A study of heuristic combinations for hyper-heuristic systems for the uncapacitated examination timetabling problem

Research in the domain of examination timetabling is moving towards developing methods that generalise well over a range of problems. This is achieved by implementing hyper-heuristic systems to find the best heuristic or heuristic combination to allocate examinations when constructing a timetable for a problem. Heuristic combinations usually take the form of a list of low-level heuristics that are applied sequentially. This study proposes an alternative representation for heuristic combinations, namely, a hierarchical combination of heuristics. Furthermore, the heuristics in each combination are applied simultaneously rather than sequentially. The study also introduces a new low-level heuristic, namely, highest cost. A set of heuristic combinations of this format have been tested on the 13 Carter benchmarks. The quality of the examination timetables induced using these combinations are comparable to, and in some cases better than, those produced by hyper-heuristic systems combining and applying heuristic combinations sequentially.     

Automated generation of constructive ordering heuristics for educational timetabling

Annals of Operations Research - Construction heuristics play an important role in solving combinatorial optimization problems. These heuristics are usually used to create an initial solution to the...     

Memetic techniques for examination timetabling

In this paper, we investigate the effectiveness of combining the main components of the memetic algorithms (MAs) on the quality of solutions produced for Uncapacitated Examination Timetabling Problem (UETP). These components are recombination, randomness, and neighbourhood structures. The Harmony Search Algorithm (HSA), which is a variation of MA, is used to perform different combinations of these components. It has three main components: Memory Consideration using the recombination, Random Consideration using the randomness and Pitch Adjustment using the neighbourhood structures (or local search). The combinations among MA components are evaluated using 17 different scenarios each of which reflects a combination of one, two or three components. The results show that the system that combines the three components (recombination, randomness, and neighbourhood structures) provides the best results. Furthermore, the best results obtained from the convergence scenarios were compared with 22 other methods that used a de facto dataset defined by Carter et al. (in Journal of the Operational Research Society 74:373–383, 1996) for UETP. The results exceed those produced by the previous methods in 2 out of 12 datasets.     

Monte Carlo hyper-heuristics for examination timetabling

Automating the neighbourhood selection process in an iterative approach that uses multiple heuristics is not a trivial task. Hyper-heuristics are search methodologies that not only aim to provide a general framework for solving problem instances at different difficulty levels in a given domain, but a key goal is also to extend the level of generality so that different problems from different domains can also be solved. Indeed, a major challenge is to explore how the heuristic design process might be automated. Almost all existing iterative selection hyper-heuristics performing single point search contain two successive stages; heuristic selection and move acceptance. Different operators can be used in either of the stages. Recent studies explore ways of introducing learning mechanisms into the search process for improving the performance of hyper-heuristics. In this study, a broad empirical analysis is performed comparing Monte Carlo based hyper-heuristics for solving capacitated examination timetabling problems. One of these hyper-heuristics is an approach that overlaps two stages and presents them in a single algorithmic body. A learning heuristic selection method (L) operates in harmony with a simulated annealing move acceptance method using reheating (SA) based on some shared variables. Yet, the heuristic selection and move acceptance methods can be separated as the proposed approach respects the common selection hyper-heuristic framework. The experimental results show that simulated annealing with reheating as a hyper-heuristic move acceptance method has significant potential. On the other hand, the learning hyper-heuristic using simulated annealing with reheating move acceptance (L?CSA) performs poorly due to certain weaknesses, such as the choice of rewarding mechanism and the evaluation of utility values for heuristic selection as compared to some other hyper-heuristics in examination timetabling. Trials with other heuristic selection methods confirm that the best alternative for the simulated annealing with reheating move acceptance for examination timetabling is a previously proposed strategy known as the choice function.     

A new model for automated examination timetabling

Automated examination timetabling has been addressed by a wide variety of methodologies and techniques over the last ten years or so. Many of the methods in this broad range of approaches have been evaluated on a collection of benchmark instances provided at the University of Toronto in 1996. Whilst the existence of these datasets has provided an invaluable resource for research into examination timetabling, the instances have significant limitations in terms of their relevance to real-world examination timetabling in modern universities. This paper presents a detailed model which draws upon experiences of implementing examination timetabling systems in universities in Europe, Australasia and America.     

