Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based on sequential/cyclic moves and a cyclic transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world data sets for high school timetabling in the Netherlands and England.We present results of the cyclic transfer algorithm with different settings on these data sets. The costs decrease by 8–28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

Cyclic transfers in school timetabling

In this paper we propose a neighbourhood structure based\ud on sequential/cyclic moves and a Cyclic Transfer algorithm for the high school timetabling problem. This method enables execution of complex moves for improving an existing solution, while dealing with the challenge of exploring the neighbourhood efficiently. An improvement graph is used in which certain negative cycles correspond to the neighbours; these cycles are explored using a recursive method. We address the problem of applying large neighbourhood structure methods on problems where the cost function is not exactly the sum of independent cost functions, as it is in the set partitioning problem. For computational experiments we use four real world datasets for high school timetabling in the Netherlands and England. We present results of the cyclic transfer algorithm with different settings on these datasets. The costs decrease by 8% to 28% if we use the cyclic transfers for local optimization compared to our initial solutions. The quality of the best initial solutions are comparable to the solutions found in practice by timetablers

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 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

Hybridizations within a graph based hyper-heuristic framework for university timetabling problems

A significant body of recent literature has explored various research directions in hyper-heuristics (which can be thought as heuristics to choose heuristics). In this paper, we extend our previous work to construct a unified graph-based hyper-heuristic (GHH) framework, under which a number of local search-based algorithms (as the high level heuristics) are studied to search upon sequences of low-level graph colouring heuristics. To gain an in-depth understanding on this new framework, we address some fundamental issues concerning neighbourhood structures and characteristics of the two search spaces (namely, the search spaces of the heuristics and the actual solutions). Furthermore, we investigate efficient hybridizations in GHH with local search methods and address issues concerning the exploration of the high-level search and the exploitation ability of the local search. These, to our knowledge, represent entirely novel directions in hyper-heuristics. The efficient hybrid GHH obtained competitive results compared with the best published results for both benchmark course and exam timetabling problems, demonstrating its efficiency and generality across different problem domains. Possible extensions upon this simple, yet general, GHH framework are also discussed

Examination timetabling at the University of Cape Town: a tabu search approach to automation

With the rise of schedules and scheduling problems, solutions proposed in literature have expanded yet the disconnect between research and reality remains. The University of Cape Town's (UCT) Examinations Office currently produces their schedules manually with software relegated to error-checking status. While they have requested automation, this study is the first attempt to integrate optimisation techniques into the examination timetabling process. Tabu search and Nelder-Mead methodologies were tested on the UCT November 2014 examination timetabling data with tabu search proving to be more effective, capable of producing feasible solutions from randomised initial solutions. To make this research more accessible, a user-friendly app was developed which showcased the optimisation techniques in a more digestible format. The app includes data cleaning specific to UCT's data management system and was presented to the UCT Examinations Office where they expressed support for further development: in its current form, the app would be used as a secondary tool after an initial solution has been manually obtained

Search with evolutionary ruin and stochastic rebuild: a theoretic framework and a case study on exam timetabling

This paper presents a state transition based formal framework for a new search method, called Evolutionary Ruin and Stochastic Recreate, which tries to learn and adapt to the changing environments during the search process. It improves the performance of the original Ruin and Recreate principle by embedding an additional phase of Evolutionary Ruin to mimic the survival-of-the-fittest mechanism within single solutions. This method executes a cycle of Solution Decomposition, Evolutionary Ruin, Stochastic Recreate and Solution Acceptance until a certain stopping condition is met. The Solution Decomposition phase first uses some problem-specific knowledge to decompose a complete solution into its components and assigns a score to each component. The Evolutionary Ruin phase then employs two evolutionary operators (namely Selection and Mutation) to destroy a certain fraction of the solution, and the next Stochastic Recreate phase repairs the “broken” solution. Last, the Solution Acceptance phase selects a specific strategy to determine the probability of accepting the newly generated solution. Hence, optimisation is achieved by an iterative process of component evaluation, solution disruption and stochastic constructive repair. From the state transitions point of view, this paper presents a probabilistic model and implements a Markov chain analysis on some theoretical properties of the approach. Unlike the theoretical work on genetic algorithm and simulated annealing which are based on state transitions within the space of complete assignments, our model is based on state transitions within the space of partial assignments. The exam timetabling problems are used to test the performance in solving real-world hard problems