School Timetabling Optimisation Using Artificial Bee Colony Algorithm Based on a Virtual Searching Space Method

Although educational timetabling problems have been studied for decades, one instance of this, the school timetabling problem (STP), has not developed as quickly as examination timetabling and course timetabling problems due to its diversity and complexity. In addition, most STP research has only focused on the educators’ availabilities when studying the educator aspect, and the educators’ preferences and expertise have not been taken into consideration. To fill in this gap, this paper proposes a conceptual model for the school timetabling problem considering educators’ availabilities, preferences and expertise as a whole. Based on a common real-world school timetabling scenario, the artificial bee colony (ABC) algorithm is adapted to this study, as research shows its applicability in solving examination and course timetabling problems. A virtual search space for dealing with the large search space is introduced to the proposed model. The proposed approach is simulated with a large, randomly generated dataset. The experimental results demonstrate that the proposed approach is able to solve the STP and handle a large dataset in an ordinary computing hardware environment, which significantly reduces computational costs. Compared to the traditional constraint programming method, the proposed approach is more effective and can provide more satisfactory solutions by considering educators’ availabilities, preferences, and expertise levels.

School Timetabling Optimisation Using Artificial Bee Colony Algorithm Based on a Virtual Searching Space Method

Although educational timetabling problems have been studied for decades, one type, the STP, has not developed as quickly as the other two types due to its diversity and complexity. Also, most of the STP research has only focused on the educators’ availabilities when studying the educator aspect, and the educators’ preferences and expertise have not been taken into consideration. This paper proposes a conceptual model for the school timetabling problem considering educators’ availabilities, preferences and expertise as a whole, and chooses a common real-world school timetabling scenario to study. A mathematical model is presented. A Virtual search space for dealing with the large search space is introduced, and the artificial bee colony algorithm is adapted and applied to the proposed model. The proposed approach is simulated with a random-generated large dataset. The experimental results demonstrate that the proposed approach is able to solve the STP and handle a large dataset in an ordinary computer hardware environment, which significantly reduces computational costs. Compared to the traditional CP method, the proposed approach is more effective and can provide more satisfactory solutions in considering educators’ availabilities, preferences, and expertise levels.

A Mathematical Programming Model and Enhanced Simulated Annealing Algorithm for the School Timetabling Problem

Despite significant research efforts for School Timetabling Problem (STP) and other timetabling problems, an effective solution approach (model and algorithm) which provides boundless use and high quality solution has not been developed. Hence, this paper presents a novel solution approach for solving school timetabling problem which characterizes the problem-setting in the timetabling problem of the high school system in Nigeria. We developed a mixed integer linear programming model and meta-heuristic method - Enhanced Simulated Annealing (ESA) algorithm. Our method incorporates specific features of Simulated Annealing (SA) and Genetic Algorithms (GA) in order to solve the school timetabling problem. Both our solution approach and SA approach were implemented using Matrix Laboratory 8.6 software. In order to validate and demonstrate the performance of the developed solution approach, it was tested with the highly constrained school timetabling datasets provided by a Nigerian high school using constraints violation, simulation time and solution cost as evaluation metrics. Our developed solution approach is able to find optimal solution as it satisfied all the specified hard and soft constraints with average simulation time of 37.91 and 42.16 seconds and solution cost of 17.03 and 18.99, respectively, for JSS and SSS to the problem instance. A comparison with results obtained with SA approach shows that the developed solution approach produced optimal solution in smaller simulation time and solution cost, and has a great potential to solve school timetabling problems with satisfactory results. The developed ESA algorithm can be used for solving other related optimization problems.

A Hidden Markov Model Approach to the Problem of Heuristic Selection in Hyper-Heuristics with a Case Study in High School Timetabling Problems

Operations research is a well-established field that uses computational systems to support decisions in business and public life. Good solutions to operations research problems can make a large difference to the efficient running of businesses and organisations and so the field often searches for new methods to improve these solutions. The high school timetabling problem is an example of an operations research problem and is a challenging task which requires assigning events and resources to time slots subject to a set of constraints. In this article, a new sequence-based selection hyper-heuristic is presented that produces excellent results on a suite of high school timetabling problems. In this study, we present an easy-to-implement, easy-to-maintain, and effective sequence-based selection hyper-heuristic to solve high school timetabling problems using a benchmark of unified real-world instances collected from different countries. We show that with sequence-based methods, it is possible to discover new best known solutions for a number of the problems in the timetabling domain. Through this investigation, the usefulness of sequence-based selection hyper-heuristics has been demonstrated and the capability of these methods has been shown to exceed the state of the art.

SAT-Based Approaches for the General High School Timetabling Problem

High School Timetabling (HSTT) is a well known and widespread problem. It consists of coordinating resources (e.g. teachers, rooms), times, and events (e.g. lectures) with respect to various constraints. In this paper, I summarize the work I have done towards exploring the relationship between propositional logic and HSTT. This includes various modeling techniques in the form of maxSAT and bitvectors, data structures for local search algorithms, and the combination of maxSAT and metaheuristic algorithms. In addition, I discuss possible directions for future work as a part of a long-term research goal to combine complete and metaheuristic algorithms.