Adaptive automated construction of hybrid heuristics for exam timetabling and graph colouring problems

In this paper, we present a random iterative graph based hyper-heuristic to produce a collection of heuristic sequences to construct solutions of different quality. These heuristic sequences can be seen as dynamic hybridisations of different graph colouring heuristics that construct solutions step by step. Based on these sequences, we statistically analyse the way in which graph colouring heuristics are automatically hybridised. This, to our knowledge, represents a new direction in hyper-heuristic research. It is observed that spending the search effort on hybridising Largest Weighted Degree with Saturation Degree at the early stage of solution construction tends to generate high quality solutions. Based on these observations, an iterative hybrid approach is developed to adaptively hybridise these two graph colouring heuristics at different stages of solution construction. The overall aim here is to automate the heuristic design process, which draws upon an emerging research theme on developing computer methods to design and adapt heuristics automatically. Experimental results on benchmark exam timetabling and graph colouring problems demonstrate the effectiveness and generality of this adaptive hybrid approach compared with previous methods on automatically generating and adapting heuristics. Indeed, we also show that the approach is competitive with the state of the art human produced methods.     

Evolving timetabling heuristics using a grammar-based genetic programming hyper-heuristic framework

This paper introduces a Grammar-based Genetic Programming Hyper-Heuristic framework (GPHH) for evolving constructive heuristics for timetabling. In this application GP is used as an online learning method which evolves heuristics while solving the problem. In other words, the system keeps on evolving heuristics for a problem instance until a good solution is found. The framework is tested on some of the most widely used benchmarks in the field of exam timetabling and compared with the best state-of-the-art approaches. Results show that the framework is very competitive with other constructive techniques, and did outperform other hyper-heuristic frameworks on many occasions.     

Evolving hyper-heuristics for the uncapacitated examination timetabling problem

This paper reports on the use of an evolutionary algorithm (EA) to search a space of heuristic combinations for the uncapacitated examination timetabling problem. The representation used by an EA has an effect on the difficulty of the search and hence the overall success of the system. The paper examines three different representations of heuristic combinations for this problem and compares their performance on a set of benchmark problems for the uncapacitated examination timetabling problem. The study has revealed that certain representations do result in a better performance and generalization of the hyper-heuristic. An EA-based hyper-heuristic combining the use of all three representations (CEA) was implemented and found to generalize better than the EA using each of the representations separately.     

Variants of simulated annealing for the examination timetabling problem

This paper is concerned with the use of simulated annealing in the solution of the multi-objective examination timetabling problem. The solution method proposed optimizes groups of objectives in different phases. Some decisions from earlier phases may be altered later as long as the solution quality with respect to earlier phases does not deteriorate. However, such limitations may disconnect the solution space, thereby causing optimal or near-optimal solutions to be missed. Three variants of our basic simulated annealing implementation which are designed to overcome this problem are proposed and compared using real university data as well as artificial data sets. The underlying principles and conclusions stemming from the use of this method are generally applicable to many other multi-objective type problems.     

Extended clique initialisation in examination timetabling

Many examination timetabling procedures employ a phased approach in which the first phase is often the allocation of a large set of mutually conflicting examinations which form a clique in the associated problem graph. The usual practice is to identify a single maximum clique, often quite arbitrarily, in this first phase. We show that in typical examination timetabling problems, unlike random graphs, there are often many alternative maximum cliques, and even larger dense subsets of nodes that are almost cliques. A number of methods are proposed for extending the scope of the clique initialisation to include a larger subset of examinations by considering sub-maximum cliques and/or quasi-cliques.     

A multiobjective framework for heavily constrained examination timetabling problems

University examination timetabling is a challenging set partitioning problem that comes in many variations, and real world applications usually carry multiple constraints and require the simultaneous optimization of several (often conflicting) objectives. This paper presents a multiobjective framework capable of solving heavily constrained timetabling problems. In this prototype study, we focus on the two objectives: minimizing timetable length while simultaneously optimizing the spread of examinations for individual students. Candidate solutions are presented to a multiobjective memetic algorithm as orderings of examinations, and a greedy algorithm is used to construct violation free timetables from permutation sequences of exams. The role of the multiobjective algorithm is to iteratively improve a population of orderings, with respect to the given objectives, using various mutation and reordering heuristics.     

