**1.
Introduction**

EHO was inspired by social behavior of elephants in herds. It was proposed by Wang et al. Nature-Inspired methods are playing a vital role to solve various real-life problems, which may be very difficult or sometimes impossible to be solved using analytical methods [1]. So far, numerous optimization algorithms inspired by genetics, nervous systems, and swarm intelligence, based on the behavior of birds, fishes, bees, ants, bats, frog, elephant, cats, wolf, etc., have been suggested in the literature. These algorithms are applied to solve various complex power system optimization problems and are found to be very effective in searching the global or near-global solutions. The ever increasing complexity of the real-world problems is making it extremely difficult for the traditional methods to address those. On the other hand, though modern metaheuristic methods cannot provide exact answers, they can generate satisfactory solutions within a reasonable time span [2]. Over the past few years, various kinds of metaheuristic algorithms have been proposed and successfully applied to solve myriads of real-world optimization problems. Among all metaheuristic methods, swarm-based algorithms are one of the most representative paradigms & widely used ones.

In general, wide elephants are social in nature and the elephant group is composed of several clans. The elephants belonging to different clans live together under the leadership of a matriarch, and male elephants remain solitary and will leave their family group while growing up. Inspired by the herding behavior of elephant group, a new kind of swarm based heuristic search method, called EHO, is proposed for solving global optimization tasks. This habitation of elephants can be used to solve optimization problems. The behavior of elephant herding in nature are idealized into clan updating operator and separating operator. In EHO, each elephant implements clan updating operator to update its position based on its current position and matriarch in the responding clan. Subsequently, the worst elephant is replaced by separating operator. By comparing with BBO, DE and GA, the performance of EHO is investigated by several experiments implemented on fifteen test cases. The results show that EHO can find much fitter solutions on most benchmark problems than the three other methods [3].

**2. Life Cycle of Elephant Herding Optimization Algorithm**

**2.1.
Endangered**

** **Population: Estimated to
be fewer than 1500.

Habitat: They spend most of their time in lowlands and valleys.

Characteristics: Shy and generally avoid people [4].

**2.2.
Forest herbivores**

** **Diet:
An adult elephant can eat up to 150kg of vegetation per day, feeding on palms,
grass and wild bananas.

**3. Structure of Elephant**

**3.1.
Trunk**

** **This
is an elephant’s most useful body part! A trunk is an elongation of the nose
and upper lip. Elephants use their trunks to: smell, bring water to their
mouths to drink, store water to drink later, dig holes, spray water over their
bodies to bathe, breathe air (like a snorkel) when swimming, pick up branches, plant
leaves, fruits, and other foods to eat, knock over trees (trunks are very muscular and
powerful!), greet other elephants (touch trunks!), help move baby elephants,
especially if they get stuck in the mud, toss dirt and mud onto their backs to
protect against the sun and insects, make sounds, like loud trumpet calls,
playfully wrestle or fight with each other [5].

**3.2.
Ears **

** **Elephant ears are very
thin, full of blood vessels and important to help keep elephants cool. They are
specialized to hear very low sounds [6].

**3.3.
Tusks**

** **Tusks are teeth that
stick out from the elephant’s mouth. They are made of a special material called
ivory. Elephants use tusks to: dig in the ground for water, minerals, and
roots, crack open hard-shelled fruits, peel bark off trees to eat or to mark
territories, fight [7].

**3.4.
Feet**

Elephant feet must be large and strong to support the weight of the elephant’s body.

**3.5.
Tail**

Elephants have long tails ending in tufts of hair which they swing back and forth to swat away irritating insects.

**4.
Elephant Herding Optimization (EHO) Algorithm**

** **Elephants are one of the
largest mammals on land. The African elephant and the Asian elephant are two of
traditionally recognized species. A long trunk is the most representative
feature that is multipurpose, such as breathing, lifting water and grasping
objects. In nature, elephants are social animals, and they have complex social
structures of females and calves. An elephant group is composed of several clans
under the leadership of a matriarch, often the oldest cow [8]. A clan consists
of one female with her calves or certain related females. Females prefer to
live in family groups, while male elephants tend to live in isolation, and they
will leave their family group when growing up. Though male elephants live away
from their family group, they can stay in contact with elephants in their clan
through low-frequency vibrations. In this paper, the herding behavior of the
elephants is considered as two operators, which are subsequently idealized to
form a general-purpose global optimization method [9].

