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

Offline Learning for Sequence-based Selection Hyper-heuristics

This thesis is concerned with finding solutions to discrete NP-hard problems. Such problems occur in a wide range of real-world applications, such as bin packing, industrial flow shop problems, determining Boolean satisfiability, the traveling salesman and vehicle routing problems, course timetabling, personnel scheduling, and the optimisation of water distribution networks. They are typically represented as optimisation problems where the goal is to find a ``best'' solution from a given space of feasible solutions. As no known polynomial-time algorithmic solution exists for NP-hard problems, they are usually solved by applying heuristic methods. Selection hyper-heuristics are algorithms that organise and combine a number of individual low level heuristics into a higher level framework with the objective of improving optimisation performance. Many selection hyper-heuristics employ learning algorithms in order to enhance optimisation performance by improving the selection of single heuristics, and this learning may be classified as either online or offline. This thesis presents a novel statistical framework for the offline learning of subsequences of low level heuristics in order to improve the optimisation performance of sequenced-based selection hyper-heuristics. A selection hyper-heuristic is used to optimise the HyFlex set of discrete benchmark problems. The resulting sequences of low level heuristic selections and objective function values are used to generate an offline learning database of heuristic selections. The sequences in the database are broken down into subsequences and the mathematical concept of a logarithmic return is used to discriminate between ``effective'' subsequences, that tend to lead to improvements in optimisation performance, and ``disruptive'' subsequences that tend to lead to worsening performance. Effective subsequences are used to improve hyper-heuristics performance directly, by embedding them in a simple hyper-heuristic design, and indirectly as the inputs to an appropriate hyper-heuristic learning algorithm. Furthermore, by comparing effective subsequences across different problem domains it is possible to investigate the potential for cross-domain learning. The results presented here demonstrates that the use of well chosen subsequences of heuristics can lead to small, but statistically significant, improvements in optimisation performance

Non-linear great deluge with learning mechanism for solving the course timetabling problem

International audienc

Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

Hybrid heuristic for multi-carrier transportation plans

This paper describes a hybrid heuristic approach to construct transportation plans for a singlecustomer multi-carrier scenario that arises at 3T Logistics Ltd, a UK company that provides outsourced transportation planning and management services. The problem consists on planning the delivery, using a set of carrier companies, of a set of shipments from a warehouse to different consignees across the UK. The problem tackled resembles a vehicle routing problem with time windows but there are several differences in our scenario. The hybrid heuristic algorithm described here combines a clustering algorithm, constructive and local search heuristics, and exact assignment based on integer programming. This approach is being currently evaluated at the company and results so far indicate the suitability of the algorithm to produce practical transportation plans at reduced cost compared to current practice

A methodology for determining an effective subset of heuristics in selection hyper-heuristics

We address the important step of determining an effective subset of heuristics in selection hyper-heuristics. Little attention has been devoted to this in the literature, and the decision is left at the discretion of the investigator. The performance of a hyper-heuristic depends on the quality and size of the heuristic pool. Using more than one heuristic is generally advantageous, however, an unnecessary large pool can decrease the performance of adaptive approaches. Our goal is to bring methodological rigour to this step. The proposed methodology uses non-parametric statistics and fitness landscape measurements from an available set of heuristics and benchmark instances, in order to produce a compact subset of effective heuristics for the underlying problem. We also propose a new iterated local search hyper-heuristic usingmulti-armed banditscoupled with a change detection mechanism. The methodology is tested on two real-world optimisation problems: course timetabling and vehicle routing. The proposed hyper-heuristic with a compact heuristic pool, outperforms state-of-the-art hyper-heuristics and competes with problem-specific methods in course timetabling, even producing new best-known solutions in 5 out of the 24 studied instances

A stochastic local search algorithm with adaptive acceptance for high-school timetabling

Automating high school timetabling is a challenging task. This problem is a well known hard computational problem which has been of interest to practitioners as well as researchers. High schools need to timetable their regular activities once per year, or even more frequently. The exact solvers might fail to find a solution for a given instance of the problem. A selection hyper-heuristic can be defined as an easy-to-implement, easy-to-maintain and effective 'heuristic to choose heuristics' to solve such computationally hard problems. This paper describes the approach of the team hyper-heuristic search strategies and timetabling (HySST) to high school timetabling which competed in all three rounds of the third international timetabling competition. HySST generated the best new solutions for three given instances in Round 1 and gained the second place in Rounds 2 and 3. It achieved this by using a fairly standard stochastic search method but significantly enhanced by a selection hyper-heuristic with an adaptive acceptance mechanism. © 2014 Springer Science+Business Media New York

Automated generation of constructive ordering heuristics for educational timetabling

Construction heuristics play an important role in solving combinatorial optimization problems. These heuristics are usually used to create an initial solution to the problem which is improved using optimization techniques such as metaheuristics. For examination timetabling and university course timetabling problems essentially graph colouring heuristics have been used for this purpose. The process of deriving heuristics manually for educational timetabling is a time consuming task. Furthermore, according to the no free lunch theorem different heuristics will perform well for different problems and problem instances. Hence, automating the induction of construction heuristics will reduce the man hours involved in creating such heuristics, allow for the derivation of problem specific heuristics and possibly result in the derivation of heuristics that humans have not thought of. This paper presents generation construction hyper-heuristics for educational timetabling. The study investigates the automatic induction of two types of construction heuristics, namely, arithmetic heuristics and hierarchical heuristics. Genetic programming is used to evolve arithmetic heuristics. Genetic programming, genetic algorithms and the generation of random heuristic combinations is examined for the generation of hierarchical heuristics. The hyper-heuristics generating both types of heuristics are applied to the examination timetabling and the curriculum based university course timetabling problems. The evolved heuristics were found to perform much better than the existing graph colouring heuristics used for this domain. Furthermore, it was found that the while the arithmetic heuristics were more effective for the examination timetabling problem, the hierarchical heuristics produced better results than the arithmetic heuristics for the curriculum based course timetabling problem. Genetic algorithms proved to be the most effective at inducing hierarchical heuristics