METHODOLOGIES AND APPLICATION Enhanced crow search algorithm for AVR optimization Amrit Kaur Bhullar 1 • Ranjit Kaur 1 • Swati Sondhi 2 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract This paper proposes an enhanced crow search algorithm (ECSA) for solving numerical and real-life engineering problems. Novelties of the proposed method are fourfold: (1) addition of an archive component in the standard crow search algorithm (CSA) to incorporate past experience of finding solution (2) formulation of non-hideout position so that crow will remain near its hideout position, (3) Rechenberg’s 1/5th rule is exploited to change the flight length (instead of fixed) to speed up optimization process and (4) awareness probability is regulated to set a trade-off between local and global exploration. The performance of proposed technique is investigated on 23 benchmark functions such as unimodal, multimodal and fixed- dimension multimodal benchmark functions. The results of ECSA are compared to other state-of-the-art metaheuristic algorithms, in which ECSA outperformed other algorithms in majority of the benchmark functions. Further, to validate the effectiveness of the proposed method, ECSA has been used for optimization of proportional–integral–derivative (PID) controller. Results of ECSA–PID have been compared with conventional CSA as well as with other state-of-the-art techniques like Ziegler–Nichols (Z–N), Kitamori, ACO, multi-objective ACO, multi-objective GA and fuzzy and space gravitational optimization algorithm. The proposed algorithm is implemented on the AVR system and tested under various conditions for robustness. Consistency in the results on benchmark systems as well as on their variants and AVR system and its variants prove the robustness of the proposed method. Also, the performance of the proposed algorithm is found to be better than the existing techniques. Keywords Crow search algorithm (CSA)  Enhanced crow search algorithm (ECSA)  Proportional–integral–derivative (PID) controller  Automatic voltage regulator (AVR) 1 Introduction The classical PID controller is a popular process controller among the industries worldwide. Its popularity can be attributed to its simple structure, cost effectiveness and ease of implementation into modern hardware (Astrom and Hagglund 1995). The performance of PID controller depends on the tuning of three parameters, namely pro- portional gain (K P ), integral gain (K I ) and derivative gain (K D ). Tuning of the controller refers to ‘‘best’’ adjustment of these controller parameters to achieve the desired closed-loop response of any control system or process. Since 1942, various tuning methods have been proposed by researchers to find the PID gains for better control system response. Even a small improvement in PID tuning can have a significant impact in industries and control pro- cesses. Numerous tuning rules have been proposed by the researchers for the PID controller, based on the control objective such as percent overshoot, settling time, rise time and integral of absolute error (IAE). PID tuning methods are classified as classical methods such as Ziegler–Nichols (Ziegler and Nichols 1993) and Cohen–Coon method (Cohen and Coon 1953); analytical methods such as dominant pole design proposed by Astrom and Hagglund (1995) and internal model control (IMC) (Bequette 2003); and optimization methods. To enhance the capabilities of classical PID controllers, several intelligent approaches have been suggested to improve PID tuning such as fuzzy neural method (Lee et al. 2008), fuzzy methods (Zhao et al. 1993), genetic algorithm (Yourui et al. 2005; Bagis 2007), Communicated by V. Loia. & Swati Sondhi swatiei@gmail.com 1 Department of Electronics and Communication Engineering, Punjabi University, Patiala, India 2 Department of Electrical and Instrumentation Engineering, Thapar University, Patiala, India 123 Soft Computing https://doi.org/10.1007/s00500-019-04640-w