In order to make the herding behavior of elephants solve all kinds of global optimization problems, we preferred to simplify it into the following idealized rules.

1) The elephant population is composed of some clans, and each clan has fixed number of elephants.

2) A fixed number of male elephants will leave their family group and live solitarily far away from the main elephant group at each generation.

3) The elephants in each clan live together under the leadership of a matriarch [10].

**4.1.
Steps for EHO Algorithm**

- Generation of the Initial population
- Determination of the clan updating operator
- Calculation of the separating operator
- Memorize the best current solution
- Stopping criteria

**4.1.1.
Generation of the Initial population**

** **Elephants are the largest
animals come in category of mammals on the earth. Elephants have behavioral
structures, more size and tame character. An elephant lives in complex group such
as female elephant with her calves or certain related female elephants [11]. These
groups are called as clan. A clan consists of minimum of three up to two dozen
elephants. The leader of a clan is called matriarch. An elephant group headed
by matriarch in concentric circles. Female elephant like to live in joint
family but male elephant tends to live alone and they leave their family group
when growing up. After leaving male elephant mixed with few other adult male
elephant in small group [12]. Male elephant can live in contact with elephants
in their clan through low frequency vibrations.

**4.1.2.
Determination of the clan updating operator**

** ** A global optimization problem is solved by
using the herding behavior of elephant. We use these rules to simplify the
problem. After separating the worst values from the population. The fittest
values are updated using clan updating operator and worst values are discarded
[13].

- It is assumed that the total population of elephants is divided into two groups such as clans. These clans have a definite number of elephants.
- It is also assumed that the worst performing male elephant will leave their family group. It lives alone on a remarkable distance from the elephant group on occurrence of each generation.
- Matriarch is the leader of all elephants live in a clan.

**4.1.3.
Calculation of the separating operator**

** **The
male elephant leave their family group when they growing up. Let we consider
the elephant individual with the worst fitness will implement the separating
operator at each generation [14].

**4.1.4.
Memorize the best current solution**

Evaluate the fitness values of the
population by the newly updated positions. Sort all of the population according
to the new feasibility rules and then record the best solution as x_{best}
with the best fitness value y_{min}. The best elephant x_{best}
is transferred to the next generation as the first elephant x_{0 }[15].

**4.1.5.
Stopping criteria**

** **If the termination
criterion is met or the variable cycle is equal to the maximum number of iterations,
then the algorithm stops.

**4.2. Flow Chart of EHO Algorithm**

**5.
Numerical Method of EHO Algorithm**

The cultural based, EHO, and biased algorithm can achieve the best costs in the three-bar problem [16].

**6. Applications of EHO Algorithm**

- Travelling salesman problem
- Industrial applications
- Load frequency control[17]
- Spam detection
- Support vector machine (SVM)
- Feature selection
- Vehicle path planning
- Artificial neural networks[18]

**7. Advantages of EHO Algorithm**

- The optimal sites and sizes of DERs to maximize the overall benefits of utility and consumers [19]
- Low-cost
- High-security
- High survival ability
- good maneuvering performance [20]
- It is a powerful classifier widely used in the past for various problems [21]

**Reference**

[1] Chakraborty, F., Roy, P. and Nandi, D. (2019). Oppositional elephant herding optimization with dynamic Cauchy mutation for multilevel image thresholding. Evolutionary Intelligence.

[2] Meena, N., Parashar, S., Swarnkar, A., Gupta, N. and Niazi, K. (2018). Improved Elephant Herding Optimization for Multiobjective DER Accommodation in Distribution Systems. IEEE Transactions on Industrial Informatics, 14(3), pp.1029-1039.

[3] Tuba, E., Ribic, I., Capor-Hrosik, R. and Tuba, M. (2017). Support Vector Machine Optimized by Elephant Herding Algorithm for Erythemato-Squamous Diseases Detection. Procedia Computer Science, 122, pp.916-923.

