Global Optimization Using Local Search Approach for Course Scheduling Problem

Course scheduling problem is a combinatorial optimization problem which is defined over a finite discrete problem whose candidate solution structure is expressed as a finite sequence of course events scheduled in available time and space resources. This problem is considered as non-deterministic polynomial complete problem which is hard to solve. Many solution methods have been studied in the past for solving the course scheduling problem, namely from the most traditional approach such as graph coloring technique; the local search family such as hill-climbing search, taboo search, and simulated annealing technique; and various population-based metaheuristic methods such as evolutionary algorithm, genetic algorithm, and swarm optimization. This article will discuss these various probabilistic optimization methods in order to gain the global optimal solution. Furthermore, inclusion of a local search in the population-based algorithm to improve the global solution will be explained rigorously

An Assignment Problem and Its Application in Education Domain: A Review and Potential Path

This paper presents a review pertaining to assignment problem within the education domain, besides looking into the applications of the present research trend, developments, and publications. Assignment problem arises in diverse situations, where one needs to determine an optimal way to assign n subjects to m subjects in the best possible way.With that, this paper classified assignment problems into two, which are timetabling problem and allocation problem. The timetabling problem is further classified into examination, course, and school timetabling problems, while the allocation problem is divided into student-project allocation, new student allocation, and space allocation problems. Furthermore, the constraints, which are of hard and soft constraints, involved in the said problems are briefly elaborated.In addition, this paper presents various approaches to address various types of assignment problem. Moreover, direction and potential paths of problem solving based on the latest trend of approaches are also highlighted.As such, this review summarizes and records a comprehensive survey regarding assignment problem within education domain, which enhances one's understanding concerning the varied types of assignment problems, along with various approaches that serve as solution

Otimização de grades horárias no ensino superior : um modelo matemático para minimizar atrasos na conclusão de cursos

Orientador: Prof. Dr. Gustavo Valentim LochDissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa : Curitiba, 14/08/2023Inclui referênciasResumo: A construção de grades horárias é um problema recorrente no ambiente das instituições de ensino superior. Trata-se de um problema complexo, uma vez que a qualidade da grade impacta diretamente na vida dos professores e discentes. A oferta de disciplinas sem um processo de otimização pode gerar limitações aos discentes no momento de definir quais disciplinas irão cursar, contribuindo para possíveis atrasos na conclusão de seus cursos. O presente trabalho descreve um modelo matemático de programação linear inteira mista (PLIM) baseado no University Course Timetabling Problem (UCTTP) que possibilita encontrar os melhores horários para oferta de disciplinas de modo a minimizar o número de períodos necessários para que um discente conclua a sua graduação. Diferentemente dos trabalhos já apresentados na literatura, focados nos docentes, esse modelo prioriza as necessidades dos discentes em sua construção. Para realizar a validação do modelo e testar a sua aplicabilidade utilizou-se de dados anônimos reais de uma universidade pública brasileira. Os resultados obtidos apontam que o modelo apresentou bom desempenho quando implementado, atingindo o objetivo proposto.Abstract: The construction of schedules is a recurring problem in higher education institutions. It is a complex problem since the quality of the schedule directly impacts the lives of teachers and students. The offer of courses without an optimization process can generate limitations to students when defining which subjects, they will take, contributing to possible delays in the conclusion of their courses. This paper presents a mathematical model of mixed integer linear programming (PLIM) based on the University Course Timetabling Problem (UCTTP) that makes it possible to find the best times to offer courses to minimize the number of periods required for a student to complete his/her undergraduate degree. Unlike the papers already presented in the literature, which focus on teachers, this model prioritizes the needs of students in its construction. To validate the model and test its applicability, real anonymous data from a public Brazilian university was used. The results obtained indicate that the model presented good performance when implemented, reaching the proposed objective

