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 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

Incorporating Machine Learning to Evaluate Solutions to the University Course Timetabling Problem

Evaluating solutions to optimization problems is arguably the most important step for heuristic algorithms, as it is used to guide the algorithms towards the optimal solution in the solution search space. Research has shown evaluation functions to some optimization problems to be impractical to compute and have thus found surrogate less expensive evaluation functions to those problems. This study investigates the extent to which supervised learning algorithms can be used to find approximations to evaluation functions for the university course timetabling problem. Up to 97 percent of the time, the traditional evaluation function agreed with the supervised learning regression model on the result of comparison of the quality of pair of solutions to the university course timetabling problem, suggesting that supervised learning regression models can be suitable alternatives for optimization problems’ evaluation functions

Monte Carlo Tree Search in Finding Feasible Solutions for Course Timetabling Problem

We are addressing the course timetabling problem in this work. In a university, students can select their favorite courses each semester. Thus, the general requirement is to allow them to attend lectures without clashing with other lectures. A feasible solution is a solution where this and other conditions are satisfied. Constructing reasonable solutions for course timetabling problem is a hard task. Most of the existing methods failed to generate reasonable solutions for all cases. This is since the problem is heavily constrained and an effective method is required to explore and exploit the search space. We utilize Monte Carlo Tree Search (MCTS) in finding feasible solutions for the first time. In MCTS, we build a tree incrementally in an asymmetric manner by sampling the decision space. It is traversed in the best-first manner. We propose several enhancements to MCTS like simulation and tree pruning based on a heuristic. The performance of MCTS is compared with the methods based on graph coloring heuristics and Tabu search. We test the solution methodologies on the three most studied publicly available datasets. Overall, MCTS performs better than the method based on graph coloring heuristic; however, it is inferior compared to the Tabu based method. Experimental results are discussed

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

Improved local search approaches to solve the post enrolment course timetabling problem

In this work, we are addressing the post enrollment course timetabling (PE-CTT) problem. We combine different local search algorithms into an iterative two stage procedure. In the first stage, Tabu Search with Sampling and Perturbation (TSSP) is used to generate feasible solutions. In the second stage, we propose an improved variant of Simulated Annealing (SA), which we call Simulated Annealing with Reheating (SAR), to improve the solution quality of feasible solutions. SAR has three features: a novel neighborhood examination scheme, a new way of estimating local optima and a reheating scheme. SAR eliminates the need for extensive tuning as is often required in conventional SA. The proposed methodologies are tested on the three most studied datasets from the scientific literature. Our algorithms perform well and our results are competitive, if not better, compared to the benchmarks set by the state of the art methods. New best known results are provided for many instances