Short term hydrothermal scheduling (STHTS) is a non-linear, multi-modal and very complex constrained optimization problem which has been solved using several conventional and modern metaheuristic optimization algorithms. A number of research articles have been published addressing STHTS using different techniques. This article presents a comprehensive review of research published for solving the STHTS problem in the last four decades.

Short-term hydrothermal scheduling (STHTS) is a highly non-linear, multi-model, non-convex, and multi-dimensional optimization problem that has been worked upon for about 5 decades. Many research articles have been published in solving different test cases of STHTS problem, while establishing the superiority of one type of optimization algorithm over the type, in finding the near global best solution of these complex problems. This paper presents the implementation of an improved version of a variant of the Particle Swarm Optimization algorithm (PSO), known as Accelerated Particle Swarm Optimization (APSO) on three benchmark test cases of STHTS problems. The adaptive and variable nature of the local and global search coefficients for the proposed APSO significantly improve its performance in obtaining the optimal solution for the STHTS test cases. Two of these cases are non-cascaded cases of STHTS problem (NCSTHTS) and one case is cascaded case of STHTS problem (CSTHTS). The results are compared with the results of the previous implementations of the other algorithms as presented in the literature. Due to the stochastic nature of the meta-heuristic algorithms, the parametric and non-parametric statistical tests have been implemented to establish the superiority of results of one type of algorithm over the results of the other type of algorithms.

Cascaded Short Term Hydro-Thermal Scheduling problem (CSTHTS) is a single objective, non-linear multi-modal or convex (depending upon the cost function of thermal generation) type of Short Term Hydro-Thermal Scheduling (STHTS), having complex hydel constraints. It has been solved by many metaheuristic optimization algorithms, as found in the literature. Recently, the authors have published the best-achieved results of the CSTHTS problem having quadratic fuel cost function of thermal generation using an improved variant of the Accelerated PSO (APSO) algorithm, as compared to the other previously implemented algorithms. This article discusses and presents further improvement in the results obtained by both improved variants of APSO and PSO algorithms, implemented on the CSTHTS problem.

The Accelerated Particle Swarm Optimization (APSO) algorithm is an efficient and the easiest to implement variant of the famous Particle Swarm Optimization (PSO) algorithm. PSO and its variant APSO have been implemented on the famous Short-Term Hydrothermal Scheduling (STHTS) problem in recent research, and they have shown promising results. The APSO algorithm can be further modified to enhance its optimizing capability by deploying dynamic search space squeezing. This paper presents the implementation of the improved APSO algorithm that is based on dynamic search space squeezing, on the short-term hydrothermal scheduling problem. To give a quantitative comparison, a true statistical comparison based on comparing means is also presented to draw conclusions.

Harmonics worsen the quality of electrical signals, hence, there is a need to eliminate them. The test objects under discussion are single-phase versions of cascaded H-bridge (CHB) multilevel inverters (MLIs) whose switching angles are optimized to eliminate specific harmonics. The Dragonfly Algorithm (DA) is used to eradicate low-order harmonics, and its statistical performance is compared to that of many other optimization techniques, including Particle Swarm Optimization (PSO), Accelerated Particle Swarm Optimization (APSO), Differential Evolution (DE), and Grey Wolf Optimization (GWO). Various scenarios of the algorithms’ search agent population for inverters with seven, nine, and eleven levels of output voltages are comprehensively addressed in this research. No algorithm shows total dominance in every scenario. The DA is least impacted by the change in dimensions of the narrated problem.

The Cascaded Short-Term Hydrothermal Scheduling (CSTHTS) problem is a highly non-linear, multi-modal, non-convex, and NP-hard optimization problem that has been solved by conventional and metaheuristic algorithms in the past. As the CSTHTS problem falls under the category of applied operational research, therefore, the work is still on-going to find new algorithms and variants of the existing algorithms that would better approximate the optimal global solution in a shorter computational time. This article proposes a novel deterministic thermal economic dispatch method embedded with the improved Accelerated Particle Swarm Optimization (APSO) algorithm to infinitesimally reduce the Big O time complexity for the standard benchmark test case of the CSTHTS optimization problem. Then, it discusses and presents the importance of performing standard statistical tests to establish the supremacy of one metaheuristic algorithm over the other one in solving the CSTHTS problem. The results obtained are better than the results of the many state-of-the-art algorithms applied to solve the considered test case of the CSTHTS problem in the literature, and the superiority of the improved APSO algorithm has been established statistically using the parametric independent samples t-test and the non-parametric Mann–Whitney U-test over the other metaheuristic algorithms such as particle swarm optimization in solving the chosen test case of the CSTHTS problem.