Recommendation System for Collegian Student's Weekly Course Schedule

Existing research on course scheduling was conducted only from the institutional side.  However, students usually have other considerations, such as routine activities outside of class, course time, holidays in a week of study, and lead time between courses. These conditions had never been taken into consideration in existing research.  In this paper, a recommendation system was proposed using Depth First Search and Simple Multi Attribute Ranking Technique methods.  Depth First Search method was used to find all possible alternative schedules. All the possible alternative schedules were used to determine the schedule that best suits student preferences using Simple Multi Attribute Ranking Technique method. The system performance was measured through simulation to get course schedule recommendations for 28 students.  The simulation results were compared with the ideal schedule desired by the students and the real course schedule for those students. The accuracy of the recommended schedule against the ideal schedule desired by students was 70.8% with an average processing time of 1.05 seconds. The accuracy of the recommended schedule increased to about 91% when compared to the actual student courses schedule.  So it can be concluded that the research can help to recommend students' weekly class schedules in real terms.Selama ini, penelitian terkait dengan penjawalan mata kuliah hanya  dilakukan dengan mempertimbangkan sisi institusi.  Namun, biasanya mahasiswa memiliki pertimbangan lain, seperti kegiatan rutin di luar kuliah, waktu perkuliahan, hari libur kuliah, dan jeda waktu tunggu antar mata kuliah.  Kondisi ini tidak pernah dipertimbangkan dalam penelitian yang ada. Penelitian yang dilakukan bertujuan untuk mengembangkan sebuah sistem rekomendasi dengan menggunakan gabungan antara metode Depth First Search dan Simple Multi Attribute Ranking Technique. Metode Depth First Search digunakan untuk mencari semua kemungkinan alternatif jadwal. Semua alternatif jadwal yang didapatkan akan digunakan untuk menentukan jadwal yang paling sesuai dengan preferensi mahasiswa menggunakan metode Simple Multi Attribute Ranking Technique. Kinerja dari sistem dievaluasi melalui simulasi untuk mendapatkan rekomendasi jadwal mata kuliah bagi 28 mahasiswa. Hasil simulasi kemudian dibandingkan dengan jadwal ideal yang diinginkan oleh mahasiswa dan jadwal mata kuliah yang riil dijalani mahasiswa.  Akurasi dari jadwal yang direkomendasikan terhadap jadwal ideal yang diinginkan mahasiswa mencapai 70,8% dengan rata-rata waktu untuk menghasilkan jadwal yang direkomendasikan adalah 1,05 detik. Akurasi jadwal yang direkomendasikan meningkat menjadi sekitar 91% jika dibandingkan dengan jadwal mata kuliah yang riil dijalani oleh mahasiswa yang bersangkutan.  Jadi dapat disimpulkan bahwa penelitian yang dilakukan dapat membantu merekomendasikan jadwal kuliah mingguan mahasiswa secara rii

Scheduling Problems

Scheduling is defined as the process of assigning operations to resources over time to optimize a criterion. Problems with scheduling comprise both a set of resources and a set of a consumers. As such, managing scheduling problems involves managing the use of resources by several consumers. This book presents some new applications and trends related to task and data scheduling. In particular, chapters focus on data science, big data, high-performance computing, and Cloud computing environments. In addition, this book presents novel algorithms and literature reviews that will guide current and new researchers who work with load balancing, scheduling, and allocation problems

An investigation of Monte Carlo tree search and local search for course timetabling problems

The work presented in this thesis focuses on solving course timetabling problems, a variant of education timetabling. Automated timetabling is a popular topic among researchers and practitioners because manual timetable construction is impractical, if not impossible, as it is known to be NP-hard. A two-stage approach is investigated. The first stage involves finding feasible solutions. Monte Carlo Tree Search (MCTS) is utilized in this stage. As far as we are aware, it is used for the first time in addressing the timetabling problem. It is a relatively new search method and has achieved breakthrough in the domain of games particularly Go. Several enhancements are attempted on MCTS such as heuristic based simulations and pruning. We also compare the effectiveness of MCTS with Graph Coloring Heuristic (GCH) and Tabu Search (TS) based methods. Initial findings show that a TS based method is more promising, so we focus on improving TS. We propose an algorithm called Tabu Search with Sampling and Perturbation (TSSP). Among the enhancements that we introduced are event sampling, a novel cost function and perturbation. Furthermore, we hybridize TSSP with Iterated Local Search (ILS). The second stage focuses on improving the quality of feasible solutions. We propose a variant of Simulated Annealing called Simulated Annealing with Reheating (SAR). SAR has three features: a novel neighborhood examination scheme, a new way of estimating local optima and a reheating scheme. The rigorous setting of initial and end temperature in conventional SA is bypassed in SAR. Precisely, reheating and cooling were applied at the right time and level, thus saving time allowing the search to be performed efficiently. One drawback of SAR is having to preset the composition of neighborhood structures for the datasets. We present an enhanced variant of the SAR algorithm called Simulated Annealing with Improved Reheating and Learning (SAIRL). We propose a reinforcement learning based method to obtain a suitable neighborhood structure composition for the search to operate effectively. We also propose to incorporate the average cost changes into the reheated temperature function. SAIRL eliminates the need for tuning parameters in conventional SA as well as neighborhood structures composition in SAR. Experiments were tested on four publicly available datasets namely Socha, International Timetabling Competition 2002 (ITC02), International Timetabling Competition 2007 (ITC07) and Hard. Our results are better or competitive when compared with other state of the art methods where new best results are obtained for many instances

An investigation of Monte Carlo tree search and local search for course timetabling problems

