# A Novel Complex-Valued Encoding Grey Wolf Optimization Algorithm
## 1 Introduction  
Over the last few decades, various heuristic optimizations have been developed to solve complex computational problems. Some of the most popular are: particle swarm optimization (PSO) [1], genetic algorithm (GA) [2], differential evolution (DE) [3, 4], simulated annealing (SA) [5], ant colony optimization (ACO) [6], artificial bee colony optimization (ABC) [7], gravitational search algorithm (GSA) [8, 9], charged system search (CSS) [10], magnetic optimization algorithm (MOA) [11], biogeography-based optimization algorithm (BBO) [12, 13], and teaching learning-based optimization (TLBO) [14]. The swarm intelligence optimization algorithm can flexibly and effectively deal with different problems that conventional optimization techniques cannot solve. For this reason, optimization techniques have been widely used in many domains of study. In addition, it has been demonstrated that there is no heuristic optimization that can solve all optimization problems [15]. In other words, existing algorithms give satisfactory results in solving some problems, but not all problems. Therefore, several new heuristic algorithms are proposed every year, and research in this field is active.  
The real-value grey wolf optimization (GWO) is a new population-based meta-heuristic approach initially proposed by [PERSON] _et al._ (2014) [16]. Due to the fact that the GWO algorithm is simple, flexible and efficient, it can be successfully applied to practical applications [17, 18, 19]. There are many modified versions of the GWO algorithm. For example, some people study the parameters of the GWO algorithm or combine the GWO algorithm with other heuristic optimization algorithms. However, these methods all use binary or decimal encoders to position the grey wolf, the individual gene contains information to be limited.  
The complex-valued encoding method has been applied in expressing neural network weights [20] and representing individual genes for evolutionary algorithms [21]. It uses a diploid to express genes and greatly expand the information capacity of the individual. Starting from the individual encoding method, this article studies the improvement of the performance of the grey wolf with the complex-valued method. The value of the independent variables for an objective function is determined by modules and the signthe independent variables is determined by angles. For the GWO algorithm, the grey wolf individual is divided into two parts, namely: a real part gene and an imaginary gene. Additionally, the two parts represent a variable being able to enhance the information of a grey wolf individual and a diverse population, avoiding the local optimum. Based on the above advantages, we provide a new method for the GWO algorithm to solve practical problems.  
The rest of the paper is organized as follows: Section 2 presents a brief introduction to GWO. Section 3 discusses the basic principles of a complex-valued version of GWO. The experimental results of test functions and infinite impulse response (IIR) system identification problem are shown in Sections 4 and 5 respectively. Finally, Section 6 concludes the work and suggests some directions for future study.