S. Mirjalili, S. M. Mirjalili, A. Lewis, Grey Wolf Optimizer, Advances in Engineering Software , vol. 69, pp.

46-61, 2014, DOI: http://dx.doi.org/10.1016/j.advengsoft.2013.12.007

Evolution Strategy (ES) [18, 19], Probability-Based Incremental Learning (PBIL), Genetic Programming (GP)

[20], and Biogeography-Based Optimizer (BBO) [21].

As an example, the BBO algorithm was first proposed by Simon in 2008 [21]. The basic idea of this

algorithm has been inspired by biogeography which refers to the study of biological organisms in terms of

geographical distribution (over time and space). The case studies might include different islands, lands, or even

continents over decades, centuries, or millennia. In this field of study different ecosystems (habitats or

territories) are investigated for finding the relations between different species (habitants) in terms of

immigration, emigration, and mutation. The evolution of ecosystems (considering different kinds of species

such as predator and prey) over migration and mutation to reach a stable situation was the main inspiration of

the BBO algorithm.

The second main branch of meta-heuristics is physics-based techniques. Such optimization algorithms

typically mimic physical rules. Some of the most popular algorithms are Gravitational Local Search (GLSA)

[22], Big-Bang Big-Crunch (BBBC) [23], Gravitational Search Algorithm (GSA) [24], Charged System Search

(CSS) [25], Central Force Optimization (CFO) [26], Artificial Chemical Reaction Optimization Algorithm

(ACROA) [27], Black Hole (BH) [28] algorithm, Ray Optimization (RO) [29] algorithm, Small-World

Optimization Algorithm (SWOA) [30], Galaxy-based Search Algorithm (GbSA) [31], and Curved Space

Optimization (CSO) [32]. The mechanism of these algorithms is different from EAs, in that a random set of

search agents communicate and move throughout search space according to physical rules. This movement is

implemented, for example, using gravitational force, ray casting, electromagnetic force, inertia force, weights,

and so on.

For example, the BBBC algorithm was inspired by the big bang and big crunch theories. The search agents of

BBBC are scattered from a point in random directions in a search space according to the principles of the big

bang theory. They search randomly and then gather in a final point (the best point obtained so far) according to

the principles of the big crunch theory. GSA is another physics-based algorithm. The basic physical theory from

which GSA is inspired is Newton’s law of universal gravitation. The GSA algorithm performs search by

employing a collection of agents that have masses proportional to the value of a fitness function. During iteration,

the masses are attracted to each other by the gravitational forces between them. The heavier the mass, the bigger

the attractive force. Therefore, the heaviest mass, which is possibly close to the global optimum, attracts the other

masses in proportion to their distances.

The third subclass of meta-heuristics is the SI methods. These algorithms mostly mimic the social behavior

of swarms, herds, flocks, or schools of creatures in nature. The mechanism is almost similar to physics-based

algorithm, but the search agents navigate using the simulated collective and social intelligence of creatures. The

most popular SI technique is PSO. The PSO algorithm was proposed by Kennedy and Eberhart [3] and inspired

from the social behavior of birds flocking. The PSO algorithm employs multiple particles that chase the position

of the best particle and their own best positions obtained so far. In other words, a particle is moved considering

its own best solution as well as the best solution the swarm has obtained.

Another popular SI algorithm is ACO, proposed by Dorigo et al. in 2006 [2]. This algorithm was inspired

by the social behavior of ants in an ant colony. In fact, the social intelligence of ants in finding the shortest path

between the nest and a source of food is the main inspiration of ACO. A pheromone matrix is evolved over the

course of iteration by the candidate solutions. The ABC is another popular algorithm, mimicking the collective

behavior of bees in finding food sources. There are three types of bees in ABS: scout, onlooker, and employed

bees. The scout bees are responsible for exploring the search space, whereas onlooker and employed bees

exploit the promising solutions found by scout bees. Finally, the Bat-inspired Algorithm (BA), inspired by the

echolocation behavior of bats, has been proposed recently [33]. There are many types of bats in the nature. They

are different in terms of size and weight, but they all have quite similar behaviors when navigating and hunting.

Bats utilize natural sonar in order to do this. The two main characteristics of bats when finding prey have been

adopted in designing the BA algorithm. Bats tend to decrease the loudness and increase the rate of emitted

ultrasonic sound when they chase prey. This behavior has been mathematically modeled for the BA algorithm.

The rest of the SI techniques proposed so far are as follows:

Marriage in Honey Bees Optimization Algorithm (MBO) in 2001 [34]

Artificial Fish-Swarm Algorithm (AFSA) in 2003 [35]

Termite Algorithm in 2005 [36]

Wasp Swarm Algorithm in 2007 [37]

Monkey Search in 2007 [38]

Bee Collecting Pollen Algorithm (BCPA) in 2008 [39]

Cuckoo Search (CS) in 2009 [40]

Dolphin Partner Optimization (DPO) in 2009 [41]