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

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 article, 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 the art

Heuristic sequence selection for inventory routing problem

In this paper, an improved sequence-based selection hyper-heuristic method for the Air Liquide inventory routing problem, the subject of the ROADEF/EURO 2016 challenge, is described. The organizers of the challenge have proposed a real-world problem of inventory routing as a difficult combinatorial optimization problem. An exact method often fails to find a feasible solution to such problems. On the other hand, heuristics may be able to find a good quality solution that is significantly better than those produced by an expert human planner. There is a growing interest toward self-configuring automated general-purpose reusable heuristic approaches for combinatorial optimization. Hyper-heuristics have emerged as such methodologies. This paper investigates a new breed of hyper-heuristics based on the principles of sequence analysis to solve the inventory routing problem. The primary point of this work is that it shows the usefulness of the improved sequence-based selection hyper-heuristic, and in particular demonstrates the advantages of using a data science technique of hidden Markov model for the heuristic selection

Offline learning with a selection hyper-heuristic: an application to water distribution network optimisation

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordA sequence-based selection hyper-heuristic with online learning is used to optimise 12 water distribution networks of varying sizes. The hyper-heuristic results are compared with those produced by five multi-objective evolutionary algorithms. The comparison demonstrates that the hyper-heuristic is a computationally efficient alternative to a multi-objective evolutionary algorithm. An offline learning algorithm is used to enhance the optimisation performance of the hyper-heuristic. The optimisation results of the offline trained hyper-heuristic are analysed statistically, and a new offline learning methodology is proposed. The new methodology is evaluated, and shown to produce an improvement in performance on each of the 12 networks. Finally, it is demonstrated that offline learning can be usefully transferred from small, computationally inexpensive problems, to larger computationally expensive ones, and that the improvement in optimisation performance is statistically significant, with 99% confidence

An analysis of heuristic subsequences for offline hyper-heuristic learning

This is the final version. Available on open access from Springer Verlag via the DOI in this recordA selection hyper-heuristic is used to minimise the objective functions of a well-known set of benchmark problems. The resulting sequences of low level heuristic selections and objective function values are used to generate a database of heuristic selections. The sequences in the database are broken down into subsequences and the mathematical concept of a logarithmic return is used to discriminate between “effective” subsequences, which tend to decrease the objective value, and “disruptive” subsequences, which tend to increase the objective value. These subsequences are then employed in a sequenced based hyper-heuristic and evaluated on an unseen set of benchmark problems. Empirical results demonstrate that the “effective” subsequences perform significantly better than the “disruptive” subsequences across a number of problem domains with 99% confidence. The identification of subsequences of heuristic selections that can be shown to be effective across a number of problems or problem domains could have important implications for the design of future sequence based hyper-heuristics

Asignación de salones por medio de una hiper-heurística

El problema de horarios y cursos basado en currículum (abreviado por sus siglas en inglés, CBCT), es un problema de optimización, donde se plantea la generación de un calendario escolar respetando una serie de restricciones, además existe una función objetivo con la capacidad de evaluar cada horario propuesto, por lo que el objetivo es obtener el calendario con el menor costo posible. Los origines del problema pueden ser rastreados hasta los años setentas, aunque en el presente trabajo se considera la descripción dada por la Competencia Internacional de Horarios 2007 (por sus siglas en inglés: ITC2007), evento donde se reunieron investigadores alrededor del mundo y que continúa siendo utilizado como campo de estudio para algoritmos. En el presente trabajo se propone una hiper-heurística como técnica para abordar el CBCT. El algoritmo por medio de diferentes heurísticas de bajo nivel, intenta minimizar el número de restricciones no satisfechas con el objetivo de generar un calendario de mejor calidad. Finalmente se utilizó la base de datos de la ITC2007 la cual consta de 21 instancias distintas con lo cual, se puede tener marco de referencia sobre el desempeño de la propuesta. Los resultados obtenidos por el algoritmo, son comparados con otras técnicas encontradas en la literatura. Los resultados obtenidos son alentadores, el programa obtiene soluciones competitivas en tiempos aceptables, e incluso en algunos casos cercanas al mejor valor conocido