Issue 58

S. Khatir et alii, Frattura ed Integrità Strutturale, 58 (2021) 416-433; DOI: 10.3221/IGF-ESIS.58.30

  Iter MOA C presents the function value at the t

where

th iteration, which is figured out by Eqn. (19).

Iter C indicates the

current iteration, which is between 



 1 Iter M . Min and Max the accelerated function's minimum and maximum values,

respectively. The most straightforward rule, which can simulate the action of Arithmetic operators, has been presented. The following position updating calculations for the exploration sections are shown in the following formulation:

  



    j best x MOP





  

   



UB LB

LB r

0.5

j

j

j

2





    1

(20)

, i j x C





  j





Iter

  best x MOP UB LB 

   

LB

Otherwise

j

j

j



  1





i Iter x C

denotes the i

, i j Iter x C represents the j

th position of the i th solution at

where

th solution in the next iteration,

  j best x is the j

th position in the best-obtained solution so far.  is a small integer number, j UB

the current iteration, and

th position, respectively.  indicates a control parameter to adapt

and j LB represents the upper and lower values of the j

the search process, can be presented by 0.5 based on the analyzed problem.



1

C





Iter

  1

MOP C

(21)

Iter



1

M

Iter

Math Optimizer probability is used as a coefficient, represents the function value at the tth iteration,   Iter C indicates the  Iter M indicates the maximum number of iterations. denotes a sensitive parameter and defines the exploitation accuracy over the iterations, which is fixed equal to 5. The MOA function value conditions this phase of searching for the condition of r1 is not greater than the current   Iter MOP C value (see Eqn. (18)). In AOA, the exploitation operators (Subtraction (S) and Addition (A)) of AOA Explore the search field in-depth on many dense regions and use two fundamental search techniques to come up with a better solution that is modeled. current iteration, and 

 

 

    j j

 

 



 

  best x MOP UB LB

  



LB r

0.5

j

j

j

3





    1

(22)

, i j x C

Iter

  best x MOP UB LB 

  

LB

Otherwise

j

j

j

The AOA is a relatively new algorithm, and this work is one of the early attempts to test its performance in damage quantification. Horse herd optimization algorithm [20] Iraj and Farshid [20] present a new optimizer algorithm called the wild horse optimizer (WHO), inspired by the social life behavior of wild horses. The wild horse optimizer consists of five main steps as follows:  Creating an initial population and forming horse groups, and selecting leaders; The basic framework of all optimization algorithms is the same. The algorithm starts with           1 2 , , , n x x x x an initial random population. The target function repeatedly evaluates this random population, and a target value is determined        1 2 , , , n O O O O . It is also improved by a set of rules that are the core of an optimization technique.  Grazing and mating of horses; Eqn. (23) simulates grazing behavior. Eqn. (23) causes group members to move and search around the leader with a different radius.

421