A great deluge algorithm for a real-world examination timetabling problem

The examination timetabling problem involves assigning exams to a specific or limited number of timeslots and rooms with the aim of satisfying all hard constraints (without compromise) and satisfying the soft constraints as far as possible. Most of the techniques reported in the literature have been applied to simplified examination benchmark data sets. In this paper, we bridge the gap between research and practice by investigating a problem taken from the real world. This paper introduces a modified and extended great deluge algorithm (GDA) for the examination timetabling problem that uses a single, easy to understand parameter. We investigate different initial solutions, which are used as a starting point for the GDA, as well as altering the number of iterations. In addition, we carry out statistical analyses to compare the results when using these different parameters. The proposed methodology is able to produce good quality solutions when compared with the solution currently produced by the host organisation, generated in our previous work and from the original GDA.     

A tabu-based large neighbourhood search methodology for the capacitated examination timetabling problem

Neighbourhood search algorithms are often the most effective known approaches for solving partitioning problems. In this paper, we consider the capacitated examination timetabling problem as a partitioning problem and present an examination timetabling methodology that is based upon the large neighbourhood search algorithm that was originally developed by Ahuja and Orlin. It is based on searching a very large neighbourhood of solutions using graph theoretical algorithms implemented on a so-called improvement graph. In this paper, we present a tabu-based large neighbourhood search, in which the improvement moves are kept in a tabu list for a certain number of iterations. We have drawn upon Ahuja–Orlin's methodology incorporated with tabu lists and have developed an effective examination timetabling solution scheme which we evaluated on capacitated problem benchmark data sets from the literature. The capacitated problem includes the consideration of room capacities and, as such, represents an issue that is of particular importance in real-world situations. We compare our approach against other methodologies that have appeared in the literature over recent years. Our computational experiments indicate that the approach we describe produces the best known results on a number of these benchmark problems.     

Universiti Malaysia Pahang examination timetabling problem: scheduling invigilators

This paper presents a real-world examination timetabling problem from Universiti Malaysia Pahang (UMP), Malaysia. The problem involves assigning invigilators to examination rooms. This problem has received less attention than the examination timetabling problem from the research community partly because no data sets are available in the literature. In modelling, and solving, this problem we assume that there is already an examination timetable in place (this was the subject of our previous work) and the task is to assign invigilators to that timetable. The contributions of this paper are to formally define the invigilator scheduling problem and to present a constructive algorithm that is able to produce good quality solutions that are superior to the solutions produced when using the university's current software. We also include additional constraints taking into account the comments made by the invigilators, which the current system fails to capture. The model we present, we believe, accurately reflects the real-world problem, capturing various aspects of the problem that have not been presented before in the scientific literature. Moreover, the proposed approach adheres to all hard constraints, which the university's current system fails to do.     

Linear combinations of overlapping variance estimators for simulation

We estimate the variance parameter of a stationary simulation-generated process using a linear combination of overlapping standardized time series (STS) area variance estimators based on different batch sizes. We establish the linear-combination estimator's asymptotic distribution, presenting analytical and simulation-based results exemplifying its potential for improvements in accuracy and computational efficiency.     

Linear combinations from power domains

The well-known concept of power domains defined via subsets of a finite set S of weighted points in R ^d is exploited to obtain various linear combinations among the points in S. This generalizes a result of Sibson who considered the special case of singleton subsets and unweighted points.     

Linear combinations of hypersurfaces in hyperbolic space

In this article we introduce and investigate linear combinations of hypersurfaces in hyperbolic space. For this purpose we use some linear structure in the space of horospheres.     

一类多商品设施选址问题的基于线性松弛解的启发式方法

多商品设施选址问题是众多设施选址问题中一类重要而困难的问题.在这一问题中,顾客的需求可能包含不止一种商品.对于大规模问题,成熟的商业求解器往往不能在满意的时间内找到高质量的可行解.研究了无容量限制的单货源多商品设施选址问题的一般形式,并给出了应用于此类问题的两个启发式方法.这两个方法基于原选址问题的线性规划松弛问题的最优解,分别通过求解紧问题和邻域搜索的方式给出了原问题的一个可行上界.理论分析指出所提方法可以实施于任意可行问题的实例.数值结果表明所提方法可以显著地提高求解器求解此类设施选址问题的求解效率.