## 1 Introduction  
Active disturbance rejection control (ADRC) is a promising and relatively new control technology, which was formally proposed by [PERSON] in 2009 [1], while the origin of ADRC could date back to the year of 1995 [2]. Its core idea is to treat both internal uncertainty and external disturbance as \"generalized interference\", estimate the generalized interference through a mechanism called \"extended state observer (ESO)\" in real time, and then compensate the generalized interference by a nonlinear feedback controller using the estimation of ESO. The greatest advantage of ADRC is that it only needs the relative order of the controlled object; thus, it is independent of a precise model of the controlled object. So far ADRC has been widely applied in many fields such as motion control [3], energy [4], chemical industry [5], power parafoil control [6], paper tension adjustment [7], and so on. ADRC has also shown broad commercial application value, one of the examples is InstaSPIN-MOTION motor control solution produced by Texas Instruments, which integrates ADRC inside to achieve high control performance. Generally speaking, in the field of control engineering, how to obtain a set of controller parameters which can meet the specific performance index has always been a research topic. A set of optimized parameters can achieve better control performance, and this means a lot in industrial manufacturing, such as economic effects and even environment benefits. A properly designed and well-tuned ADRC can make the control system achieve good performance and robustness. However, in the design framework of origin ADRC, there are too many parameters that need to be adjusted, and the number of parameters will increase as the relative order of the controlled object increases. The number of parameters is one thing, the other complex thing is that these parameters interact with each other. [PERSON] [8] proposed linear ADRC (LADRC) with scaling and a bandwidth parameterization method. The number of parameters of LADRC is successfully reduced to two, but the coupling effect between parameters still remains, and even becomes more obvious. Thus, it is rather difficult to analytically find the optimal parameters that can achieve good control performance. What's more, if LADRC is applied on industrial processes with time delay, due to the existence of time delay, the characteristic function of system is a pseudo polynomial, which makes it even impossible to have an analytical solution. Although it is easy to find a set of parameters that make the control system stable, how to find the optimal system performance parameters has always been a problem demanding prompt study. On the other hand, the process of finding optimal parameters of a control system can be regarded as an optimization problem with system performance index as the objective function [9]. Usually, the optimization problem designed by this method is a non-convex optimization problem, and it is difficult to solve by conventional optimization methods, which urges researchers to find a new way to solve this kind of optimization problem. In recent years, with the development of digital computers, more and more researchers turned their attention to meta-heuristic algorithms to solve engineering and practical problems. [PERSON], [PERSON], et al. [10] used a simulated annealing algorithm to improve an interval type-2 fuzzy sets and achieved an outstanding result for an electric charging station location problem. [PERSON] and [PERSON] [11] successfully optimized medium-scale airline crew pairing problems by a modified genetic algorithm. Meta-heuristic algorithms benefit from the use of random operators [12]. Random operators make these algorithms exhibit completely different behaviors from deterministic algorithms and that is the reason why meta-heuristic algorithms usually have stronger global search ability.