In this research work, a new evolutionary optimization method has been used for tuning the parameters of MPC strategy for force control of EHSS. This algorithm is inspired by the lifestyle of a bird family called cuckoo. Specific breeding and egg laying of cuckoos bird is the main basis of this optimization algorithm (Abdelaziz, A. Y., and Ali, E. S., 2015). Cuckoos used in this modeling exist in two forms: mature cuckoos and eggs. CSA is firstly developed by Xin-she yang and Suash in 2009 (Kaur, P., and Kaur, M.., 2017). The CSA is considered as a meta-heuristic search method (Kaur, P., and Kaur, M.., 2017). It has an advantage of only one parameter needs to be examined. The used search method in CSA is Levy flights method (Yang, X. S., & Deb, S., 2009). This means that the CSA can discover each optimum in the design space and it has been completely compared with others. The principals of cuckoo algorithm operation are as Cuckoos lay their eggs in foreign cuckoo’s nests and depend on those cuckoos will host their eggs. Some of the other host birds find out that an egg is not their own. It might throw away the foreign egg or move it to new locations. A cuckoo may follow the color, size, and shape of the host eggs to defend their egg from being revealed. Some of the cuckoo birds may throw away other citizen eggs from the host nest to increase the hatching probability of cuckoo birds own eggs. In other hands, a chick of hatched cuckoo will also throw other eggs out from nest to increase its feeding distribute (Yang, X. S., ; Deb, S., 2009). There are a number of idealized rules used to explain the Cuckoo Search operation in a simple way as follows (Yang, X. S., ; Deb, S., 2009):
Cuckoos select a random nest for laying their eggs; a cuckoo can place only one egg at the time.
Only the eggs with the highest quality (solutions) are carried over to the next generation;
The available number of host nests must is fixed.
The host can detect an alien egg with a probability P_a? 0, 1.
In the detection case, the host bird can either throw the egg out or give up the nest so as to construct a fully new nest in a new location.
Modeling of Cuckoo Algorithm
In the case of generating new solutions x^(t+1) for a cuckoo i, a Le ?vy flight method is applied as follows (Yang, X. S., ; Deb, S., 2009).
x_i^((t+1))= x_i^((t))+? ? Le ?vy (?) (12)
Which ? is the step size and ?? 0 and it must be related to the scales of the studied problem. In most cases, it may be selected to be as ? = ?( L?10 ) where L refers to the studied problem characteristic scale. ? is a variable takes the values as follow 1