[4] Prasad, C., Subbaramaiah, K. and Sujatha, P. (2019). Cost–benefit analysis for optimal DG placement in distribution systems by using elephant herding optimization algorithm. Renewables: Wind, Water, and Solar, 6(1).

[5] Hakli, H. (2019). A Novel Approach Based On Elephant Herding Optimization For Constrained Optimization Problems. Selcuk University Journal of Engineering, Science and Technology, 7(2), pp.405-419.

[6] Kok, K. and Rajendran, P. (2016). Differential-Evolution Control Parameter Optimization for Unmanned Aerial Vehicle Path Planning. PLOS ONE, 11(3), p.e0150558.

[7] Eissa, M. (2019). Novel Fuzzy-Based Self-Adaptive Single Neuron PID Load Frequency Controller for Power System. Power Electronics and Drives, 0(0).

[8] Pan, Z., Guo, Q. and Sun, H. (2015). Impacts of optimization interval on home energy scheduling for thermostatically controlled appliances. CSEE Journal of Power and Energy Systems, 1(2), pp.90-100.

[9] Stumberger, I., Minovic, M., Tuba, M. and Bacanin, N. (2019). Performance of Elephant Herding Optimization and Tree Growth Algorithm Adapted for Node Localization in Wireless Sensor Networks. Sensors, 19(11), p.2515.

[10] Parashar, S., Swarnkar, A., Niazi, K. and Gupta, N. (2017). Modified elephant herding optimisation for economic generation co-ordination of DERs and BESS in grid connected micro-grid. The Journal of Engineering, 2017(13), pp.1969-1973.

[11].Tahani, M., Babayan, N., Mehrnia, S. and Shadmehri, M. (2016). A novel heuristic method for optimization of straight blade vertical axis wind turbine. Energy Conversion and Management, 127, pp.461-476.

[12] Padhan, D. and Majhi, S. (2013). A new control scheme for PID load frequency controller of single-area and multi-area power systems. ISA Transactions, 52(2), pp.242-251.

[13] Kougias, I. and Theodossiou, N. (2012). Multiobjective Pump Scheduling Optimization Using Harmony Search Algorithm (HSA) and Polyphonic HSA. Water Resources Management, 27(5), pp.1249-1261.

[14] Cardoso, A., Tavares, Y., Nedjah, N. and Mourelle, L. (2018). Co-Design System for Template Matching Using Dedicated Co-Processor and Cuckoo Search. International Journal of Swarm Intelligence Research, 9(1), pp.58-74.

[15] Elhosseini, M., El Sehiemy, R., Rashwan, Y. and Gao, X. (2019). On the performance improvement of elephant herding optimization algorithm. Knowledge-Based Systems, 166, pp.58-70.

[16] Jafari, M., Salajegheh, E. and Salajegheh, J. (2018). An efficient hybrid of elephant herding optimization and cultural algorithm for optimal design of trusses. Engineering with Computers, 35(3), pp.781-801.

[17] Saud, S., Kodaz, H. and Babaoğlu, İ. (2018). Solving Travelling Salesman Problem by Using Optimization Algorithms. KnE Social Sciences, 3(1), p.17.

[18] Chen, Z., Wu, L. and Fu, Y. (2012). Real-Time Price-Based Demand Response Management for Residential Appliances via Stochastic Optimization and Robust Optimization. IEEE Transactions on Smart Grid, 3(4), pp.1822-1831.

[19] Ismaeel, A., Elshaarawy, I., Houssein, E., Ismail, F. and Hassanien, A. (2019). Enhanced Elephant Herding Optimization for Global Optimization. IEEE Access, 7, pp.34738-34752.

[20] Vijay, R. (2018). Optimal Allocation of Electric Power Distributed Generation on Distributed Network Using Elephant Herding Optimization Technique. CVR Journal of Science & Technology, 15(1), pp.73-79.

[21] Yuan, Y., Zhang, W. and Yuan, B. (2012). A Max-Min clustering method for $k$-means algorithm of data clustering. Journal of Industrial and Management Optimization, 8(3), pp.565-575.

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