Harmony Search in Therapeutic Medical Physics - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 193

case, is at least 5 times faster and in the worst case 3 times faster when compared to
the genetic algorithm. On average, about a 400% improvement can be realized by us-
ing Harmony Search over the genetic algorithm as the optimization algorithm.
The reason that Harmony Search is so much faster than genetic algorithm can be
attributed to the fact that the former selects values from all available vectors in the Har-
mony Memory. The genetic algorithm chooses values only from two vectors. Both algo-
rithms however, do have the ability to introduce variability into each decision variable
by replacing a value at random (Harmony Memory Considering Rate / Pitch Adjusting
Rate for the Harmony Search and crossover / mutation for the genetic algorithm).
These results are in line with prior studies [5-9]. The reason that the optimization is
slower with the DVH-based objective function compared to simple mathematical cases
of finding the solution to the “six hump camel back” function [15], is that the dose cal-
culation involves much more decision variables (dwell positions) versus only 2 decision
variables. In all of the patients listed above, the number of dwell positions was at least
200 and was sometimes over 400. This number was dependent on the specific patient
data imported, where a shorter step distance involves more possible dwell positions.
A note of interest is the average time per iteration. In Table 3, a selection of patients is
shown with the corresponding time per iteration values. Although the genetic algorithm is
slower to reach the convergence point, the time per iteration is slightly faster. The reason
is that, for each iteration, Harmony Search must assemble a vector from the Harmony
Memory and compare it once per iteration, while the genetic algorithm only has to select
two individuals, create an offspring and create a new population once per generation.

Table 3. Comparison of Harmony Search and genetic algorithm optimization - average time
per iteration

Patient Optimization Method Average Time / Iteration (s)

2 Harmony Search

Genetic Algorithm

21.68
19.53

3 Harmony Search

Genetic Algorithm

19.58
17.28

4 Harmony Search

Genetic Algorithm

19.28
15.53

5 Harmony Search

Genetic Algorithm

6.84
6.32

Average % Difference 11.34%

For example, if the Harmony Memory Size was set to 5, then, for each dwell posi-
tion, the algorithm must select a value either from the 5 vectors in memory or choose
a random value. If the value is selected from memory, the algorithm also must vary
the pitch, according to the Pitch Adjusting Rate. In this simulation, that would be
equivalent to increasing or decreasing the dwell time by one. This whole process must
be repeated for each dwell position. After this, the new vector has to be compared
against the existing vectors in the Harmony Memory. If it is better, it replaces the vec-
tor with the worst function value.