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

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 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

A hybrid meta-heuristic for the generation of feasible large-scale course timetables using instance decomposition

This study introduces a hybrid meta-heuristic for generating feasible course timetables in large-scale scenarios. We conducted tests using our university's instances. The current commercial software often struggles to meet constraints and takes hours to find satisfactory solutions. Our methodology combines adaptive large neighbourhood search, guided local search, variable neighbourhood search, and an innovative instance decomposition technique. Constraint violations from various groups are treated as objective functions to minimize. The search focuses on time slots with the most violations, and if no improvements are observed after a certain number of iterations, the most challenging constraint groups receive new weights to guide the search towards non-dominated solutions, even if the total sum of violations increases. In cases where this approach fails, a shaking phase is employed. The decomposition mechanism works by iteratively introducing curricula to the problem and finding new feasible solutions while considering an expanding set of lectures. Assignments from each iteration can be adjusted in subsequent iterations. Our methodology is tested on real-world instances from our university and random subdivisions. For subdivisions with 400 curricula timetables, decomposition reduced solution times by up to 27%. In real-world instances with 1,288 curricula timetables, the reduction was 18%. Clustering curricula with more common lectures and professors during increments improved solution times by 18% compared to random increments. Using our methodology, viable solutions for real-world instances are found in an average of 21 minutes, whereas the commercial software takes several hours

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