New Nature Inspired Metaheuristic Algorithm for Elephants: Elephant Herding Optimization (EHO) Algorithm

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 x₀ [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

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[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.

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[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.

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[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.