## 1 Introduction  
The PSO algorithm has gained much popularity among the metaheuristic optimization algorithms in the recent past due to its ease of implementation and promise towards finding good approximates to global optimum solutions of complex optimization problems [1]. APSO is a simpler yet brilliant variant of PSO, and it has be proven to find good approximates of global optimum solutions in less time and fewer iterations as compared to PSO algorithms [2]. Dynamic search space squeezing has been applied on PSO to make yet another variant of PSO named improved PSO, and it gives better performance for some optimization problems as compared to PSO itself [3]. Short-term hydrothermal scheduling is a non-linear and multi-modal optimization problem, which has many forms. These can be of a non-cascaded form to a cascaded form. In the non-cascaded form, there is only one reservoir of water, whereas in the cascaded form, there is a series of downstream reservoirs. It can be single objective or multi-objective. In the single-objective Short-Term Hydrothermal Scheduling (STHTS) problem, the objective is only to minimize the cost of the operation of the thermal generating units, whereas in the multi-objective STHTS problem, the other objectives are to reduce the emission of COx, NOx, and SOx gases, as well. The works in [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19] discussed all these types of the STHTS problem and the implementations of conventional and non-conventional metaheuristic optimization algorithms on STHTS problems and presented the superiority of one type of algorithm (usually metaheuristic) over other types. Improved PSO, PSO, cuckoo search optimization, quantum behaved PSO, teaching-learning-based optimization, the multi-objective differential algorithm, the gravitational search algorithm, the artificial bee colony algorithm, the genetic algorithm, civilized swarm optimization algorithms, and gravitational search algorithms are better choices for those types of STHTS problems as presented in [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. The works in [20; 21; 22; 23; 24; 25; 26; 27] discussed specifically the non-cascaded and single-objective STHTS problems in which one hydel and one equivalent thermal unit of a number of thermal units are dispatched to supply the power demand. PSO and APSO have the shown best results for such problems. Specially, according to [24; 25], the APSO algorithm has outperformed the other previously-implemented deterministic and metaheuristic optimization algorithms on non-cascaded and single-objective STHTS problems. The works in [19; 20; 21; 22; 23; 24; 25] discussed specifically the non-cascaded problems in which one hydel and one thermal unit are dispatched to supply the power demand. PSO and APSO have shown the best results for such problems. Especially, according to [24; 25], the APSO algorithm has outperformed the other previously-implemented deterministic and metaheuristic optimization algorithms. Due to the stochastic nature, it is required that there must be a true statistical comparison between the implementations of various algorithms on one type of optimization problem, which was not presented in previous works [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. The work in [28] also presented this thesis while applying the PSO algorithm using digital pheromones. In the STHTS problem, it is therefore also required to present the quantitative analysis by applying statistical hypothesis tests. This paper is an extended work of [24; 25], already published by the authors, and presents the implementation of the improved APSO algorithm on the non-cascaded STHTS problems (two cases) and gives its statistical comparison with the previous APSO implementations on the same problems, by the authors of this paper, in [24; 25].