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Combinatorial optimization is a fundamental area in operations research and computer science, focusing on identifying optimal solutions from a finite set of possibilities. This study explores the integration of branch and bound methods with heuristic algorithms to address optimization problems in graph theory and discrete mathematics. Python was employed for algorithm implementation due to its flexibility and comprehensive computational libraries, enabling efficient data analysis and visualization. Several benchmark problems were examined, including the Traveling Salesman Problem (TSP), Minimum Spanning Tree (MST), and Graph Coloring. Simulations were conducted using datasets of varying sizes (small, medium, and large) to evaluate performance across different scales. The results demonstrate that the hybrid approach achieves a balance between solution quality and computational efficiency, outperforming brute-force methods in terms of speed while maintaining near-optimal accuracy. Tabulated results and graphical comparisons highlight the reduction in computation time and improved scalability of the proposed method. The findings suggest that combining systematic search strategies with heuristics offers a practical and effective framework for solving complex combinatorial optimization problems. Recommendations for future research include testing scalability with larger datasets, incorporating advanced metaheuristics, and applying the approach to real-world domains such as logistics and network design.

This article examines a potential solution to the well-known Travelling Salesman Problem (TSP), which is classified as an NP-hard problem. We also provide a theoretical synopsis of several approaches that have been employed to tackle this problem. A prominent example of a combinatorial problem is the traveling salesman problem (TSP). To address the fundamental PSO algorithm's premature convergence issue and stagnation behavior on TSP, a scout characteristic-based PSO algorithm is suggested.We address Particle Swarm Optimization (PSO), a member of the evolutionary methods class, and outline the methodology for applying PSO to the TSP. Among population-based metaheuristic optimization methods, Particle Swarm Optimization (PSO) is one of the most widely used. Scientific domains such as engineering, chemistry, medicine, advanced physics, and humanities have all effectively employed PSO. Numerous theoretical and empirical results on the convergence and parameterization of PSO versions have been produced as a result of the method's extensive investigation since its introduction in 1995. Hundreds of PSO versions have been developed. It is well recognized that population size has a significant impact on the effectiveness of metaheuristics; nevertheless, no comprehensive research has been done on the appropriate selection of PSO swarm size to date.Through the application of this approach, we examine the effects of various control settings. The ideal solution and the quality of the solution are contrasted.    

This research aims to reveal the history and changes in the implementation procession in the village medical tradition during the month of Muharram, in Kalang Bahu Hamlet, Jawai Laut Village, South Jawai District. The research method used is the historical research method and consists of the following elements; heuristics (data collection); verification (source criticism); interpretation (interpretation of sources); and historiography (writing). The results of the research show that the village medical tradition is a religious tradition, an expression of gratitude for the blessings that God has bestowed upon us, and a tradition of asking God for help to always provide safety and keep us away from danger. The village medical tradition in Kalang Bahu Hamlet underwent a process of change so that it was divided into three periods, the first period 1950-1973, the second period 1973-1983, and the third period 1983-Present. The changes that occur in village medical traditions are caused by the increasing development of people's understanding of religious teachings. Apart from that, the village medical tradition has values ​​contained in it such as religious values, mutual cooperation, solidarity and tolerance.    

The SIKONTRAS application is a web-based application that has previously been used to socialize contraceptives to support government programs in broadcasting family planning programs, however, with technological developments and the large number of user demands who want comfort and ease in accessing information with attractive visuals, especially in terms of system appearance. used, the author took the initiative to carry out an evaluation of the SIKONTRAS application by going through the initial stages, namely distributing questionnaires to SIKONTRAS users and experts in the field of information system development, then from the results of the assessment, they will then be analyzed using the heuristic evaluation method. The research method is heuristic evaluation, method to identify design problems in user interfaces. The evaluator assesses the design based on a set of guidelines (called heuristics) that make the system easy to use. This Heuristic Evaluation is used to obtain usability testing results from SIKONTRAS. Testing was carried out on 5 respondents in the IT sector and the process included the following stages in carrying out the test. Based on the results of data analysis using heuristic evaluation, it can be concluded that the evaluation results of the SIKONTRAS system contained the greatest value in the flexibility and efficiency of use variable indicators, which means SIKONTRAS is flexible in using the system and easy for new users to understand, but development recommendations are still given based on comments and input by respondents, where respondents have professions in the field of information systems.

