Analyzing stochastic algorithms for comprehensive performance and comparison across diverse contexts is essential. By evaluating and adjusting algorithm effectiveness across a wide spectrum of test functions, including both classical benchmarks and CEC-C06 2019 conference functions, distinct patterns of performance emerge. In specific situations, underscoring the importance of choosing algorithms contextually. Additionally, researchers have encountered a critical issue by employing a statistical model randomly to determine significance values without conducting other studies to select a specific model for evaluating performance outcomes. To address this concern, this study employs rigorous statistical testing to underscore substantial performance variations between pairs of algorithms, thereby emphasizing the pivotal role of statistical significance in comparative analysis. It also yields valuable insights into the suitability of algorithms for various optimization challenges, providing professionals with information to make informed decisions. This is achieved by pinpointing algorithm pairs with favorable statistical distributions, facilitating practical algorithm selection. The study encompasses multiple nonparametric statistical hypothesis models, such as the Wilcoxon rank-sum test, single-factor analysis, and two-factor ANOVA tests. This thorough evaluation enhances our grasp of algorithm performance across various evaluation criteria. Notably, the research addresses discrepancies in previous statistical test findings in algorithm comparisons, enhancing result reliability in the later research. The results proved that there are differences in significance results, as seen in examples like Leo versus the FDO, the DA versus the WOA, and so on. It highlights the need to tailor test models to specific scenarios, as p-value outcomes differ among various tests within the same algorithm pair.

The COVID-19 pandemic profoundly affected global patterns, and the period of the declared virus pandemic has had a negative influence on all aspects of life. This research focuses on categorizing and empirically investigating the role of digital platforms in learning and business processes during the COVID-19 pandemic outbreak. The main purpose of this paper is to investigate to what extent the use of electronic learning (EL) has been boosted by COVID-19’s spread, and EL’s effectiveness on the sustainable development of electronic commerce due to the demand for a variety of electronic devices. For this purpose, the information has been collected through an online questionnaire applied to 430 participants from the Kurdistan Region of Iraq (KRI). The results indicate that participant usage and skills with electronic devices and online software programs are increasing, as the ratio indicated a level of 68% for both genders. Thus, the significance of EL concerning electronic commercial enterprises has been openly acknowledged and influenced by numerous factors. In addition, several suggestions and steps to be undertaken by the government are highlighted. Finally, this research mentions the current limitations of EL and suggests future works to build sustainable online experiences.

Metaheuristic algorithms have gained significant acceptance in large areas of optimization, giving unique and novel solutions to complicated problems across various areas. This research dives into the wide classification of state-of-the-art real-world applications that depend on metaheuristic algorithms, acknowledging their prevalence and the diversity of real-world applications where their performances are evaluated. The major goal is to evaluate forty-eight metaheuristic algorithms from 2020 to 2024 based on the results presented in their original research articles, emphasizing their effectiveness in tackling six prevalent real-world applications. In addition, the study classifies the algorithms and compares them to determine which ones are most effective for the particular applications. The results point out the necessity to solve the actual problems using opting for a metaheuristic algorithm. Nevertheless, it becomes very obvious that no algorithm works well in all the cases pointed out, as a demand for an informed selection based on the task complexity. This research contributes to the ongoing development and application of metaheuristic algorithms in diverse practical settings by providing valuable insights into the dynamic landscape of metaheuristics.

The Fifteen Puzzle problem is one of the most classical problems that has captivated mathematics enthusiasts for centuries. This is mainly because of the huge size of the state space with approximately 10¹³ states that have to be explored, and several algorithms have been applied to solve the Fifteen Puzzle instances. In this paper, to manage this large state space, the bidirectional A* (BA*) search algorithm with three heuristics, such as Manhattan distance (MD), linear conflict (LC), and walking distance (WD), has been used to solve the Fifteen Puzzle problem. The three mentioned heuristics will be hybridized in a way that can dramatically reduce the number of states generated by the algorithm. Moreover, all these heuristics require only 25 KB of storage, but help the algorithm effectively reduce the number of generated states and expand fewer nodes. Our implementation of the BA* search can significantly reduce the space complexity, and guarantee either optimal or near-optimal solutions.