Implementation of combined new optimal cuckoo algorithm with a gray wolf algorithm to solve unconstrained optimization nonlinear problems

Indonesian Journal of Electrical Engineering and Computer Science Vol. 19, No. 3, September 2020, pp. 1582~1589 ISSN: 2502-4752, DOI: 10.11591/ijeecs.v19.i3.pp1582-1589  1582 Implementation of combined new optimal cuckoo algorithm with a gray wolf algorithm to solve unconstrained optimization nonlinear problems Ali A. Al-Arbo1, Rana Z. Al-Kawaz2 1 College of Arts, University of Mosul, Iraq Department of Mathematics, College of Basic Education, University of Telafer, Iraq 2 Article Info ABSTRACT Article history: In this article, a combined optimization algorithm was proposed which combines the optimal adaptive Cuckoo algorithm (OACS) which is a Natureinspired algorithm with a Gray Wolf optimizer algorithm (GWO). Sometimes considering the cuckoo algorithm alone, it may fail to find the local minimum-point and also fails to reach the solution because of the slow speed of its convergence property. Therefore, considering the new proposed adaptive combined algorithm gave a strong improvement for using this to reach the minimum point in solving (12) nonlinear test problems. This is suitable to solve a large number of nonlinear unconstraint optimization test functions with obtaining good and robust numerical results. Received Des 19, 2019 Revised Mar 1, 2020 Accepted Mar 22, 2020 Keywords: Adaptive cuckoo algorithm Combined algorithm Gray wolf algorithm Minimum point Unconstraint optimization Copyright © 2020 Institute of Advanced Engineering and Science. All rights reserved. Corresponding Author: Rana Z. Al-Kawaz, Department of Mathematics, College of Basic Education, University of Telafer, Mosul, Iraq. Email: 1. INTRODUCTION Optimization algorithms, in the present day, have become one of the most important algorithms that address life or applied problems as they contain multiple algorithms to solve these issues. Most of the minimum point search algorithms, especially gradient-based search methods, are local search algorithms. The search process usually starts with a guess and continues to improve the quality of solutions in terms of the number of iterations possible. If the functions are univariate, convexity can ensure that the ultimate optimal solution is global. If the functions are multivariate, the search is likely to be disrupted global optimally. Therefore, some variations with randomness should be used as an example of the genetic algorithm, which is a global search algorithm. Another example is simulated annealing, which is also used for global research and ensures that the optimal global solution is reached as computing time approaches infinity. Finding the best global solution is more efficient for these issues. For this was the development of many algorithms known as metaheuristic, which means here meta "beyond" or "higher level" and heuristic means "find" or "discovery by experiment and error" [1]. These metaheuristic methods include: a) Local search-based algorithms: it works with a single pass solution by repeatedly developing and increasing the fitness function until stopping criteria are reached for more details [2-5]. b) Evolutionary search-based algorithm: the population strategy uses a set of randomly generated solutions, which blend interactively until the acceptable solution is reached until it reaches new and optimal solutions in terms of its fitness function for more details [6-9]. Journal homepage: http://ijeecs.iaescore.com Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752  1583 c) Swarm search-based algorithm: the principle of the work of these algorithms is to use the population method in each iteration, as the current solutions are produced using historical information obtained by the generations generated in the previous iterations for more details note [10-16]. The cuckoo search algorithm proposed for the first time by Yang and Deb at (2009) [17] is one of the evolutionary search algorithms used to solve optimization problems in various fields of engineering and science on a large scale. This algorithm is very effective in solving global optimization because it can maintain a balance between local and global random paths using the switch parameter. There are two stages to generating possibilities in traditional methods: a) The first stage is a randomly generated Levi's flight. b) The second stage the work of the host birds to give up the cuckoo eggs. If we compare the behavior of the cuckoo with the flight of Lévy, we notice that it is as random as the flight of Lévy. There are three types of brood parasitism (brood parasitism within the species), nest rearing and cooperative breeding. n most cases, the behavior of the parasite cuckoo is chosen as a nest, where the host bird lays its eggs and lays its eggs, too [18]. There are three steps in the iterative search process including (global Lévy flight random walk, local random walk, and selection operation). The first steps to find the new solutions and are generated by Lévy flights (Levy flights by Mantegna's algorithm) as: Lévy = a 1 |𝑏| ⁄𝜌 , 𝜌 ∈ [1,3] (1) Where a is the normal distribution and b is the standard normal distribution s.t. (c>0 step size for updating new solution): 𝑎~𝑁(0, 𝜎 2 ) & 𝑏~𝑁(0,1) 1 𝜋𝜌 ) 𝜌 2 1+𝜌 )𝜌2(𝜌−1)/2 Γ( 2 𝜎=[ Γ(1+𝜌)sin( ] (2) (3) 𝑠𝑡𝑒𝑝𝑖 (𝑘) = 𝑐 ⊕ Lévy (𝜌) (4) 𝑥𝑖 (k + 1) = 𝑥𝑖 (k) + 𝑠𝑡𝑒𝑝𝑖 (𝑘) (5) Steps have been drawing local random walk through trips Lévy through the big steps that follow the distribution of Lévy: Lévy ∼ 𝑢 = 𝑘 −𝜌 (6) The above is the details of the operation of the local random walk that produces the second new solution generation by cuckoo search algorithm: 𝑥𝑖 (k + 1) = 𝑥𝑖 (k) + 𝑠𝑡𝑒𝑝𝑖 (𝑘) ⊕ randn ⊕ (𝑥𝑖 (k) − 𝑥𝑔𝑏𝑒𝑠𝑡 ) (7) Where 𝑥𝑔𝑏𝑒𝑠𝑡 is the global best solution among all 𝑥𝑖 for i (for i = 1, 2, . . ., N) at time k, that is very effective for global optimization problems since it maintains a balance between local random walk and the global random walk that is controlled by a switching parameter 𝑝𝑐 ∈[0,1], [19-21]. “ The grey wolf optimizer (GWO) as a novel swarm intelligence optimization algorithm was put forward by Seyedali Mirjalili et. al. in 2014 [22], this algorithm is a metaheuristic algorithm inspired by nature as it mimics the characteristics (leadership and hunting of gray wolves). Members of the Gray Wolves family can be divided into a somewhat hierarchical, as we note through the study that they prefer to search for prey in a box of 5-12 wolves. To define pyramid levels, we take these assumptions into conventional GWO to simulate their efficacy over gray wolves: the wolf α is at the top level being the leader of the wolf pack (it makes all kinds of decisions like hunting, maintaining discipline, sleeping and waking time for a full package), β wolf is the second-best player in the group has the highest probability of becoming a leader in the group α (at this level are subordinate wolves and help the α leader in decision-making or other activities), δ wolves, dominates wolves from back and the last le (...truncated)