MOR is motivated by the need for increased system complexity. Understanding the complex system is not easy and design of the system also very cumbersome. Interestingly, due to its approximate response and preserving the important characteristics of the HOS, it becomes a wide area of research including control, power, chemical and mechanical, design engineering with many more. The varieties of MOR approaches are accessible from the literature and each has quite a unique approach. These techniques only differ with system design characteristics as stability, matching steady-state value, frequency and time response. They all maintain a mutual goal of diminishing the HOS.

The mixed method basically uses two methods for the reduced order finding in order to improve the response of approximation. In recent time the method is integrated with the nature motivated optimization methods. The traditional procedures such as particle swarm optimization(PSO) ^{th} order two input two output practical power system model is diminished in 3^{rd} order. The important methods are Eigen permutation for finding the numerator parameter with Jaya algorithm for finding the denominator parameter

In recent, the study based on the behavior of natural process, animals, physics, genetic and swam based algorithms are in development and improvement phases. The behavior of hunting animal converted into a systematic mathematical procedure via making a rigorous study. Some of the important algorithm based on the process are grey wolf in which a group of wolf encircles the prey, blue whale in which 7-8 whales encircle the prey by making mimic sound in spiral formation, harris hawk optimization, the hawk searches the prey from a height like a high tree or pole and make some glide attack on prey in order to catch it and many more. The

The paper is based on the harris hawk optimization. The section compares the swarm based algorithm and justifying the selection for implementing HHO.

Algorithms |
Inspiration |
Advantages |
Disadvantages |

Particle swam optimization |
Bird flock |
Simple ,effective |
Depend on stochastic process like evolutionary programming. |

Cuckoo algorithm |
Cuckoo |
The number of parameters to be tuned is less than GA and PSO, and thus it is potentially more generic to adapt to a wider class of optimization problems |
Complex, the step length is heavy- tailed, and any large step is possible. |

Fruit fly optimization |
Fruit fly |
Easy and execution speed will be faster |
The stability of the fruit fly swarm search route is related to fruit fly quantity. The swarm with fewer fruit fly numbers will have disadvantages of an unstable search route and a slower convergence speed; |

Marriage in Honey bee optimization algorithm |
Honey Bee |
Algorithm preserved concepts and achieve the good performance. |
Multi behavior; Mating process is hard to observe |

Dolphin Partner optimization |
Dolphin |
It has rapid and niche character and good adaptability for different objective functions. |
The particle exchange only global best positions , the fitness is ignored |

Dolphin Echolocation |
Dolphin |
Affordable computer cost Parameter is better to be chosen according to the size of search space. Capability of adopting itself by type of problem |
The time lapse between click and echo enables the dolphin to evaluate the distance from the object; the varying strength of the signal as it is received on the two sides of the dolphin’s head enabling him to evaluate the direction |

Artificial fish swarm algorithm |
Fish swarm and social behaviors |
High convergence speed, flexibility, fault tolerance and high accuracy. |
High complexity, lack of balance between and local search, lack of benefiting from experience of group members for next movement |

Bat Inspired algorithm |
Bat herd |
Potentially powerful, simple. |
Implementation is complicated. Solution is not depend on the quality of solutions |

Termite algorithm |
Termite colony |
Decisions making is good |
Random in the search space, trajectory are biased. |

Ant colony optimization |
Ant colony |
Positive feedback, distributed computation, Rapid discovery of solutions |
Premature convergence |

Wasp swarm algorithm |
Parasitic wasp |
The quality of best solution is always high |
Chances in falling into local minima caused by saturation of Local search |

Firefly algorithm |
Firefly |
Convergence makes quickly and global optimization achieve naturally |
The algorithms stopes when the variations of functions values is less than a given tolerance <=10-5 |

Hunting search |
Group search |
Preserves the history of past vectors |
Depend on the corporation of members the optimum solution is static and does not change it position |

Whale algorithm |
Whale bubble net strategy |
Success rate of solving problem is high, high exploration ability due to position updating parameters |
Search space is large |

Grey wolf optimization |
Grey wolf herd |
Exploration ability is high. |
Based on social hierarchy. Prone to stagnation in local solutions |

Harris Hawk optimization |
Hawk behavior |
Capable of finding excellent solutions due to cooperative behavior and chasing the prey. |
Depend on the energy of prey. |

The harris hawk is one of the Eagle variety and its behavior study converted into the meta heuristic algorithm

The paper is separated into six sections. Starting from the introduction and followed by the statement of problem, methodologies, implementation in numerical examples with discussion and the last conclusion of the paper is given further references are listed

The SISO system transfer function with unknown order of may be represented by the following Equation

Harris Hawk optimization (HHO) is based on the studies of hawk behavior usually in the period of hunting. The study is done by Louis Lefebvre. The mathematical implementation using the algorithm is Mirjili.

To start this phase, the Hawk reaches on the peak of tree/pole/top of hill in order to trace the prey and also consider the other of Hawks positions. Situation of

The exploration to exploitation changes between exploitation performances founded on the absconding energy of the prey. The energy of a prey reduces throughout the escaping. The energy of the prey is modelled as in Eq. (5)

E designate the absconding energy of prey. T the maximum number of iteration and E_{0} initial state of energy.

