## 1 Introduction  
Short-term hydrothermal scheduling considers optimization horizon from one day to one week, involving the hour-by-hour generation planning of all generating units in the hydrothermal system, so that the total generation fuel cost of thermal units is minimized, while satisfying all constraints from hydropower plants, including hydroelectric power plant constraints, such as water discharge limits, volume reservoir limits, continuity water, generation limits, and thermal power plant constraints, including prohibited operating zone and generation limits. There is a fact that the load demand changes cyclically over one day or one week, and varies corresponding to the short-term scheduling horizon, which is in a range from one day to one week. A set of beginning conditions, consisting of initial and final reservoir volumes for the scheduling horizon, inflow into the reservoir, and the water amount to be used for the scheduling horizon, is assumed to be known. During the schedulinggeneration process, it is necessary to consider the capacity of the reservoir and inflow once they have significant impacts on the water head variations, and lead to being represented by different hydro models. In this paper, a fixed-head short-term hydrothermal scheduling with reservoir volume constraints is considered. The reservoir water head is supposed to be fixed during the scheduling horizon [1]. Therefore, the water discharge is still the second-order function of hydro generation and given coefficients. The total amount of water is not required to be calculated and constrained. However, the initial and final values of the Reservoir Volume Should Be met with the optimal operation of the hydrothermal system. The capacity of the reservoir to contain water during the operation must be observed and followed by the constrained values, such as minimum volume corresponding to the deadhead and maximum volume corresponding to the highest head. Moreover, the continuity of water is always constrained at each subinterval over the scheduling horizon. Other issues related to power transmission lines, such as power balance and power losses, are also taken into account for most test systems. The problem has been studied so far and obtained many intentions from researchers. Several algorithms, such as Gradient Search Algorithm (GSA) [2], Newton-Raphson Method (NRM) [3], Hopfield Neural Networks (HNN) [4], Simulated Annealing Algorithm (SAA) [5], Evolutionary Programming Algorithm (EPA) [6; 7; 8], Genetic Algorithm (GA) [9], modified EPA (MEPA) [10], Fast Evolutionary Programming Algorithm (FEPA) [10], Improved FEPA (IFEPA) [10], Hybrid EPA (HEPA) [11], Particle Swarm Optimization (PSO) [12], Improved Bacterial Foraging Algorithm (IBFA) [13], Self-Organization Particle Swarm Optimization (SOPSO) [14], Running IFEPA (RIFEPA) [15], Improved Particle Swarm Optimization (IPSO) [16; 17], Clonal Selection Optimization Algorithm (CSOA) [18], Full Information Particle Swarm Optimization (FIPSO) [19], One-Rank Cuckoo Search Algorithm with the applications of Cauchy (ORCSA-Cauchy) and Levy distribution (ORCSA-Levy) [20], Cuckoo Search Algorithm with the applications of Gaussian distribution (CSA-Gauss), Cauchy distribution (CSA-Cauchy), and Levy distribution (CSA-Levy) [21], Adaptive Cuckoo Search Algorithm (ACSA) [22], Improved Cuckoo Search Algorithm (ICSA) [23], Modified Cuckoo Search Algorithm (MCSA) [24], and Adaptive Selective Cuckoo Search Algorithm (ASCSA) [24] have been applied to solve the problem of hydrothermal scheduling. Almost all of the above-mentioned methods are mainly meta-heuristic algorithms, excluding GSA and NRM. Regarding the development history, GSA and NMR are the oldest methods, with the worst capabilities to deal with constraints and finding high-quality parameters of the problem, and they are applied for hydropower generation function with the piecewise linear form or polynomial approximation form.