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Top1. Introduction
Carpentier has introduced the term optimal power flow (OPF) in 1962 (Carpentier 1962). The OPF is an important tool for an efficient power system operation and planning in modern power system (Shaheen, Ragab, and Sobhy 2016). The main purpose of the OPF is to set control variable in such a way that economic and secure operation of power system take place. Active and reactive power generations at the generating station, reactive power output from the different reactive power sources like shunt capacitor, on load tap changing transformer etc. are chosen to control their parameters for getting multi-objective solutions. The OPF problem is a non-linear and highly constrained problem. Many traditional optimization techniques have been successfully implemented to solve the OPF problems. Most common traditional techniques can be mentioned as gradient algorithms (Peschon, Bree, and Hajdu 1971; Burchett et al. 1982), Newton method (Crisan and Mohtadi 1992), linear programming (LP) (Lobato et al. 2001; Zehar and Sayah 2008), quadratic programming (QP) (Reid and Hasdorff 1973; Granelli and Montagna 2000) and interior point method (IPM) (Vargas, Quintana, and Vannelli 1993; Momoh and Zhu 1999). These methods have average convergence characteristics and some of them widely popular in common practice. However, these methods give local optimum solution for complex objective function problems in a power system. Many meta-heuristic techniques, single objective and multi objective structures (Houssein et al. 2022a, 2022b; Bhattacharjee et al. 2014, 2015, Sony et al. 2022; Rani 2016; Das 2014) are also used to solve OPF problems. The modelling of OPF reflects operating issues as per its objective function. Genetic algorithm (GA) (Bakirtzis, Anastasios G., et al. 2002; Attia, Turki, and Abusorrah 2012) is one of the most popular techniques. In (Bakirtzis, Anastasios G., et al. 2002), authors have used enhanced genetic algorithm (EGA) to solve the OPF problem. Various control variables such as switchable shunt devices, transformer tap-setting, generator bus voltage magnitudes, and active power outputs are considered for the optimization. Authors have proposed adaptive genetic algorithm in (Attia, Turki, and Abusorrah 2012). The main contribution, for adaptive genetic algorithm, is described as adjusting population size. Kritsana and Akihiko (2009) have presented improved evolutionary programming (EP) to solve OPF problem considering voltage stability problem. Differential evaluation (DE) based approach has been proposed by the authors (Abou, Abido, and Spea 2010). In the proposed DE method, non-smooth piecewise quadratic function has been used. Improved evolutionary programming (IEP) has been offered by authors (Ongsakul, and Tantimaporn 2006) with Gaussian and Cauchy mutation operators for solving OPF problems. Multi-objective OPF has been solved with particle swarm optimization (PSO) (Choudhury and Patra 2016). Simulated annealing optimization technique is used in (Roa-Sepulveda and Pavez-Lazo 2003). Authors Roy, Ghoshal, and Thakur (2010) have proposed a novel biogeography based optimization (BBO) method to solve OPF with valve point non-linearities of generators. Optimal reactive power flow problem has been solved using artificial bee colony algorithm in (Kürşat and Kılıç 2012). Modified shuffle frog leaping algorithm (Niknam, Narimani, Jabbari, and Malekpour 2011) has been applied to OPF considering environmental and emission issues. Modified sine-cosine algorithm (MSCA) has been applied to OPF problems considering fuel cost minimization and reactive power allocations in (Attiaa, Sehiemya, and Hasanienb 2018). An Enhanced genetic algorithm (EGA) called NSGA –III integrated with adaptive elimination stratagem (Zhangab, Wanga, Tanga, Zhoua, Zengb 2019). A modified teaching learning based optimization for multi-objective OPF problem implemented in (Haghighia, Seifia, and Niknamb 2014). Quasi- Oppositional modified Jaya algorithm for multi-objective implemented in (Warid, Hizam, Mariun, and Wahab 2018).