**1.
Introduction**

Spotted Hyena Optimizer is a metaheuristic bio-inspired optimization algorithm developed by Dhiman et al. The fundamental concept of this algorithm is to simulate the social behaviors of spotted hyenas. The main steps of SHO algorithm are inspired by their hunting behavior. Further, the SHO algorithm is tested on real-life constrained engineering design problems with more than four variables [1]. The results reveal that the performance of SHO performs better than the other competitor algorithms for real-life approaches. The motivation behind this work is to propose a novel multi-objective optimization algorithm called Multi-objective Spotted Hyena Optimizer (MOSHO) which is based on Spotted Hyena Optimizer (SHO). The last phase is swarm intelligence-based algorithms that are based on the collective behaviors of social creatures. These collective behaviors are inspired by natural colonies, schools, flock, and herds. The well-known algorithms of swarm intelligence-based techniques are Ant Colony Optimization (ACO), Bat-inspired Algorithm (BA), Hunting Search (HUS), Particle Swarm Optimization (PSO), and Bee Collecting Pollen Algorithm (BCPA). The social relation and hunting behaviors of spotted hyenas are the main inspiration of this algorithm. SHO algorithm mimics the cohesive clusters between the trusted spotted hyenas [2]. The four main steps of SHO are searching, encircling, hunting, and attacking. In SHO algorithm, the hunting behavior is guided by the group of trusted friends (so far solutions) towards the best search agent and saves the best optimal solutions. Optimization is the technique for determining the decision variables of a function to minimize or maximize its values. Most of the real-world problems have nonlinear constraints, high computational cost, are non-convex and complicated, and large number of solution spaces. Therefore, solving such problems incorporating the variety of variables and constraints is very tedious and complex. Secondly, there are many local optimum solutions that do not guarantee the best overall solution using classical numerical methods. To overcome these problems, metaheuristic optimization algorithms are introduced, which are capable of solving such complex problems during the course of iterations. Single-solution based algorithms are those in which a solution is randomly generated and improved until the best result is obtained. Population-based algorithms are those in which a set of solutions is randomly generated in a given search space and solution values are updated during iterations until the best solution is found [3].

**2. Inspiration of Spotted Hyena Optimization Algorithm**

The adaptive grid mechanism is used to produce the distributed Pareto fronts. The grid has to be recalculated and relocate each individual if the inserted individual into population lies outside the current bounds of the grid [4]. The adaptive grid is a space formed by hyper cubes and is used to distribute in a uniform way. The social relation and hunting behaviors of spotted hyenas are the main inspiration of this algorithm. SHO algorithm mimics the cohesive clusters between the trusted spotted hyenas. The four main steps of SHO are searching, encircling, hunting, and attacking. In SHO algorithm, the hunting behavior is guided by the group of trusted friends towards the best search agent and saves the best optimal solutions.

**3.
Spotted Hyena Optimizer (SHO) Algorithm**

** **The basic concepts of SHO
followed by brief description of multi-objective version of SHO. Social
relationships are dynamic in nature. These are affected by the changes in
relationship among comprising the network and individual leaving or joining the
population [5]. The animal behavior has been classified into three categories.

- The first category includes environmental factors such as resource availability and competition with other animal species.
- The second category focuses on social preferences based on individual behavior [6].
- The third category has less attention from scientists which includes the social relations of species itself.

The social relation between animals is the inspiration of our work and correlates this behavior to spotted hyena which is scientifically named as Crocuta. Hyenas are large dog-like carnivores. They live in savannas, grasslands, sub-deserts, and forests of both Africa and Asia. They live 10-12 years in the wild and up to 25 years in imprisonment. There are four known species of hyena such as spotted, striped, brown, and aardwolf. These differ in size, behavior, and type of diet. All of these species have a bear-like attitude. Hyenas are skillful hunters and largest of three other hyena species (i.e., striped, brown, and aardwolf) [7]. Spotted Hyena is also known as laughing hyena because its sounds are much similar to a human laugh. There are spots on their fur reddish brown in color with black spots. Spotted hyenas are complicated, intelligent, and highly social animals with really dreadful reputation. They have the ability to fight endlessly for territory and food.

