Harmony Search Methods for Multi-modal and Constrained Optimization - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 39

Random Solutions

Selection

Evaluation

Harmony Memory Worst Member Comparison

No

Better
Fitness ?

Elimination

Yes

Replacement

Fig. 1. Harmony Search (HS) method

Step 1. Initialize a harmony memory (HM). The initial HM consists of a certain number of
randomly generated solutions for the optimization problem under consideration. For an n -
dimension problem, an HM with the size of HMS can be represented as follows:

⎡

1
1

1
2

1

⎤

x , x , " , x

n

⎢ ⎥

2
1

2
2

2

⎢ x , x , " , x ⎥

n

HM = ,

(1)

⎢ ⎥

#

⎢ ⎥

⎢ ⎥

HMS HMS HMS

n

x , x , " , x

⎣ ⎦

1 2

( )

i i i

n

where x , x , " ( , x i = 1 " 2 , HMS ) is a candidate solution. HMS is typically set

1 2

to be between 10 and 100.

( )

′ ′ ′

Step 2. Improvise a new solution x , x , " from the HM. Each component of , x

1 2 n

x ′ this solution, , is obtained based on the Harmony Memory Considering Rate

j