Harmony Search as a Metaheuristic Algorithm - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 10

3.2.5 Firefly Algorithm
The fascinating flashing light of fireflies in the tropical summer can be used to de-
velop interesting nature-inspired metaheuristic algorithms for optimization. The Fire-
fly Algorithm was developed by Xin-She Yang [4], based on the idealization of the
flashing characteristics of fireflies. There are three major components in the FA op-
timization: 1) A firefly will be attracted to more brighter or more attractive fireflies,
and at the same time they will move randomly; 2) the attractiveness is proportional to
the brightness of the flashing light which will decrease with distance, therefore, the at-
tractiveness will be evaluated in the eye of the beholders (other fireflies); 3) The de-
crease of light intensity is controlled by the light absorption coefficient γ which is in
turn linked to a characteristic scale.
The new solution is generated by

t
i

+ 1 t

i

2

x = x + α ε + β exp[ − γ r ] ε ( x − x ), (10)

1 ij 2 i j

where r ij is the distance, not necessarily the physical distance, between two fireflies i
and j . In addition, FA is obviously a population-based algorithm, which may share
many similarities with particle swarm optimization. In fact, it has been proved by
Yang [4] that when γ→∞, the firefly algorithm will become an accelerated version of
PSO, while γ→0, the FA reduces to a version of random search algorithms.
In the FA optimization, the diversification is represented by the random movement
component, while the intensification is implicitly controlled by the attraction of dif-
ferent fireflies and the attractiveness strength β. Unlike other metaheuristics, the in-
teraction between exploration and exploitation is intermingled in some way; this
might be an important factor for its success in solving multiobjective and multimodal
optimization problems.
Obviously, there are many other metaheuristic algorithms that are currently used,
including, but not limited to, tabu search, cross-entropy, scatter search, cultural algo-
rithm, flog leaping algorithm, artificial immune system, artificial bee algorithms, pho-
tosynthetic algorithm, enzyme algorithm, etc [15-20]. As we will discuss later, the
hybridization of diversification and intensification components is a useful technique
to develop new algorithms.

4 Characteristics of HS and Comparison

After the brief introduction to other metaheuristic algorithms, we are now ready to
analyze the similarities and differences of the Harmony Search algorithm in the gen-
eral context of metaheuristics.

4.1 Diversification and Intensification

In reviewing other metaheuristic algorithms, we have repetitively focused on two ma-
jor components: diversification and intensification. They are also referred to as explo-
ration and exploitation [6]. These two components are seemingly contradicting each
other, but their balanced combination is crucially important to the success of any
metaheuristic algorithms [4, 6].