Harmony Search as a Metaheuristic Algorithm - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 12

while the pitch adjustment ensures that the newly generated solution is good enough,
or not too far from existing good solutions.
The intensification in the HS algorithm is represented by the harmony memory ac-
cepting rate r accept . A high harmony acceptance rate means that good solutions from
the history/memory are more likely to be selected or inherited. This is equivalent to a
certain degree of elitism. Obviously, if the acceptance rate is too low, solutions will
converge more slowly. As mentioned earlier, this intensification is enhanced by the
controlled pitch adjustment. Such interactions between various components could be
another important factor for the success of the HS algorithm over other algorithms, as
it will be demonstrated again in other chapters of this topic.
In addition, the structure of the HS algorithm is relatively easier. This advantage
makes it very versatile to combine HS with other metaheuristic algorithms [22]. For
algorithm parameters, there are some evidences to suggest that HS is less sensitive to
chosen parameters, which means that we may not have to fine-tune these parameters
to get quality solutions.
Furthermore, the HS algorithm is a population-based metaheuristic, which means
that a group of multiple harmonies can be used in parallel. Proper parallelism usually
leads to better performance with higher efficiency. The good combination of parallel-
ism with elitism as well as a fine balance of intensification and diversification is the
key to the success of the HS algorithm.
5 Further Research
The power and efficiency of the HS algorithm seem obvious after discussion and
comparison with other metaheuristics; however, there are some unanswered questions
concerning the whole class of the algorithm. Currently, the HS algorithm like other
popular metaheuristics works well under appropriate conditions. However, we usually
do not fully understand why and how they work so well. For example, when choosing
the harmony accepting rate, we usually use a higher value, say, 0.7 to 0.95. This value
is determined by experience or inspiration from genetic algorithm where the mutation
rate should be low, and thus the accepting rate of the existing gene components
should be high. However, it is very difficult to say what range of values and which
combinations are surely better than others.
In general, there lacks a theoretical framework for metaheuristics to provide some
analytical guidance to the following important issues: How to improve the efficiency
for a given problem? What conditions are needed to guarantee a good rate of conver-
gence? How to prove the global optima are reached for the given metaheuristic algo-
rithm? These are still open questions that need further research. The encouraging
thing is that many researchers are interested in tackling these difficult challenges, and
important progress has been made concerning the convergence of certain algorithm
(SA). Any progress concerning the convergence of HS and other algorithms would be
influentially profound.
Even without a solid framework, this does not discourage scientists to develop
more variants and/or hybrid algorithms. In fact, the algorithm development itself is a
metaheuristic process in a similar manner to the key components of HS: using exist-
ing successful algorithms; developing slightly different variants based on the existing