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

Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem

We consider the university course timetabling problem, which is one of the most studied problems in educational timetabling. In particular, we focus our attention on the formulation known as the curriculum-based course timetabling problem, which has been tackled by many researchers and for which there are many available benchmarks. The contribution of this paper is twofold. First, we propose an effective and robust single-stage simulated annealing method for solving the problem. Secondly, we design and apply an extensive and statistically-principled methodology for the parameter tuning procedure. The outcome of this analysis is a methodology for modeling the relationship between search method parameters and instance features that allows us to set the parameters for unseen instances on the basis of a simple inspection of the instance itself. Using this methodology, our algorithm, despite its apparent simplicity, has been able to achieve high quality results on a set of popular benchmarks. A final contribution of the paper is a novel set of real-world instances, which could be used as a benchmark for future comparison

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

Global Optimization Using Local Search Approach for Course Scheduling Problem

Course scheduling problem is a combinatorial optimization problem which is defined over a finite discrete problem whose candidate solution structure is expressed as a finite sequence of course events scheduled in available time and space resources. This problem is considered as non-deterministic polynomial complete problem which is hard to solve. Many solution methods have been studied in the past for solving the course scheduling problem, namely from the most traditional approach such as graph coloring technique; the local search family such as hill-climbing search, taboo search, and simulated annealing technique; and various population-based metaheuristic methods such as evolutionary algorithm, genetic algorithm, and swarm optimization. This article will discuss these various probabilistic optimization methods in order to gain the global optimal solution. Furthermore, inclusion of a local search in the population-based algorithm to improve the global solution will be explained rigorously

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

Iterated local search using an add and delete hyper- heuristic for university course timetabling

Hyper-heuristics are (meta-)heuristics that operate at a higher level to choose or generate a set of low-level (meta-)heuristics in an attempt of solve difficult optimization problems. Iterated local search (ILS) is a well-known approach for discrete optimization, combining perturbation and hill-climbing within an iterative framework. In this study, we introduce an ILS approach, strengthened by a hyper-heuristic which generates heuristics based on a fixed number of add and delete operations. The performance of the proposed hyper-heuristic is tested across two different problem domains using real world benchmark of course timetabling instances from the second International Timetabling Competition Tracks 2 and 3. The results show that mixing add and delete operations within an ILS framework yields an effective hyper-heuristic approach

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

A Methodology for Classifying Search Operators as Intensification or Diversification Heuristics

Selection hyper-heuristics are generic search tools that dynamically choose, from a given pool, the most promising operator (low-level heuristic) to apply at each iteration of the search process. The performance of these methods depends on the quality of the heuristic pool. Two types of heuristics can be part of the pool: diversification heuristics, which help to escape from local optima, and intensification heuristics, which effectively exploit promising regions in the vicinity of good solutions. An effective search strategy needs a balance between these two strategies. However, it is not straightforward to categorize an operator as intensification or diversification heuristic on complex domains. Therefore, we propose an automated methodology to do this classification. This brings methodological rigor to the configuration of an iterated local search hyper-heuristic featuring diversification and intensification stages. The methodology considers the empirical ranking of the heuristics based on an estimation of their capacity to either diversify or intensify the search. We incorporate the proposed approach into a state-of-the-art hyper-heuristic solving two domains: course timetabling and vehicle routing. Our results indicate improved performance, including new best-known solutions for the course timetabling problem

An online learning selection hyper-heuristic for educational timetabling

Examination and course timetabling are computationally difficult real-world resource allocation problems. In 2007, an International Timetabling Competition (ITC) consisting of three classes: (i) examination timetabling, (ii) post enrollment-based, and (iii) curriculum-based course timetabling was organised. One of the competing algorithms, referred to as CPSolver, successfully achieved the first place in two out of these three tracks. This study investigates the performance of various multi-stage selection hyper-heuristics sequencing low-level heuristics/operators extending the CPSolver framework which executes hill climbing and two well-known local search metaheuristics in stages. The proposed selection hyper-heuristic is a multi-stage approach making use of a matrix which maintains transitional probabilities between each low-level heuristic to select the next heuristic in the sequence. A second matrix tracks the probabilities of ending the sequence on a given low-level heuristic. The best configuration for the selection hyper-heuristic is explored tailoring the heuristic selection process for the given timetabling problem class. The empirical results on the ITC 2007 problem instances show that the proposed selection hyper-heuristics can reduce the number of soft constraint violations, producing improved solutions over CPSolver as well as some other previously proposed solvers, particularly, in examination and curriculum-based course timetabling