A Hidden Markov Model Approach to the Problem of Heuristic Selection in Hyper-Heuristics with a Case Study in High School Timetabling Problems

Abstract

Operations research is a well established field that uses computational systems to support decisions in business and public life. Good solutions to operations research problems can make a large difference to the efficient running of businesses and organisations and so the field often searches for new methods to improve these solutions. The high school timetabling problem is an example of an operations research problem and is a challenging task which requires assigning events and resources to time slots subject to a set of constraints. In this paper a new sequence-based selection hyper-heuristic is presented that produces excellent results on a suite of high school timetabling problems. In this study, we present an easy-to-implement, easy-to-maintain and effective sequence-based selection hyper-heuristic to solve high school timetabling problems using a benchmark of unified real-world instances collected from different countries. We show that with sequence-based methods, it is possible to discover new best known solutions for a number of the problems in the timetabling domain. Through this investigation, the usefulness of sequence-based selection hyper-heuristics has been demonstrated and the capability of these methods has been shown to exceed the state-of-theart.

Local Search Heuristic for the Optimisation of Flight Connections

“…Furthermore, based on our findings the use of greedy approach for initialising the solutions of medium and large size instances leads to improved performance. The application of advanced algorithms, such as hyper-heuristics [15], [16] and evolutionary algorithms [17]- [19], is suggested for further research in order to escape local minima and achieve improved solutions for medium and large instances.…”

Modelling and solving the combined inventory routing problem with risk consideration

“…We propose a sequence-based selection hyper-heuristic utilising a hidden Markov model [4,5]. This adaptive approach maintains scores representing the probability of choosing a low level heuristic considering the previously invoked heuristic, learning effective sequences of low level heuristics to employ.…”

Tackling a VRP challenge to redistribute scarce equipment within time windows using metaheuristic algorithms

“…A new field of hyper-heuristic methods embedding data science techniques has recently been developed (Asta andÖzcan, 2015). Experiments on a hyper-heuristic benchmark framework (Kheiri and Keedwell, 2015), urban transit route design problem (Ahmed et al, 2019), wind farm layout optimization problem (Wilson et al, 2018), high school timetabling problem (Kheiri and Keedwell, 2017) and on water distribution optimization problem (Kheiri et al, 2015) have shown that applying a sequence of low level heuristics can potentially improve the quality of solutions more than those that simply select and apply a single low level heuristic.…”