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.     

Effective learning hyper-heuristics for the course timetabling problem

Course timetabling is an important and recurring administrative activity in most educational institutions. This article combines a general modeling methodology with effective learning hyper-heuristics to solve this problem. The proposed hyper-heuristics are based on an iterated local search procedure that autonomously combines a set of move operators. Two types of learning for operator selection are contrasted: a static (offline) approach, with a clear distinction between training and execution phases; and a dynamic approach that learns on the fly. The resulting algorithms are tested over the set of real-world instances collected by the first and second International Timetabling competitions. The dynamic scheme statistically outperforms the static counterpart, and produces competitive results when compared to the state-of-the-art, even producing a new best-known solution. Importantly, our study illustrates that algorithms with increased autonomy and generality can outperform human designed problem-specific algorithms.     

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.     

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.     

Linear combinations of heuristics for examination timetabling

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In this paper, we explore this direction and introduce a new strategy of using linear combinations of heuristics for weighted graphs which model the timetabling problems under consideration. The weights of the heuristic combinations define specific roles that each simple heuristic contributes to the process of ordering vertices. We include specific explanations for the design of our strategy and present the experimental results on a set of benchmark real world examination timetabling problem instances. New best results for several instances have been obtained using this method when compared with other constructive methods applied to this benchmark dataset.     

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.     

Monte Carlo optimization

Monte Carlo optimization techniques for solving mathematical programming problems have been the focus of some debate. This note reviews the debate and puts these stochastic methods in their proper perspective.     

Population Monte Carlo

Importance sampling methods can be iterated like MCMC algorithms, while being more robust against dependence and starting values. The population Monte Carlo principle consists of iterated generations of importance samples, with importance functions depending on the previously generated importance samples. The advantage over MCMC algorithms is that the scheme is unbiased at any iteration and can thus be stopped at any time, while iterations improve the performances of the importance function, thus leading to an adaptive importance sampling. We illustrate this method on a mixture example with multiscale importance functions. A second example reanalyzes the ion channel model using an importance sampling scheme based on a hidden Markov representation, and compares population Monte Carlo with a corresponding MCMC algorithm.     

Evolutionary Monte Carlo Methods for Clustering

The problem of clustering a group of observations according to some objective function (e.g., K-means clustering, variable selection) or a density (e.g., posterior from a Dirichlet process mixture model prior) can be cast in the framework of Monte Carlo sampling for cluster indicators. We propose a new method called the evolutionary Monte Carlo clustering (EMCC) algorithm, in which three new “crossover moves,” based on swapping and reshuffling sub cluster intersections, are proposed. We apply the EMCC algorithm to several clustering problems including Bernoulli clustering, biological sequence motif clustering, BIC based variable selection, and mixture of normals clustering. We compare EMCC's performance both as a sampler and as a stochastic optimizer with Gibbs sampling, “split-merge” Metropolis–Hastings algorithms, K-means clustering, and the MCLUST algorithm.     

Useful Monte Carlo optimization

This contribution to the debate on Monte Carlo optimization methods shows that there exist techniques that may be useful in many technical applications.     

Unbiased multi-index Monte Carlo

We introduce a new class of Monte Carlo-based approximations of expectations of random variables such that their laws are only available via certain discretizations. Sampling from the discretized versions of these laws can typically introduce a bias. In this paper, we show how to remove that bias, by introducing a new version of multi-index Monte Carlo (MIMC) that has the added advantage of reducing the computational effort, relative to i.i.d. sampling from the most precise discretization, for a given level of error. We cover extensions of results regarding variance and optimality criteria for the new approach. We apply the methodology to the problem of computing an unbiased mollified version of the solution of a partial differential equation with random coefficients. A second application concerns the Bayesian inference (the smoothing problem) of an infinite-dimensional signal modeled by the solution of a stochastic partial differential equation that is observed on a discrete space grid and at discrete times. Both applications are complemented by numerical simulations.     

Improved Diffusion Monte Carlo

We propose a modification, based on the RESTART (repetitive simulation trials after reaching thresholds) and DPR (dynamics probability redistribution) rare event simulation algorithms, of the standard diffusion Monte Carlo (DMC) algorithm. The new algorithm has a lower variance per workload, regardless of the regime considered. In particular, it makes it feasible to use DMC in situations where the “naïve” generalization of the standard algorithm would be impractical due to an exponential explosion of its variance. We numerically demonstrate the effectiveness of the new algorithm on a standard rare event simulation problem (probability of an unlikely transition in a Lennard‐Jones cluster), as well as a high‐frequency data assimilation problem. © 2014 Wiley Periodicals, Inc.     

Partition-Weighted Monte Carlo Estimation

Although various efficient and sophisticated Markov chain Monte Carlo sampling methods have been developed during the last decade, the sample mean is still a dominant in computing Bayesian posterior quantities. The sample mean is simple, but may not be efficient. The weighted sample mean is a natural generalization of the sample mean. In this paper, a new weighted sample mean is proposed by partitioning the support of posterior distribution, so that the same weight is assigned to observations that belong to the same subset in the partition. A novel application of this new weighted sample mean in computing ratios of normalizing constants and necessary theory are provided. Illustrative examples are given to demonstrate the methodology.