Harmony Search in Therapeutic Medical Physics - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 196

3.3.3 Harmony Search Parameters
When using Harmony Search, a number of parameters can be modified in order to
change the outcome of the optimization. The Harmony Search parameters: HMS,
HMCR, and PAR were modified independently in order to determine the best values
for HDR prostate brachytherapy optimization.
For each parameter investigation, the number of iterations was set to 300. Addi-
tionally, the constraints were modified so that the prostate D95 was set to 100% and
the urethra, rectum, and bladder weights were increased to 50. This was done to speed
up the convergence time due to repeated simulations. For each Harmony Memory
Size, the experiment was repeated five times to improve statistical significance.

3.3.3.1 Harmony Memory Size. The Harmony Memory Size is an analogous con-
struct to the population size of the genetic algorithm. Typical values from previous
studies range from 4 to 10 [5-9].
A new patient (#10) was selected to run the optimization and the Harmony Mem-
ory Size was set to 1, 5, 10, and 20. The results are shown in Table 5. The results
show that as the Harmony Memory Size increases in value, the convergence of the so-
lution gets worse, based on the final solution value. Additionally, the time each itera-
tion takes increases as well. The reasoning behind this is that during each iteration,
the algorithm selects randomly from the Harmony Memory to construct a new vector.
If the Harmony Memory Size increases, the chance of a better solution to be chosen
decreases since the HM is populated with more, but inferior solutions.

Table 5. Harmony Memory Size (HMS) comparison

HMS Solution Value Time / Iteration (s) D95 prostate (cGy)

1 689 ± 65 6.58 ± 0.64 947.0 ± 3.46

5 838 ± 57 6.91 ± 0.62 954.0 ± 4.24

10 1104 ± 145 7.50 ± 0.86 948.0 ± 0.00

20 1536 ± 168 9.95 ± 1.03 944.0 ± 5.13

When the Harmony Memory Size is set to a value of 1, the convergence is the fast-
est. At first, it may seem that this condition may result in premature convergence in a
local minimum / maximum. However, Harmony Search introduces random values
based on the Harmony Memory Considering Rate, and therefore, decreases this possi-
bility since it allows to escape the current minimum / maximum.
Sample DVHs were constructed for each of the HMS values chosen. The differ-
ence between each DVH is minimal, but if inspected closely, and correlated with the
solution value, the DVH from HMS sizes 1 and 5 are slightly better than 10 and 20 as
the urethra receives less of a dose than the prostate.

3.3.3.2 Harmony Memory Considering Rate. The Harmony Memory Considering
Rate (HMCR) is a variable that determines whether the value for the current decision
variable in the new vector should come from Harmony Memory or be randomly gen-
erated. This allows variability so that the optimization does not get trapped in a local
minimum maximum. Prior studies have used a value of 0.95 for the HMCR.