The process begins by surprise and the imagined prey of the previous stage is hostile. Preys are trying to get out of the case. The probability of fleeing from the prey is (r<0.5) or not to escape efficaciously (r>=0.5). The hawk executes rough or soft besieges in relation to prey activity to capture the prey. Based on the vitality of the prey, the hawk encircles around the beast in various ways. The hawk getting closer to the desired prey to maximize its odds of cooperating in killing the rabbit. The gentle assault begins and the rough assault takes place.

The prey has energy and try to escape using random confusing jumps. The value for escaping energy must be

The prey is exhausted and has less energy when value

To catch the prey, the Hawk, decide their subsequent move founded on Eq. (9)

Dive is founded on the LF-based designs using the law represented in Eq. (10)

D dimension problem and s is a random vector by size 1XD and LF is the levy fight function, and calculated as in Eq. (11)

u,v are random values inside

The last tactic for apprising the locations of hawks. The soft besiege stage can be achieved and given in Eq. (12)

The Y and Z are obtained using the Eq. (11) and Eq. (12)

The prey has not adequate energy

The Y and Z are gained by the Equation. (14) and Equation. (15)

The abridged denominator can be achieved by the Routh stability array of the denominator polynomial. For convenience the even and odd portions are separated

Now, the Routh- Horwitz stability array is moulded for the denominator polynomial

The well-known routh algorithm for the overhead array

Where i>3 and

The response indices

The reduced recond order denominatro polyn mial of the system represented in Equation (21) using the routh approxiamtion method

The coefficeient of the unknown numerator paramter is obtained using the harris hawk optimization taking the values as methioned in

So , the obtained reduced order of Example 1 from Equation (20) is given in Equation (21)

The parameters used for obtaining the numerator part from HHO is listed in

Name |
Values of Example 1 |

Dim |
2 (N1, N2) |

N |
30 |

Rabbit Energy/Best Fitness of HHO |
0.0050304 |

T` |
100 |

Ub |
[0.5,0.7] |

LB |
[0.9000, 0.7] |

Elapsed Time |
1551.326298 seconds |

The integral square error is 0.000245 and the proposed method. To avoid ambiguity only the response of the few reduction techniques is revealed in

Author/Year/Method ROM Response indices ISE IAE ITAE Original
- - - Proposed with algorithm 0.000245 0.04087 0.1544 Sambariya; 2016; RA+CSA 0.0002455 0.04279 0.2264 Desai; 2013; BBBC+RA 0.0002835 0.04466 0.2217 Parmar; 2007; FDA+ESA 0.0002637 0.02613 0.06642 Sikander 0.000132 0.02739 0.1224 Sikander; 2015; SE+PSO 0.001519 0.1471 1.348 Sikander; 2015; SE+FDA 0.00278 0.1319 0.5537 Sikander; 2016 0.001536 0.1443 1.239 Sambariya; 2016; RSA+SE 0.01307 0.2319 0.767 Sambariya 0.3217 0.8988 2.04 Narwal; 2016; MCA 0.0002128 0.03058 0.1092 Narwal;2015; SE+CSO 0.001991 0.1108 0.5743 Lucas; 1983; FD 0.0003284 0.03205 0.0925 Howitt; 1990; 0.0003053 0.04576 0.2311

The error obtained from the proposed method is very less than compared to the methods available in literature. The algorithm based on swarm, physics and traditional methods are compared. The particle swarm optimization with stability equation in ^{[}^{31}^{]}, cuckoo search algorithm ^{[}^{30}^{]}, Cuckoo search algorithm with SE ^{[}^{34}^{]} are compared along with the traditional methods and mixed methods and proposed result is better. This proves that the HHO is effective in MOR field. The

Author/Year/Method Step Response Characteristics ST RT Peak PT Original 3.9308 2.2603 0.9990 6.8847 Proposed with algorithm 3.6289 2.2753 1.0023 6.0082 Sambariya;2016; RA+CSA 3.6319 2.2767 1.0022 6.0624 Desai; 2013; BBBC+RA 3.6199 2.2785 1.0027 5.9728 Parmar; 2007; FDA+ESA 4.0176 2.2646 0.9993 7.3222 Sikander 3.6722 2.2409 1.0002 6.9078 Sikander; 2015 3.1669 2.1574 1.0072 4.9273 Sikander; 2015 3.4104 2.3011 1.0107 5.2442 Sikander; 2016 3.2143 2.1850 1.0073 4.9905 Sambariya; 2016 3.4554 2.3769 0.9727 5.2223 Sambariya 2.0937 0.5040 1.0382 1.2688 Narwal ; 2016 4.0867 2.3373 1.0001 11.2454 Narwal; 2015 3.1562 2.1514 1.0139 4.8652 Lucas ; 1983 4.0642 2.3197 0.9992 7.3222 Howitt; 1990 3.5769 2.2548 1.0030 5.8944

The proposed reduced-order using the HHO and RHA is compared in ^{nd} second order in red near amplitude value 1 and second-order present in the literature is given in

The manuscript presented a novel method to reduce a higher order system. The novel method consists the hunting behaviour of harris hawk and escaping of the prey in a systematic manner and Routh Hurwitz array. The proposed method implemented on an LTI SISO system.