A guided search non-dominated sorting genetic algorithm for the multi-objective university course timetabling problem

Copyright @ Springer-Verlag Berlin Heidelberg 2011.The university course timetabling problem is a typical combinatorial optimization problem. This paper tackles the multi-objective university course timetabling problem (MOUCTP) and proposes a guided search non-dominated sorting genetic algorithm to solve the MOUCTP. The proposed algorithm integrates a guided search technique, which uses a memory to store useful information extracted from previous good solutions to guide the generation of new solutions, and two local search schemes to enhance its performance for the MOUCTP. The experimental results based on a set of test problems show that the proposed algorithm is efficient for solving the MOUCTP

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

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

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

An efficient memetic, permutation-based evolutionary algorithm for real-world train timetabling

Train timetabling is a difficult and very tightly constrained combinatorial problem that deals with the construction of train schedules. We focus on the particular problem of local reconstruction of the schedule following a small perturbation, seeking minimisation of the total accumulated delay by adapting times of departure and arrival for each train and allocation of resources (tracks, routing nodes, etc.). We describe a permutation-based evolutionary algorithm that relies on a semi-greedy heuristic to gradually reconstruct the schedule by inserting trains one after the other following the permutation. This algorithm can be hybridised with ILOG commercial MIP programming tool CPLEX in a coarse-grained manner: the evolutionary part is used to quickly obtain a good but suboptimal solution and this intermediate solution is refined using CPLEX. Experimental results are presented on a large real-world case involving more than one million variables and 2 million constraints. Results are surprisingly good as the evolutionary algorithm, alone or hybridised, produces excellent solutions much faster than CPLEX alone

A grouping hyper-heuristic framework: application on graph colouring

Grouping problems are hard to solve combinatorial optimisation problems which require partitioning of objects into a minimum number of subsets while a given objective is simultaneously optimised. Selection hyper-heuristics are high level general purpose search methodologies that operate on a space formed by a set of low level heuristics rather than solutions. Most of the recently proposed selection hyper-heuristics are iterative and make use of two key methods which are employed successively; heuristic selection and move acceptance. In this study, we present a novel generic selection hyper-heuristic framework containing a fixed set of reusable grouping low level heuristics and an unconventional move acceptance mechanism for solving grouping problems. This framework deals with one solution at a time at any given decision point during the search process. Also, a set of high quality solutions, capturing the trade-off between the number of groups and the additional objective for the given grouping problem, is maintained. The move acceptance mechanism embeds a local search approach which is capable of progressing improvements on those trade-off solutions. The performance of different selection hyper-heuristics with various components under the proposed framework is investigated on graph colouring as a representative grouping problem. Then, the top performing hyper-heuristics are applied to a benchmark of examination timetabling instances. The empirical results indicate the effectiveness and generality of the proposed framework enabling grouping hyper-heuristics to achieve high quality solutions in both domains. ©2015 Elsevier Ltd. All rights reserved