or off (0)
# -reportfile file - Channel to write verbose output to
# Any others can be used via the getOption procedure
# in the body.
#
# Result:
# Estimated minimum and the parameters involved:
# function value, list of values
#
# Note:
# The parameters have the values 0 or 1
#
# The stop criterion is that if the result value does not change in
# sqrt(trials) then the iteration stops. Experiments with the
# example below show that the function to be minimised can show
# a very wide minimum due to the parameters being discrete.
# sqrt(trials) is just an arbitrary value.
#
proc ::simulation::annealing::findCombinatorialMinimum {args} {
variable ann_option
#
# Handle the options
#
set ann_option(-number-params) {}
set ann_option(-initial-values) {}
set ann_option(-function) {}
set ann_option(-code) {}
set ann_option(-init) {}
set ann_option(-final) {}
set ann_option(-trials) 300
set ann_option(-reduce) 0.95
set ann_option(-initial-temp) 1.0
set ann_option(-scale) {}
set ann_option(-estimate-scale) 0
set ann_option(-verbose) 0
set ann_option(-reportfile) stdout
foreach {option value} $args {
set ann_option($option) $value
}
if { $ann_option(-scale) == {} } {
if { ! $ann_option(-estimate-scale) } {
set ann_option(-scale) 1.0
}
}
if { $ann_option(-code) != {} } {
set ann_option(-function) {}
}
if { $ann_option(-code) == {} && $ann_option(-function) == {} } {
return -code error "Neither code nor function given! Nothing to optimize"
}
if { $ann_option(-number-params) == {} } {
return -code error "Number of parameters not given! Nothing to optimize"
}
if { $ann_option(-initial-values) == {} } {
for { set i 0 } { $i < $ann_option(-number-params) } { incr i } {
lappend ann_option(-initial-values) 0
}
}
if { $ann_option(-function) != {} } {
set ann_option(-code) "set result \[expr {$ann_option(-function)}\]"
}
#
# Create the procedure
#
proc FindCombMin {params} [string map \
[list CODE $ann_option(-code) \
INIT $ann_option(-init) \
FINAL $ann_option(-final)] {
set _trials_ [getOption trials]
set _temperature_ [getOption initial-temp]
set _reduce_ [getOption reduce]
set _noparams_ [llength $params]
set _verbose_ [getOption verbose]
set _reportfile_ [getOption reportfile]
INIT
#
# Estimate the scale
#
if { [getOption estimate-scale] == 1 } {
set _sum_ 0.0
set _old_params_ $params
for { set _trial_ 0 } { $_trial_ < $_trials_/3 } { incr _trial_ } {
set _randp_ [expr {int($_noparams_*rand())}]
lset params $_randp_ [expr {rand()>0.5? 0 : 1}]
CODE
set _sum_ [expr {$_sum_ + abs($result)}]
}
set _scale_ [expr {3.0*$_sum_/$_trials_}]
set params $_old_params_
} else {
set _scale_ [getOption scale]
}
if { $_verbose_ } {
puts $_reportfile_ "Scale value: $_scale_"
}
#
# Start the outer loop
#
set _changes_ 1
#
# Get the initial value of the function
#
CODE
set _old_result_ $result
set _result_same_ 0
set _result_after_loop_ $result
if { $_verbose_ } {
puts $_reportfile_ "Result -- Mean of accepted values -- % accepted"
}
while {1} {
set _sum_ $_old_result_
set _accepted_ 1
for { set _trial_ 0 } { $_trial_ < $_trials_} { incr _trial_ } {
set _old_params_ $params
set _randp_ [expr {int($_noparams_*rand())}]
lset params $_randp_ [expr {rand()>0.5? 0 : 1}]
CODE
#
# Accept the new solution?
#
set _rand_ [expr {rand()}]
if { log($_rand_) < -($result-$_old_result_)/($_scale_*$_temperature_) } {
incr _changes_
set _old_result_ $result
set _sum_ [expr {$_sum_ + $result}]
incr _accepted_
} else {
set params $_old_params_
}
}
if { $_verbose_ } {
puts $_reportfile_ \
[format "%.5g -- %.5g -- %.2f %%" $_old_result_ \
[expr {$_sum_/$_accepted_}] [expr {100.0*double($_changes_)/$_trials_}]]
}
set _temperature_ [expr {$_reduce_ * $_temperature_}]
if { $_changes_ == 0 || $_result_same_ > sqrt($_trials_) } {
break
} else {
set _changes_ 0
}
if { $_result_after_loop_ == $_old_result_ } {
incr _result_same_
} else {
set _result_after_loop_ $_old_result_
}
}
set result [list result $_old_result_] ;# Note: we need the last accepted result!
lappend result solution $params
FINAL
return $result
}]
#
# Do the actual computation and return the result
#
return [FindCombMin $ann_option(-initial-values)]
}
# Announce the package
#
package provide simulation::annealing 0.2
# main --
# Example
#
if { 0 } {
puts [::simulation::annealing::findMinimum \
-trials 300 \
-verbose 1 \
-parameters {x -5.0 5.0 y -5.0 5.0} \
-function {$x*$x+$y*$y+sin(10.0*$x)+4.0*cos(20.0*$y)}]
puts "Constrained:"
puts [::simulation::annealing::findMinimum \
-trials 3000 \
-reduce 0.98 \
-parameters {x -5.0 5.0 y -5.0 5.0} \
-code {
if { hypot($x-5.0,$y-5.0) < 4.0 } {
set result [expr {$x*$x+$y*$y+sin(10.0*$x)+4.0*cos(20.0*$y)}]
} else {
set result 1.0e100
}
}]
}
#
# A simple combinatorial problem:
# We have 100 items and the function is optimal if the first 10
# values are 1 and the result is 0. Can we find this solution?
#
# What if we have 1000 items? Or 10000 items?
#
# WARNING:
# 10000 items take a very long time!
#
if { 0 } {
proc cost {params} {
set cost 0
foreach p [lrange $params 0 9] {
if { $p == 0 } {
incr cost
}
}
foreach p [lrange $params 10 end] {
if { $p == 1 } {
incr cost
}
}
return $cost
}
foreach n {100 1000 10000} {
break
puts "Problem size: $n"
puts [::simulation::annealing::findCombinatorialMinimum \
-trials 300 \
-verbose 0 \
-number-params $n \
-code {set result [cost $params]}]
}
#
# Second problem:
# Only the values of the first 10 items are important -
# they should be 1
#
proc cost2 {params} {
set cost 0
foreach p [lrange $params 0 9] {
if { $p == 0 } {
incr cost
}
}
return $cost
}
foreach n {100 1000 10000} {
puts "Problem size: $n"
puts [::simulation::annealing::findCombinatorialMinimum \
-trials 300 \
-verbose 0 \
-number-params $n \
-code {set result [cost2 $params]}]
}
}
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