Harmony Search Algorithm

Harmony Search Algorithm is a heuristic method for global optimization.

Description

Harmony search tries to find a vector which optimizes (minimizes or maximizes) a certain objective function.
The algorithm has the following steps:
Step 1: Generate random vectors () as many as (harmony memory size), then store them in harmony memory (HM).

Step 2: Generate a new vector . For each component ,
with probability (harmony memory considering rate; 0 ≤ ≤ 1), pick the stored value from HM:
with probability , pick a random value within the allowed range.
Step 3: Perform additional work if the value in Step 2 came from HM.
with probability (pitch adjusting rate; 0 ≤ ≤ 1), change by a small amount: or for discrete variable; or for continuous variable.
with probability , do nothing.
Step 4: If is better than the worst vector in HM, replace with .
Step 5: Repeat from Step 2 to Step 4 until termination criterion (e.g. maximum iterations) is satisfied.
The parameters of the algorithm are
 = the size of the harmony memory. It generally varies from 1 to 100. (typical value = 30)
 = the rate of choosing a value from the harmony memory. It generally varies from 0.7 to 0.99. (typical value = 0.9)
 = the rate of choosing a neighboring value. It generally varies from 0.1 to 0.5. (typical value = 0.3)
 = the amount between two neighboring values in discrete candidate set.
 (fret width, formerly bandwidth) = the amount of maximum change in pitch adjustment. This can be (0.01 × allowed range) to (0.001 × allowed range).
It is possible to vary the parameter values as the search progresses, which gives an effect similar to simulated annealing.
Parameter-setting-free researches have been also performed. In the researches, algorithm users do not need tedious parameter setting process.

see more in :
http://en.wikipedia.org/wiki/Harmony_search

• MATLAB release: MATLAB 8.0 (R2012b)

[Andrés]

Thanks, the code has been very useful for my research on the implementation of a multi objective HS technique