In spotted hyenas, female members are dominant and live in their clan. However, male members leave their clan when they become adults and join a new clan. In a new family, they are lowest ranking members to get their share of meal. A male member who has joined the clan always stays with the same members (friends) for a long time. Whereas, a female is always assured of a stable place. An interesting fact about the spotted hyena is that they produce sound to communicate with each other during the searching of food source. According to Ilany et al, spotted hyenas usually rely on a network of trusted friends that have more than 100 members [8]. They usually tie up with another spotted hyena that is a friend of a friend or linked in some way through kinship rather than any unknown spotted hyena. Spotted hyenas are social animals that can communicate with each other through specialized calls such as postures and signals. They use multiple sensory procedures to recognize their kin and other individuals. They can also recognize third party kin and rank the relationships between their clan mates during social decision making. The spotted hyena track prey by sight, hearing, and smell. Cohesive clusters are helpful for an efficient cooperation between spotted hyenas. In this work, the hunting technique and social relation of spotted hyenas are mathematically modeled to design the multi-objective SHO algorithm [9]. Fig. 2 shows the next position of a search agent lies between its current position and the position of the prey which will helpful to meet towards an estimated position of prey.

**3.1.
Steps for SHO Algorithm**

- Encircling behavior
- Hunting
- Attacking behavior
- Search for behavior

**3.1.1.
Encircling Behavior**

** **The target behavior or
objective is considered as the best solution and the other search agents can
update their positions with respect to obtained best solution. Spotted hyenas
can know where their prey is and surround them [10]. We consider the current
best candidate is the spotted hyena closest to the target or prey because of
search space not known a priori. The locations of other search agents are
updated after the best search solution is defined.

**3.1.2.
Hunting**

The next step of SHO algorithm is the hunting strategy which makes a cluster of optimal solutions against the best search agent and updates the positions of other search agents. In order to mathematically imitate the hunting behavior of spotted hyena, we suppose that the best search agent is optimum, which is consider as the location of prey, the other search agent towards the best search agent, constantly update their positions until to find the best solutions, then save the best solution [11].

**3.1.3.
Attacking Behavior**

** **The best solution and
updates the positions of other search agents on the basis of the position of
the best agent, the spotted hyena attack the prey constantly updates their
position [12].

**3.1.4.
Search for Behavior**

** **The
searching mechanism describes the exploration capability of an algorithm. The proposed
SHO algorithm ensures thus capability using random values which are greater
than or less than 1. The vector is also responsible to show the more randomized
behavior of SHO and avoid local optimum [13].

**3.2. Flow Chart of SHO Algorithm**

**4.
Numerical Expressions of SHO Algorithm**

The mathematical model of this behavior is represented by Equations [14],

**5.
Applications of SHO Algorithm**

- Feature selection [15]
- Economic Dispatch Problem
- Fusion reaction
- Power generation [16]
- Power Flow controller
- Machine Learning [17]

**6.
Advantages of SHO Algorithm**

- To solve economic load power dispatch problem and converge toward the optimum with low computational efforts.
- To evaluate the effectiveness of MOSHEPO, the proposed algorithm has been tested on various benchmark test systems and its performance is compared with other well known approaches [18].
- The more basic SHO is compared to other acclaimed state-of-the-art optimization algorithm, the results show that the proposed algorithm can provide better results [19].
- LI-SHO method for image matching mixed together the advantages of SHO and lateral inhibition mechanism [20].
- The effects of convergence, scalability, and control parameters have been investigated. The statistical significance of the proposed approach has also been examined through ANOVA test.
- There is a lot of interest in developing metaheuristic algorithms that are computationally inexpensive, flexible, and simple by nature [21].

**Reference**

[1] Kaur, A., Kaur, S. and Dhiman, G. (2018). A quantum method for dynamic nonlinear programming technique using Schrödinger equation and Monte Carlo approach. Modern Physics Letters B, 32(30), p.1850374.

