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As can be seen in Figure 1, each musician in the orchestra has some notes in their
memories. They intend to improvise a new harmony with the question of “which note
will be played?” in their minds. Three rules of improvising a new harmony can be ex-
plained using the following way:
i) Memory Consideration
The first musician in the figure has a memory containing 3 notes, {La, Si, Do}. He
decides to choose
La
in his memory and plays it, directly. Likewise, if the first decision
variable represents the first musician, the value of 1.0 can be chosen from a memory.
ii) Pitch Adjustment
The second musician also has a 3-notes memory, {Do, Re, Mi}. Differently from
the first musician, he first chooses the note
Do
. Then, he can play its neighbor pitch
such as
Do Sharp
. Likewise, the value of 3.2 is chosen from the memory, and then it
can be adjusted into a neighbor value 3.1 in this step.
iii) Random Selection
The last musician has some notes in his memory, {Fa, Sol, La}, as well. Although
this memory was used during the past improvisations, due to his musical knowledge
he can also play all possible pitches, {Do, Re, Mi, Fa, Sol, La, Si, Do+}. Thus, when
he decides to play a note randomly, he can choose any of these notes,
Mi
in this ex-
ample. As being in the possible data set, 1.6 can be chosen in this step, randomly,
even if it doesn't exist in the memory.
After each musician has decided what to play, the new harmony is composed of
(La, Do#, Mi). Similarly, a new solution vector is determined as (1.0, 3.1, 1.6).
Step 4: Update the HM
If the newly generated harmony vector gives a better function value than the worst
one, the new harmony vector is included in the HM and the worst harmony is
excluded.
Step 5: Check the termination criterion
If the stopping criterion (i.e. maximum number of improvisations) is satisfied,
computation is terminated. Otherwise, Steps 3 to 5 are repeated.
4 Transport Energy Demand Problem
Due to its big share, transport energy consumption is an important component of total
energy consumption for countries. Modeling this component plays vital importance for
future planning studies. Transport energy planning is not possible without a reasonable
knowledge of past and present energy consumption and likely future demands [11].
The estimation of future energy demand can be represented with various forms of
mathematical expressions. The non-linear forms of the equations may better estimate
the future energy demand of Turkey due to the fluctuations of socio-economic indica-
tors. For modeling the energy demand in transport sector, Harmony Search Transport
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