A matheuristic for customized multi-level multi-criteria university timetabling

Course timetables are the organizational foundation of a university’s educational program. While students and lecturers perceive timetable quality individually according to their preferences, there are also collective criteria derived normatively such as balanced workloads or idle time avoidance. A recent challenge and opportunity in curriculum-based timetabling consists of customizing timetables with respect to individual student preferences and with respect to integrating online courses as part of modern course programs or in reaction to flexibility requirements as posed in pandemic situations. Curricula consisting of (large) lectures and (small) tutorials further open the possibility for optimizing not only the lecture and tutorial plan for all students but also the assignments of individual students to tutorial slots. In this paper, we develop a multi-level planning process for university timetabling: On the tactical level, a lecture and tutorial plan is determined for a set of study programs; on the operational level, individual timetables are generated for each student interlacing the lecture plan through a selection of tutorials from the tutorial plan favoring individual preferences. We utilize this mathematical-programming-based planning process as part of a matheuristic which implements a genetic algorithm in order to improve lecture plans, tutorial plans, and individual timetables so as to find an overall university program with well-balanced timetable performance criteria. Since the evaluation of the fitness function amounts to invoking the entire planning process, we additionally provide a proxy in the form of an artificial neural network metamodel. Computational results exhibit the procedure’s capability of generating high quality schedules

A modified migrating bird optimization for university course timetabling problem

University course timetabling problem is a dilemma which educational institutions are facing due to various demands to be achieved in limited resources. Migrating bird optimization (MBO) algorithm is a new meta-heuristic algorithm which is inspired by flying formation of migrating birds. It has been applied successfully in tackling quadratic assignment problem and credit cards fraud detection problem. However, it was reported that MBO will get stuck in local optima easily. Therefore, a modified migrating bird optimization algorithm is proposed to solve post enrolment-based course timetabling. An improved neighbourhood sharing mechanism is used with the aim of escaping from local optima. Besides that, iterated local search is selected to be hybridized with the migrating bird optimization in order to further enhance its exploitation ability. The proposed method was tested using Socha’s benchmark datasets. The experimental results show that the proposed method outperformed the basic MBO and it is capable of producing comparable results as compared with existing methods that have been presented in literature. Indeed, the proposed method is capable of addressing university course timetabling problem and promising results were obtained

Local search methods for the post enrolment-based course timetabling problem

The work presented in this thesis concerns the problem of post enrolment-based course time-tabling. The motivation for this is the increasing importance of the automation of timetabling due to the growth in popularity of Higher Education in recent years. There were 464,910 accepted applicants to universities in the United Kingdom in 2012 which is a 12% rise in five years. This will inevitably lead to an expansion in the number of courses, modules and teachers. As a result, the ability to manually construct timetables has become increasingly impractical. A two-stage approach is investigated that aims to use heuristic and metaheuristic approaches to obtain a satisfactory timetable that suits the needs of the staff and students at educational institutions. The first stage consists of using selection heuristics to construct an initial solution. Two approaches that then attempt to find feasibility are presented. The first applies a tabu search algorithm with a number of neighbourhood operators that navigate the search space for feasible solutions. The second approach implements a PartialCol algorithm. The second stage aims to improve the solution quality by minimising the number of soft constraint violations. The feasibility ratio could be an indicator of the connectivity of the search space, so methods of increasing the feasibility ratio are presented. If the feasibility ratio can be increased then the number of soft constraint violations would be expected to decrease. These techniques were applied to the 24 instances provided for track two of the International Timetabling Competition 2007. The conclusions of the experimentation and investigative processes show that the PartialCol algorithm was more successful, in terms of finding feasible solutions, than the method that employs the neighbourhood operators. However, improvements to the soft constraint penalty were achieved using these neighbourhood operators

Analysing the effects of solution space connectivity with an effective metaheuristic for the course timetabling problem

This paper provides a mathematical treatment of the NP-hard post enrolment-based course timetabling problem and presents a powerful two-stage metaheuristic-based algorithm to approximately solve it. We focus particularly on the issue of solution space connectivity and demonstrate that when this is increased via specialised neighbourhood operators, the quality of solutions achieved is generally enhanced. Across a well-known suite of benchmark problem instances, our proposed algorithm is shown to produce results that are superior to all other methods appearing in the literature; however, we also make note of those instances where our algorithm struggles in comparison to others and offer evidence as to why

Grammatical evolution hyper-heuristic for combinatorial optimization problems

Designing generic problem solvers that perform well across a diverse set of problems is a challenging task. In this work, we propose a hyper-heuristic framework to automatically generate an effective and generic solution method by utilizing grammatical evolution. In the proposed framework, grammatical evolution is used as an online solver builder, which takes several heuristic components (e.g., different acceptance criteria and different neighborhood structures) as inputs and evolves templates of perturbation heuristics. The evolved templates are improvement heuristics, which represent a complete search method to solve the problem at hand. To test the generality and the performance of the proposed method, we consider two well-known combinatorial optimization problems: exam timetabling (Carter and ITC 2007 instances) and the capacitated vehicle routing problem (Christofides and Golden instances). We demonstrate that the proposed method is competitive, if not superior, when compared to state-of-the-art hyper-heuristics, as well as bespoke methods for these different problem domains. In order to further improve the performance of the proposed framework we utilize an adaptive memory mechanism, which contains a collection of both high quality and diverse solutions and is updated during the problem solving process. Experimental results show that the grammatical evolution hyper-heuristic, with an adaptive memory, performs better than the grammatical evolution hyper-heuristic without a memory. The improved framework also outperforms some bespoke methodologies, which have reported best known results for some instances in both problem domains

A time-dependent metaheuristic algorithm for post enrolment-based course timetabling

A metaheuristic-based algorithm is presented for the post enrolment-based course timetabling problem used in track-2 of the Second International Timetabling Competition (ITC2007). The featured algorithm operates in three distinct stages—a constructive phase followed by two separate phases of simulated annealing—and is time dependent, due to the fact that various run-time parameters are calculated automatically according to the amount of computation time available. Overall, the method produces results in line with the official finalists to the timetabling competition, though experiments show that this algorithm also seems to find certain instances more difficult to solve than others. A number of reasons for this latter feature are discussed