Harmony Search as a Metaheuristic Algorithm - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 11

Proper diversification or exploration makes sure that the search in solution space
can explore as many locations and regions as possible in an efficient and effective
manner. It also ensures that the evolving system will not be trapped in biased local
optima. Diversification is often represented in the implementation as the randomiza-
tion and/or additional stochastic component superposed onto the deterministic com-
ponents. If the diversification is too strong, it may explore too many locations in a
stochastic manner, and subsequently will slow down the convergence of the algo-
rithm; if the diversification is too weak, there is a risk that the solution space explored
is so limited and the solutions are biased and trapped in local optima, or even lead to
meaningless solutions.
On the other hand, the appropriate intensification or exploitation intends to exploit
the history and experience of the search process. It aims to ensure to speed up the con-
vergence when necessary by reducing the randomness and limiting diversification. In-
tensification is often carried out by using memory such as in tabu search and/or elitism
such as in genetic algorithm. In other algorithms, it is much more elaborate to use inten-
sification such as the case in simulated annealing and firefly algorithms. If the intensifi-
cation is too strong, it could result in premature convergence, leading to biased local op-
tima or even meaningless solutions because the search space is not well explored. On
the contrary, if the intensification is too weak, convergence becomes slow.
The optimal balance of diversification and intensification is required, and such a
balance itself is an optimization process. Fine-tuning of parameters is often required
to improve the efficiency of an algorithm for a particular problem. There is No Free
Lunch in any optimization problem [21]. A substantial amount of studies might be re-
quired to choose the right algorithm for the right optimization problem [16], though a
systematic guidance lacks for such a choice.
4.2 Why HS Is Successful
Now if we analyze the Harmony Search algorithm in the context of the major compo-
nents of metaheuristics and try to compare with other metaheuristic algorithms, we
can identify its ways of handling intensification and diversification, and probably un-
derstand why it is a very successful metaheuristic algorithm.
In the HS algorithm, diversification is essentially controlled by the pitch adjustment
and randomization -- here there are two subcomponents for diversification, which
might be an important factor for the high efficiency of the HS method. The first sub-
component of playing a new pitch (or generating a new value) via randomization
would be at least at the same level of efficiency as in other algorithms that handle ran-
domization. However, an additional subcomponent for HS diversification is the pitch
adjustment operation performed with the probability of r pa . Pitch adjustment is carried
out by tuning the pitch within a given bandwidth. A small random amount is added to
or subtracted from an existing pitch (or solution) stored in HM. Essentially, pitch ad-
justment is a refinement process of local solutions. Both memory consideration and
pitch adjustment ensure that good local solutions are retained while the randomization
makes the algorithm to explore global search space effectively. The subtlety is the fact
that HS operates controlled diversification around good solutions, and intensification
as well. The randomization explores the search space more widely and efficiently;