A hybrid genetic algorithm and tabu search approach for post enrolment course timetabling

Copyright @ Springer Science + Business Media. All rights reserved.The post enrolment course timetabling problem (PECTP) is one type of university course timetabling problems, in which a set of events has to be scheduled in time slots and located in suitable rooms according to the student enrolment data. The PECTP is an NP-hard combinatorial optimisation problem and hence is very difficult to solve to optimality. This paper proposes a hybrid approach to solve the PECTP in two phases. In the first phase, a guided search genetic algorithm is applied to solve the PECTP. This guided search genetic algorithm, integrates a guided search strategy and some local search techniques, where the guided search strategy uses a data structure that stores useful information extracted from previous good individuals to guide the generation of offspring into the population and the local search techniques are used to improve the quality of individuals. In the second phase, a tabu search heuristic is further used on the best solution obtained by the first phase to improve the optimality of the solution if possible. The proposed hybrid approach is tested on a set of benchmark PECTPs taken from the international timetabling competition in comparison with a set of state-of-the-art methods from the literature. The experimental results show that the proposed hybrid approach is able to produce promising results for the test PECTPs.This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant EP/E060722/01 and Grant EP/E060722/02

Performance Analyses of Graph Heuristics and Selected Trajectory Metaheuristics on Examination Timetable Problem

Examination timetabling problem is hard to solve due to its NP-hard nature, with a large number of constraints having to be accommodated. To deal with the problem effectually, frequently heuristics are used for constructing feasible examination timetable while meta-heuristics are applied for improving the solution quality. This paper presents the performances of graph heuristics and major trajectory metaheuristics or S-metaheuristics for addressing both capacitated and un-capacitated examination timetabling problem. For constructing the feasible solution, six graph heuristics are used. They are largest degree (LD), largest weighted degree (LWD), largest enrolment degree (LE), and three hybrid heuristic with saturation degree (SD) such as SD-LD, SD-LE, and SD-LWD. Five trajectory algorithms comprising of tabu search (TS), simulated annealing (SA), late acceptance hill climbing (LAHC), great deluge algorithm (GDA), and variable neighborhood search (VNS) are employed for improving the solution quality. Experiments have been tested on several instances of un-capacitated and capacitated benchmark datasets, which are Toronto and ITC2007 dataset respectively. Experimental results indicate that, in terms of construction of solution of datasets, hybridizing of SD produces the best initial solutions. The study also reveals that, during improvement, GDA, SA, and LAHC can produce better quality solutions compared to TS and VNS for solving both benchmark examination timetabling datasets

Design, Engineering, and Experimental Analysis of a Simulated Annealing Approach to the Post-Enrolment Course Timetabling Problem

The post-enrolment course timetabling (PE-CTT) is one of the most studied timetabling problems, for which many instances and results are available. In this work we design a metaheuristic approach based on Simulated Annealing to solve the PE-CTT. We consider all the different variants of the problem that have been proposed in the literature and we perform a comprehensive experimental analysis on all the public instances available. The outcome is that our solver, properly engineered and tuned, performs very well on all cases, providing the new best known results on many instances and state-of-the-art values for the others

Automatic Class Timetable Generation using a Hybrid Genetic and Tabu Algorithm

Timetable generation is a combinatorial optimization problem. Meta Heuristic methods and Evolutionary Algorithms have given the best results when it comes to solving the problem of timetable generation. In our paper the problem of timetable generation for the Computer Science and Engineering Dept. of BMS College of Engineering is solved with the help of Genetic Algorithm and Tabu Search which belong to the class of Evolutionary Algorithms and Meta – Heuristics respectively. Genetic Algorithms help in finding multiple optimal solutions in one iteration but they can get stuck at local optima. This can be avoided by using Tabu Search procedure. DOI: 10.17762/ijritcc2321-8169.150510

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

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

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

Search methodologies for examination timetabling

Working with examination timetabling is an extremely challenging task due to the difficulty of finding good quality solutions. Most of the studies in this area rely on improvement techniques to enhance the solution quality after generating an initial solution. Nevertheless, the initial solution generation itself can provide good solution quality even though the ordering strategies often using graph colouring heuristics, are typically quite simple. Indeed, there are examples where some of the produced solutions are better than the ones produced in the literature with an improvement phase. This research concentrates on constructive approaches which are based on squeaky wheel optimisation i.e. the focus is upon finding difficult examinations in their assignment and changing their position in a heuristic ordering. In the first phase, the work is focused on the squeaky wheel optimisation approach where the ordering is permutated in a block of examinations in order to find the best ordering. Heuristics are alternated during the search as each heuristic produces a different value of a heuristic modifier. This strategy could improve the solution quality when a stochastic process is incorporated. Motivated by this first phase, a squeaky wheel optimisation concept is then combined with graph colouring heuristics in a linear form with weights aggregation. The aim is to generalise the constructive approach using information from given heuristics for finding difficult examinations and it works well across tested problems. Each parameter is invoked with a normalisation strategy in order to generalise the specific problem data. In the next phase, the information obtained from the process of building an infeasible timetable is used. The examinations that caused infeasibility are given attention because, logically, they are hard to place in the timetable and so they are treated first. In the adaptive decomposition strategy, the aim is to automatically divide examinations into difficult and easy sets so as to give attention to difficult examinations. Within the easy set, a subset called the boundary set is used to accommodate shuffling strategies to change the given ordering of examinations. Consequently, the graph colouring heuristics are employed on those constructive approaches and it is shown that dynamic ordering is an effective way to permute the ordering. The next research chapter concentrates on the improvement approach where variable neighbourhood search with great deluge algorithm is investigated using various neighbourhood orderings and initialisation strategies. The approach incorporated with a repair mechanism in order to amend some of infeasible assignment and at the same time aiming to improve the solution quality

Educational timetabling: Problems, benchmarks, and state-of-the-art results

We propose a survey of the research contributions on the field of Educational Timetabling with a specific focus on “standard” formulations and the corresponding benchmark instances. We identify six of such formulations and we discuss their features, pointing out their relevance and usability. Other available formulations and datasets are also reviewed and briefly discussed. Subsequently, we report the main state-of-the-art results on the selected benchmarks, in terms of solution quality (upper and lower bounds), search techniques, running times, and other side settings