/ 
MachineLearning-1.02
/ MachineLearning::SimulatedAnnealing

NAME

MachineLearning::SimulatedAnnealing - optimize a list of numbers according to a cost function

SYNOPSIS

use MachineLearning::SimulatedAnnealing;
my $result_array_ref = anneal({
  "Ranges" => [ [0, 3], [-1, 4], [-4, 0] ],
  "CostCalculator" => $cost_calculator_coderef,
  "CyclesPerTemperature" => 10_000});

DESCRIPTION

This module exports a single function, anneal(), which performs simulated annealing to optimize a list of numbers that have predefined ranges. The list can be of any size N.

In addition to the ranges for the numbers, the anneal() function takes a reference to a cost function that takes a list of size N and returns a number representing a cost to be minimized.

The anneal() function also takes as input a positive integer specifying the number of cycles per temperature; that is, the number of randomization cycles to perform at each temperature level during the annealing process. A higher number of cycles per temperature produces more accurate results while increasing the amount of time required for the annealing process to complete.

FUNCTIONS

anneal($args_hashref);

This function takes a reference to a hash with the following fields:

Ranges - A reference to an array of pairs of bounds, lower and
upper, where a pair is a reference to an array of two real
decimal numbers of which the first is less than the second.

CostCalculator - A reference to a function that takes a
reference to an array of numbers and returns a single number
representing a cost to be minimized.  The function must take an
input array that is the same size as the Ranges array.

CyclesPerTemperature - A positive integer specifying the number
of randomization cycles performed at each temperature level.

  NOTE:  Temperature starts at 100% (which means that each
  number gets randomized within 100% of its specified range) and
  then gradually decreases.  To randomize a number within a
  range corresponding to a temperature that is less than 100%,
  the function calculates the appropriate size for the sub-range
  and then chooses the exact location for that sub-range (within
  the total range specified for the number) such that the
  current value of the number is as close as possible to the
  sub-range center.

  The temperature, expressed as a percentage, decreases as
  follows:

      100.000, 95.000, 90.000, 85.000, 80.000, 75.000, 70.000,
       65.000, 60.000, 55.000, 50.000, 45.000, 40.000, 38.000,
       36.000, 34.000, 32.000, 30.000, 28.000, 26.000, 24.000,
       22.000, 20.000, 19.000, 18.000, 17.000, 16.000, 15.000,
       14.000, 13.000, 12.000, 11.000, 10.000, 09.500, 09.000,
       08.500, 08.000, 07.500, 07.000, 06.500, 06.000, 05.500,
       05.000, 04.500, 04.000, 03.800, 03.600, 03.400, 03.200,
       03.000, 02.800, 02.600, 02.400, 02.200, 02.000, 01.900,
       01.800, 01.700, 01.600, 01.500, 01.400, 01.300, 01.200,
       01.100, 01.000, 00.950, 00.900, 00.850, 00.800, 00.750,
       00.700, 00.650, 00.600, 00.550, 00.500, 00.450, 00.400,
       00.380, 00.360, 00.340, 00.320, 00.300, 00.280, 00.260,
       00.240, 00.220, 00.200, 00.190, 00.180, 00.170, 00.160,
       00.150, 00.140, 00.130, 00.120, 00.110, 00.100, 00.095,
       00.090, 00.085, 00.080, 00.075, 00.070, 00.065, 00.060,
       00.055, 00.050, 00.045, 00.040, 00.038, 00.036, 00.034,
       00.032, 00.030, 00.028, 00.026, 00.024, 00.022, 00.020,
       00.019, 00.018, 00.017, 00.016, 00.015, 00.014, 00.013,
       00.012, 00.011, 00.010, 00.009, 00.008, 00.007, 00.006,
       00.005, 00.004, 00.003, 00.002, 00.001, 00.000

If the CyclesPerTemperature value is not a positive integer,
the anneal() function returns a reference to an empty array.

The anneal() function returns a reference to an array of numbers that corresponds to the Ranges array (that is, the output array is the same size as the Ranges array, and each number in the output array is within the range specified by the corresponding element in the Ranges array). The output array is the list of numbers that has the lowest cost (according to the specified cost function) of any of the lists tested during the annealing process.

AUTHOR

Benjamin Fitch, <blernflerkl@yahoo.com>

COPYRIGHT AND LICENSE

Copyright 2009 by Benjamin Fitch

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.