Iterated local search using an add and delete hyper-heuristic for university course timetabling
Graphical abstract
Introduction
Hyper-heuristics are (meta-)heuristics that choose or generate a set of low level (meta-)heuristics in an attempt to solve difficult search and optimization problems [1], [2]. Heuristics can be used to search the solution space directly or construct a solution based on a sequence of moves. Hyper-heuristics aim to replace bespoke approaches by more general methodologies with the goal of reducing the expertise required to construct individual heuristics [3]. In most of the previous studies on hyper-heuristics, low-level heuristics are uniform, i.e. they are either constructive or perturbative (improvement) heuristics [4].
Educational timetabling problems are common and recurring real-world constraint optimization problems which are known to be NP-hard [5], [6], [7]. An educational timetabling problem requires scheduling of a set of events using limited resources subject to a set of constraints. There are a range of educational timetabling problems, such as examination timetabling and high school timetabling. This study focuses on the university course time-tabling problem, which can be further categorized as either post-enrollment problems, in which the student enrollment is available before the timetabling process, and curriculum-based problems in which the curricula of the students are known, but not the student enrollment [8]. There are two main types of constraints in a timetabling problem: hard and soft constraints. The hard constraints have to be satisfied in order to obtain a feasible solution, while violations of soft constraints are allowed, since they represent preferences. It is still the case at some universities that timetables are constructed by hand. Considering the inherent difficulty of generating high-quality feasible timetables which violate few soft constraints, it is usually desirable to automate timetable construction to improve upon solutions obtained by human experts [9]. However, automation of timetabling is not an easy task, since designing an automated method frequently requires a deep knowledge of the problem itself as well as the particular characteristics of the instance to be solved. This knowledge, in most cases, is not readily available to the typical researcher/end-user.
In this study, we describe an iterated local search (ILS) algorithm hybridized with a hyper-heuristic that generates heuristics based on add–delete operations to solve examination and university course timetabling problems. Re-usability, modularity and flexibility are some of the key features of the proposed approach. To evaluate the generality of the generation hyper-heuristic, it is tested on a range of problem instances across two different domains; namely, post-enrollment university course timetabling and curriculum-based university course timetabling, without modification of the underlying solution framework.
Although the problem domains we investigate are timetabling problems, each domain exhibits differing characteristics, particularly with respect to the complexity of the real-world constraints. This is the main reason why a recent competition has used two tracks. The International Timetabling Competition series was organized to create a common ground for the cross-fertilization of ideas, bridging the gap between theory and practice and creating a better understanding between researchers and practitioners in this field [8]. The second competition in the series (ITC2007) was on educational timetabling, containing an examination timetabling track and two separate tracks for post-enrollment and curriculum-based university course timetabling [8]. We have investigated the performance of the proposed approach on the last instances. The results show that our approach is promising.
This paper is organized as follows. Section 2 provides an overview of educational timetabling problems, particularly university course timetabling. This section also discusses solution methodologies. Section 3 discusses the specifics of the solution methodology including the relevant data structures and the add–delete representation. Section 4 summarizes the experimental results. Finally, Section 5 presents the conclusions and future work.
Section snippets
Hyper-heuristics
The term “hyper-heuristic” is relatively new, having first appeared in a technical report by Denzinger et al. [62] as a strategy to combine artificial intelligence methods. The un-hyphenated version of the term initially appeared in Cowling et al. [3] describing hyper-heuristics as heuristics to choose heuristics in the context of combinatorial optimization. However, the idea of automating the design of heuristic methods is not new and can be traced back to the 1960s in works such as Fisher et
Solution approach
Iterated local search (ILS) is a relatively simple methodology that has been successful in a variety of domains. It operates by iteratively alternating between applying a move operator to an incumbent solution and performing local search on the perturbed solution. This search principle has been rediscovered multiple times within different research communities and given different names [14]. The term iterated local search was proposed in Lourenço et al. [52]. In this study, we describe an ILS
Computational results
In this section, we present the results of the application of our approach to the ITC2007 benchmark.
Conclusions and future work
This study describes a novel generative hyper-heuristic entitled ‘add–delete Lists’ and details their application across two different problem domains that is Tracks 2 and 3 of the 2007 International Timetabling Competition. An Add–Delete list is a ‘ruin-and-recreate’ sequence which is applied to a solution representation.
The timetabling domain-description used here employs a layer of generality called Methodology of Design. This layer represents problem-specifics as a collection of generic
Acknowledgements
This work was supported by Consejo Nacional de Ciencia y Tecnología (CONACYT) México, the Engineering and Physical Sciences Research Council (EPSRC) Grant GR/S70197/01 and the University of Stirling UK.
Jorge A. Soria-Alcaraz PhD in Computer Science. His research interest and thesis include meta- and hyper-heuristics methodologies, Autonomous Search and Heuristic Optimization applied to timetabling problems. Dr Jorge Soria has published several papers in important journals and conferences in his field.
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2020, Alexandria Engineering JournalCitation Excerpt :This algorithm illustrated that the quality of the obtained response has improved. Soria-Alcaraz et al. [10] presented a locally based algorithm, in accordance with an iterative search, where, the UCTP is subject to two general conditions. In their assessments the two sets of hard and soft constraints are of concern.
Jorge A. Soria-Alcaraz PhD in Computer Science. His research interest and thesis include meta- and hyper-heuristics methodologies, Autonomous Search and Heuristic Optimization applied to timetabling problems. Dr Jorge Soria has published several papers in important journals and conferences in his field.
Dr Ender Özcan is a lecturer with the Automated Scheduling, Optimisation and Planning (ASAP) research group in the School of Computer Science at University of Nottingham. Before being appointed to the EPSRC funded LANCS initiative (2008), he worked at Yeditepe University (1998–2008) and served as Deputy Head of the Computer Engineering Department (2004–2007). His research focuses on adaptive decision support systems, (hyper/meta)heuristics (embedding data science techniques) and their applications to real-world problems. He is Deputy Director of EPSRC's “A National Taught Course Centre in Operational Research”. He is Associate Editor of Journal of Scheduling and Journal of Applied Metaheuristic Computing.
Jerry Swan Before entering academia, Dr Jerry Swan spent nearly 20 years in industry as a systems architect and software company owner. His research includes meta- and hyper-heuristics, symbolic computation and machine learning. He has published more than 50 papers in international journals and conferences. Jerry has lectured and presented his research worldwide, and has been running international workshops and tutorials on the automated design of metaheuristics since 2011.
Professor Graham Kendall is a Vice-Provost at the University of Nottingham Malaysia Campus (UNMC). He is also the Chief Executive Officer of MyResearch Sdn Bhd. The company enables companies to invest in Research and Development in a tax efficient way. Graham is a Fellow of the British Computer Society (FBCS) and a Fellow of the Operational Research Society (FORS). He has published over 200 peer reviewed papers, including over 70 ISI journal papers. He has edited 11 books and authored almost 20 book chapters. He is currently an Associate Editor of ten journals and the editor in chief of the IEEE Transactions on Computational Intelligence and AI in Games. As a Professor of Computer Science at the University of Nottingham he is a member of the Automated Scheduling, Planning and Optimization Group (ASAP) in the School of Computer Science. His research interests include Operations Research, Scheduling, Logistics, Vehicle Routing, Meta- and Hyper-heuristics, Evolutionary Computation and Games. Before becoming an academic Graham worked in the IT industry for almost 20 years.