Harmony Search in Therapeutic Medical Physics - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 194

On the other hand, the genetic algorithm selects two individuals (solutions) to
mate. The dwell times in each solution are crossed over and potentially mutated in
order to produce a new, but similar solution. Only after the mating process has
been completed does the comparison step occur. It is this difference that causes
Harmony Search to be somewhat slower in speed per iteration. However, due to
the significant convergence speed difference, the iteration speed becomes insig-
nificant after all.

3.3.2 Integer Versus Floating Point Dwell Time Optimization
Since the optimization can be run in both integer and floating point (FP) mode, it
is important to investigate the difference between them during the simulation. Pa-
tient #4 was selected and optimized 10 times each for Harmony Search using both
integer and floating point modes. The same experiment was repeated for the ge-
netic algorithm. The constraints for this simulation were set to the same values as
in Table 1.
As can be seen in Table 4, Harmony Search takes slightly longer (average number
of iterations and average time per iteration) to converge to the solution when using
floating point mode compared to integer mode. However, the genetic algorithm actu-
ally is slightly faster when using floating point mode.

Table 4. Comparison of Harmony Search and genetic algorithm optimization - Integer versus
Floating Point

Optimization Method Integer / FP Iterations Time / Iteration (s)

Harmony Search Integer

FP

56.70
69.33

2.84
3.19

Genetic Algorithm Integer

FP

198.20
182.43

3.21
3.18

If more iterations were performed for each type of simulation, the difference would
probably be negligible and become statistically insignificant. Still, Harmony Search is
faster than the genetic algorithm for both floating point and integer modes for each
overall simulation, corroborating the results shown above in subsection 3.3.1. In inte-
ger mode, Harmony Search is around 400% faster and in floating point mode almost
300% faster.
The DVHs for integer and floating point representations using Harmony Search are
shown in Figure 3 and Figure 4, respectively. Qualitatively, Harmony Search in float-
ing point mode meets the same constraints as the integer mode, however, the dose to
the prostate and urethra are much higher. Likewise, similar results occur with the ge-
netic algorithm in floating point mode. The reason is that there are only 21 possible
choices for the integer times (0-20), while there are infinitely more choices when us-
ing floating point. In order for the floating point simulation to minimize the remaining
dwell times, it would take significantly more time to reduce to an integer mode-like
result.