Decomposition, Reformulation, and Diving in University Course Timetabling

In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality. Our study is performed on a university course timetabling problem used in the 2007 International Timetabling Competition, also known as the Udine Course Timetabling Problem. In the proposed heuristic, an objective-restricted neighbourhood generator produces assignments of periods to events, with decreasing numbers of violations of two period-related soft constraints. Those are relaxed into assignments of events to days, which define neighbourhoods that are easier to search with respect to all four soft constraints. Integer programming formulations for all subproblems are given and evaluated using ILOG CPLEX 11. The wider applicability of this approach is analysed and discussed.Comment: 45 pages, 7 figures. Improved typesetting of figures and table

A memetic algorithm for the university course timetabling problem

This article is posted here with permission from IEEE - Copyright @ 2008 IEEEThe design of course timetables for academic institutions is a very hectic job due to the exponential number of possible feasible timetables with respect to the problem size. This process involves lots of constraints that must be respected and a huge search space to be explored, even if the size of the problem input is not significantly large. On the other hand, the problem itself does not have a widely approved definition, since different institutions face different variations of the problem. This paper presents a memetic algorithm that integrates two local search methods into the genetic algorithm for solving the university course timetabling problem (UCTP). These two local search methods use their exploitive search ability to improve the explorative search ability of genetic algorithms. The experimental results indicate that the proposed memetic algorithm is efficient for solving the UCTP

Automatically detecting neighbourhood constraint interactions using comet

The major benet of using events as the basis for our detection system is the clean separation between the neighbourhoods and detector which we can achieve. The detector simply iterates over a set of Neighbourhood objects and checks each for interactions. The acceptance function for the neighbourhood is set to accept any tness. For purposes of detecting an interaction it does not matter whether a move reduces or increases the constraint violations; both indicate that a relationship exists. The simulation is performed in two stages. Starting from a randomly created initial solution a random move from the neighbourhood is chosen, often this will lead to a constraint change and prevent the need for further exploration. For some constraints the chance of randomly selecting a move which would violate it is fairly low and so a more rigourous search is required. If the initial move has not found any interaction then the detector explores every neighbouring state from the current position. If at any stage a change of the constraint violations is detected then the exploration is stopped

Automatically detecting neighbourhood constraint interactions using Comet

Local Search has been shown to be capable of producing high quality solutions in a variety of hard constraint and optimisation problems. Typically implementing a Local Search algorithm is done in a problem specic manner. In the last few years a variety of approaches have emerged focussed on easing the implementation and creating a clean separation between the algorithm and problem. We present a system which can deduce information about the interactions between problem constraints and the search neighbourhoods whilst maintaining a loose coupling between these components. We apply this technique to the International Timetabling Competition instances and show an implementation expressed in Comet

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

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

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

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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