## 1 Introduction
GSA cannot deal with the systems with complex constraints and also the systems with a large number of constraints and variables. NRM seems to be more effective than GSA when applied to systems where the approximation of the hydro generation cannot be performed. However, this method is fully dependent on the scale of the Jacobian matrix and the capability of taking the partial derivative of the Jacobian matrix with respect to each variable. On the contrary to GSA and NRM, population-based metaheuristic algorithms are successfully applied for solving the complicated problem. Among those methods, SAA and GA are the oldest methods and found low-quality solutions for hydropower plants and thermal power plants. Differently, PSO and EPA variants are more effective in reaching better solutions with faster speed. The improved versions of EPA are not verified, while they were claimed to be much better than conventional EPA. Only one-thermal and one-hydropower plant system and quadratic fuel cost function is employed as the case study for running those methods. In order to improve the conventional PSO successfully, weight factor [16] and constriction factor [17] are respectively used to update new velocity and new position. The improvement also leads to an optimal solution with shorter execution time, but the two research studies report an invalid optimal solution, since the water discharge violates the lower limit. In [19], the new version of the updated velocity of the FIPSO is proposed and tested on a system. However, the method reports an invalid solution violating the lower limit. IBFA [13] also shows an invalid optimal solution with more water than availability. CSOA is demonstrated to be stronger than GA, EP, and Differential Evolution (DE) for this problem. CSA variants [20; 21; 22; 23; 24]are developed for the problem and reached better results. Different distributions are tested to find the most appropriate one as compared to original distribution, which is Levy distribution. Cauchy and Gaussian distributions also result in the same best solution for the system with four hydropower plants and one thermal power plant, but the two distributions cope with a low possibility of finding the best solution. In recent years, wind energy has been considered as a power source, together with conventional power plants, to supply electricity to loads. The optimal scheduling of thermal power plants and wind turbines is successfully solved using the Artificial Bee Colony Algorithm (ABCA) [25] and Wait-And-See Algorithm (WASA) [26]. Then, the wind-thermal system is expanded by integrating one more conventional power source, which is a hydropower plant, leading to the wind-hydro-thermal system. The optimal scheduling of the wind-hydro-thermal system is performed using different metaheuristic algorithms, such as Nondominated Sorting Genetic Algorithm-III (NSGA-III) [27], Multi-Objective Bee Colony Optimization Algorithm (MOBCOA) [28], Distributionally Robust Hydro-Thermal-Wind Economic Dispatch (DR-HTW-ED) method [29], nonlinear and dynamic Optimal Power Flow (OPF) method [30], Modified Particle Swarm Optimization (MPSO) [31], Mixed Binary and Real Number Differential Evolution (MBRNDE) [32], Mixed-Integer Programming (MIP) [33], Two-Stage Stochastic Programming Model Method (TSSPM) [34], and Sine Cosine Algorithm (SCA) [35]. In general, almost all applied methods are meta-heuristic algorithms and the purpose of those studies is to demonstrate the highly successful constraint handling capability of the applied metaheuristic algorithms, rather than showing high-quality solution searching capability. In this paper, wind farms, together with the hydrothermal system, are considered to supply electricity to loads, in which the fixed-head short-term hydrothermal system is investigated. The objective of the Optimal Scheduling of Wind-Hydro-Thermal System (OSWHTS) problem is to minimize total electricity generation fuel cost of thermal power plants in a day, subject to the wind farms, reservoirs, and thermal units' constraints.