The United Islamic Cultural Center of Indonesia (UICCI) or the United Islamic Cultural Center Foundation in Indonesia is an Islamic organization that operates in the social and religious fields. This foundation is an Islamic social and religious institution that produces Al-Quran Hafiz who applies the Al-Quran and Sunnah in everyday life while directing them to do good deeds with their knowledge. The UICCI Foundation is better known as Pondok Pesantren Syarief Medan which is a branch of the IFA (International Fratenity Association) or international fraternity foundation in Turkey. The history of the founding of the Central UICCI Foundation in Turkey or the Sulaimaniyah Institute began after the fall of the Ottoman Caliphate in 1924, the Turkish regime under the leadership of the nationalist figure Mustofa Kemal Attaturk began to introduce the ideas of nationalism and secularism, or rather laicism. This is an interesting study considering that Islamic boarding schools are traditional Islamic educational institutions originating from Indonesia and UICCI is a branch of Islamic education from Turkey. Because it is a branch of the Turkish Islamic boarding school, it has its own way of learning which is different from Islamic boarding schools in Indonesia in general. The differences lie in the teaching system which is controlled by the center in Turkey, the rules are based on Sufism, the students' learning activities are integrated with the Turkish language, Turkish culture is introduced to the students and the full scholarship for further education in Turkey is given to the students. In this research there are three problem formulations, namely: History and development of the UICCI Syarief Medan Foundation, dynamics, and its contribution to students and society. The approach used by researchers is Sociology. The theory used is Continuity and Change by Jhon Obert Voll. The method used is the historical method, which includes four steps, namely heuristics, verification, interpretation and historiography. The results of this research show that the UICCI Syarief Islamic Boarding School in Medan has a distinctive form and is different from Islamic boarding schools in general. The differences can be seen from the activities at the boarding school which are based on Sufism and tarekat which are followed by Islamic boarding school students, an integrated teaching system with Turkish language and Tekamul education (scholarships for further Islamic education to Turkey). Apart from that, the dynamics that occur at the UICCI Syarief Islamic boarding school can be seen from an educational and economic perspective, namely making UICCI Syarief become the center of Tadris for the Sumatra Island branch and from an economic perspective it can be seen from what was initially free to paid. In terms of contribution, this foundation only focuses on students, preparing student go to Tekamul.

The Gulf Cooperation Council (GCC) region has experienced tremendous growth in the higher education sector with many public but internationally recognized universities, colleges, and programs. Annually, within and outside of the GCC zone, high school students and guardians undergo repeatable and time-consuming experiences for inhomogeneous university, college, and program admission and tracking processes. This research project aims to provide a unified management tool to manage the admission and tracking process to multiple accredited GCC universities, colleges, and programs through one unified central mobile-based application. The research project aimed to achieve two objectives: exploring the GCC university admission process phenomena and developing and evaluating a unified mobile-based university admission application (denoted by HEIM) for higher education institutes' mobile applications. An Agile-SDLC methodology was employed, entailing two phases; the Exploratory phase to the phenomena of the university admission process and the development and evaluation phase of the potential mobile application. The 1st phase was based on an interview with the Ministry of Education (MOE), employing SLR and CA techniques for articles and mobile applications collection and analysis, and 1st questionnaire to collect user requirements. The 2nd phase employed several design techniques, including DFD, ERD, etc., a 2nd questionnaire to collect system requirements and coding by .NET MAUI, C#, and XAML, and a 3rd questionnaire to evaluate the usability of HEIM based on Nielsen heuristics at which the empirical findings revealed 97.7% of usability.

 In the current era, education is considered the main driving force to meet the needs of an increasingly globalized world, both in the field of improving the quality of information and in the field of improving morals and ethics, which focuses on education. This research aims to determine the history of the formation of the At-Taqwa Sambas Private Madrasah Ibtidaiyah as well as the factors that support and hinder the development of the At-Taqwa Sambas Private Ibtidaiyah Madrasah. The research method used is historical research methods including heuristics, verification, interpretation and historiography. The research results show that the history of the At-Taqwa Private Madrasah Ibtidaiyah was founded in 2011 and was founded by the leadership of the Islamic Education Foundation through the encouragement of community leaders who understand education for the younger generation. Mr. Aminuddin Hardigaluh as the driving force and other founding figures continues to invite children to study religious education at the At-Taqwa Sambas Private Madrasah Ibtidaiyah. Starting from a student population of only 11 people and 3 teachers, this has not dampened the children's enthusiasm for studying at the madrasa. As time went by, the At-Taqwa Sambas Private Madrasah also experienced many developments, including increasing the number of students, increasing facilities and infrastructure as well as more disciplined learning practices.

This paper aims to look at the changes in the dress of school students in Solok Regency during the reign of Gumawan Fauzi. This change was motivated by the issuance of regional regulation letter No. 6 of 2002 concerning Muslim and Muslim women's clothing. This title was taken from 1995 to 2005. The type of research used is qualitative research. The method used in this research is historical research method using steps (1) heuristics or source collection (2) source criticism, (3) interpretation, (4) historiography. From the results of the research conducted, during the reign of Mr. Gamawan Fauzi found that there was a change in the form of dress for elementary school students in Solok Regency, this was caused by a circular issued by Mr. Gamawan Fauzi regarding the way elementary school (SD) students dressed. From 1995 to March 2002 the clothes worn by elementary school students were wearing short-sleeved shirts for both men and women and wearing short skirts for women while men for men also wore short pants and did not wear headscarves for women, whereas after being expelled regional regulation letter No. 6 of 2002, namely that there was a change in the dress of female and male students wearing long sleeves and long male skirts for female students and wearing headscarves while male students wore trousers. While the meaning of changing the clothes of school students is: This change of clothes also has a meaning which means to protect the private parts, especially for female students, to guard against disturbances that will damage the genitals and also by wearing closed clothes also avoid the fires of hell in the future and also fortify themselves and the next generation of the nation so that they do not fall into a culture that is not in accordance with the teachings of Islam