Harmony Search in Therapeutic Medical Physics - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 191

able to choose either Harmony Search or genetic algorithm as the optimization algo-
rithm. A Windows XP PC with an Intel Core 2 Duo E6300 Processor (2 processor
cores at 1.86 GHz) and 2 GB of RAM was used for all of the simulations. The default
settings for the simulation can be seen in Figure 2.
For Harmony Search, the default values for the harmony memory size (HMS),
harmony memory considering rate (HMCR), and pitch adjusting rate (PAR) were 5,
0.95, and 0.9 respectively and could be modified in the simulation. For the genetic al-
gorithm, the population size (default value of 5) and the number of generations (de-
fault value of 100) could be adjusted.
The general simulation parameters include the minimum and maximum dwell
times, which were set as hard constraints. At each dwell position, the dwell times
were constrained to lie between 0 and a maximum of 20 seconds for both algorithms.
The threshold to solution of the objective function was set to 10.
Additionally, the final solution value was set to 0. With this combination, the simu-
lation would terminate if the solution value were less than 10. The number of itera-
tions was set to 300, in order to let each simulation reach the solution. This number
was determined from prior experimentation as a minimum threshold, which would al-
low the simulation to reach the goal. Increasing the number of iterations increases the
total time for the simulation, but does not necessarily produce a better solution.
Finally, the simulation could be operated in integer mode or floating point mode.
In integer mode, the dwell times are constrained to integer values as mentioned above.
In floating point mode, the dwell times are represented in computer hardware as bi-
nary fractions, and is the method how real numbers are stored. For example, the
decimal fraction 0.125 has a value of 1/10 + 2/100 and 5/1000 while the binary frac-
tion 0.001 has a value of 0/2 + 0/4 + 1/8. These two fractions have identical values,
but the only difference is the first value is written in base 10 notation and the second
is written in base 2.
Unfortunately, most decimal fractions cannot be represented exactly as binary frac-
tions. A consequence is that, in general, decimal floating point numbers that are en-
tered are only approximated by the binary floating-point numbers actually stored in
the machine. However, since the precision of time used in the HDR treatment unit is
either specified as an integer or to the tenth of a decimal point, this does not have any
adverse effects on the final optimization solution.
These modes reflect the data type for the dwell times used in the optimization. For
all of the experiments, except for subsection 3.3.2, integer mode was selected, since
the GammaMed 192 Ir HDR source (used in our institution) can only use integer sec-
onds for dwell times. However, since other sources such as the Varian VariSource can
be operated with tenth of a second precision, it is important to investigate how the
optimization differs between modes.
3.3 Results of Investigation
Harmony Search and genetic algorithm were implemented in the simulation as the
available optimization algorithms. They were compared against each other in regard to
the number of iterations and average time per iteration. Additionally, integer versus
floating point simulation modes were also investigated. Finally, the optimal parameters
for Harmony Search were determined for HDR prostate brachytherapy optimization.