/usr/share/tcltk/tcllib1.18/simulation/annealing.tcl is in tcllib 1.18-dfsg-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 | # annealing.tcl --
# 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]}]
}
}
|