The work presented in this thesis focuses on solving course timetabling problems, a variant of education timetabling. Automated timetabling is a popular topic among researchers and practitioners because manual timetable construction is impractical, if not impossible, as it is known to be NP-hard. A two-stage approach is investigated. The first stage involves finding feasible solutions. Monte Carlo Tree Search (MCTS) is utilized in this stage. As far as we are aware, it is used for the first time in addressing the timetabling problem. It is a relatively new search method and has achieved breakthrough in the domain of games particularly Go. Several enhancements are attempted on MCTS such as heuristic based simulations and pruning. We also compare the effectiveness of MCTS with Graph Coloring Heuristic (GCH) and Tabu Search (TS) based methods. Initial findings show that a TS based method is more promising, so we focus on improving TS. We propose an algorithm called Tabu Search with Sampling and Perturbation (TSSP). Among the enhancements that we introduced are event sampling, a novel cost function and perturbation. Furthermore, we hybridize TSSP with Iterated Local Search (ILS). The second stage focuses on improving the quality of feasible solutions. We propose a variant of Simulated Annealing called Simulated Annealing with Reheating (SAR). SAR has three features: a novel neighborhood examination scheme, a new way of estimating local optima and a reheating scheme. The rigorous setting of initial and end temperature in conventional SA is bypassed in SAR. Precisely, reheating and cooling were applied at the right time and level, thus saving time allowing the search to be performed efficiently. One drawback of SAR is having to preset the composition of neighborhood structures for the datasets. We present an enhanced variant of the SAR algorithm called Simulated Annealing with Improved Reheating and Learning (SAIRL). We propose a reinforcement learning based method to obtain a suitable neighborhood structure composition for the search to operate effectively. We also propose to incorporate the average cost changes into the reheated temperature function. SAIRL eliminates the need for tuning parameters in conventional SA as well as neighborhood structures composition in SAR. Experiments were tested on four publicly available datasets namely Socha, International Timetabling Competition 2002 (ITC02), International Timetabling Competition 2007 (ITC07) and Hard. Our results are better or competitive when compared with other state of the art methods where new best results are obtained for many instances

Asignación de salones por medio de una hiper-heurística

El problema de horarios y cursos basado en currículum (abreviado por sus siglas en inglés, CBCT), es un problema de optimización, donde se plantea la generación de un calendario escolar respetando una serie de restricciones, además existe una función objetivo con la capacidad de evaluar cada horario propuesto, por lo que el objetivo es obtener el calendario con el menor costo posible. Los origines del problema pueden ser rastreados hasta los años setentas, aunque en el presente trabajo se considera la descripción dada por la Competencia Internacional de Horarios 2007 (por sus siglas en inglés: ITC2007), evento donde se reunieron investigadores alrededor del mundo y que continúa siendo utilizado como campo de estudio para algoritmos. En el presente trabajo se propone una hiper-heurística como técnica para abordar el CBCT. El algoritmo por medio de diferentes heurísticas de bajo nivel, intenta minimizar el número de restricciones no satisfechas con el objetivo de generar un calendario de mejor calidad. Finalmente se utilizó la base de datos de la ITC2007 la cual consta de 21 instancias distintas con lo cual, se puede tener marco de referencia sobre el desempeño de la propuesta. Los resultados obtenidos por el algoritmo, son comparados con otras técnicas encontradas en la literatura. Los resultados obtenidos son alentadores, el programa obtiene soluciones competitivas en tiempos aceptables, e incluso en algunos casos cercanas al mejor valor conocido

Enhanced evolutionary algorithm with cuckoo search for nurse scheduling and rescheduling problem

Nurse shortage, uncertain absenteeism and stress are the constituents of an unhealthy working environment in a hospital. These matters have impact on nurses' social lives and medication errors that threaten patients' safety, which lead to nurse turnover and low quality service. To address some of the issues, utilizing the existing nurses through an effective work schedule is the best alternative. However, there exists a problem of creating undesirable and non-stable nurse schedules for nurses' shift work. Thus, this research attempts to overcome these challenges by integrating components of a nurse scheduling and rescheduling problem which have normally been addressed separately in previous studies. However, when impromptu schedule changes are required and certain numbers of constraints need to be satisfied, there is a lack of flexibility element in most of scheduling and rescheduling approaches. By embedding the element, this gives a potential platform for enhancing the Evolutionary Algorithm (EA) which has been identified as the solution approach. Therefore, to minimize the constraint violations and make little but attentive changes to a postulated schedule during a disruption, an integrated model of EA with Cuckoo Search (CS) is proposed. A concept of restriction enzyme is adapted in the CS. A total of 11 EA model variants were constructed with three new parent selections, two new crossovers, and a crossover-based retrieval operator, that specifically are theoretical contributions. The proposed EA with Discovery Rate Tournament and Cuckoo Search Restriction Enzyme Point Crossover (DᵣT_CSREP) model emerges as the most effective in producing 100% feasible schedules with the minimum penalty value. Moreover, all tested disruptions were solved successfully through preretrieval and Cuckoo Search Restriction Enzyme Point Retrieval (CSREPᵣ) operators. Consequently, the EA model is able to fulfill nurses' preferences, offer fair on-call delegation, better quality of shift changes for retrieval, and comprehension on the two-way dependency between scheduling and rescheduling by examining the seriousness of disruptions

Studies in particle swarm optimization technique for global optimization.

Ph. D. University of KwaZulu-Natal, Durban 2013.Abstract available in the digital copy.Articles found within the main body of the thesis in the print version is found at the end of the thesis in the digital version