[2] Dhiman, G. and Kumar, V. (2018). Multi-objective spotted hyena optimizer: A Multi-objective optimization algorithm for engineering problems. Knowledge-Based Systems, 150, pp.175-197.

[3] Najmi, A., Rashidi, T., Vaughan, J. and Miller, E. (2019). Calibration of large-scale transport planning models: a structured approach. Transportation.

[4] Dhiman, G. and Kaur, A. (2018). Optimizing the Design of Airfoil and Optical Buffer Problems Using Spotted Hyena Optimizer. Designs, 2(3), p.28.

[5] Worldscientific.com. (2019). ED-SHO: A framework for solving nonlinear economic load power dispatch problem using spotted hyena optimizer | Modern Physics Letters A. [online] [Accessed 5 Sep. 2019].

[6] Kaur, A., Kaur, S. and Dhiman, G. (2018). A quantum method for dynamic nonlinear programming technique using Schrödinger equation and Monte Carlo approach. Modern Physics Letters B, 32(30), p.1850374.

[7] Dhiman, G. (2019). MOSHEPO: a hybrid multi-objective approach to solve economic load dispatch and micro grid problems. Applied Intelligence.

[8] How Effective is Spotted Hyena Optimizer for Training Multilayer Perceptrons. (2019). International Journal of Recent Technology and Engineering, 8(2), pp.4915-4927.

[9] Luo, Q., Li, J. and Zhou, Y. (2019). Spotted hyena optimizer with lateral inhibition for image matching. Multimedia Tools and Applications.

[10] Kumar, V. and Kaur, A. (2019). Binary spotted hyena optimizer and its application to feature selection. Journal of Ambient Intelligence and Humanized Computing.

[11] Jia, H., Li, J., Song, W., Peng, X., Lang, C. and Li, Y. (2019). Spotted Hyena Optimization Algorithm With Simulated Annealing for Feature Selection. IEEE Access, 7, pp.71943-71962.

[12] Sahu, R., Sekhar, G. and Priyadarshani, S. (2019). Differential evolution algorithm tuned tilt integral derivative controller with filter controller for automatic generation control. Evolutionary Intelligence.

[13] Kaur, A., Jain, S. and Goel, S. (2019). SP-J48: a novel optimization and machine-learning-based approach for solving complex problems: special application in software engineering for detecting code smells. Neural Computing and Applications.

[14] Zamani, H., Nadimi-Shahraki, M. and Gandomi, A. (2019). CCSA: Conscious Neighborhood-based Crow Search Algorithm for Solving Global Optimization Problems. Applied Soft Computing, p.105583.

[15] Dhyani, A., Panda, M. and Jha, B. (2018). Moth-Flame Optimization-Based Fuzzy-PID Controller for Optimal Control of Active Magnetic Bearing System. Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 42(4), pp.451-463.

[16] 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.

[17] Deb, S., Gao, X., Tammi, K., Kalita, K. and Mahanta, P. (2019). Recent Studies on Chicken Swarm Optimization algorithm: a review (2014–2018). Artificial Intelligence Review.

[18] Dhal, K., Ray, S., Das, A. and Das, S. (2018). A Survey on Nature-Inspired Optimization Algorithms and Their Application in Image Enhancement Domain. Archives of Computational Methods in Engineering.

[19] Ugur, L., Kanit, R., Erdal, H., Namli, E., Erdal, H., Baykan, U. and Erdal, M. (2018). Enhanced Predictive Models for Construction Costs: A Case Study of Turkish Mass Housing Sector. Computational Economics, 53(4), pp.1403-1419.

[20] Dhal, K., Das, A., Ray, S., Gálvez, J. and Das, S. (2019). Nature-Inspired Optimization Algorithms and Their Application in Multi-Thresholding Image Segmentation. Archives of Computational Methods in Engineering.

[21] Yalcin, Y. and Pekcan, O. (2018). Nuclear Fission–Nuclear Fusion algorithm for global optimization: a modified Big Bang–Big Crunch algorithm. Neural Computing and Applications.

Your work is good…Can you give the MATLAB code for this algorithm…

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