Monte Carlo hyper-heuristics for examination timetabling

Automating the neighbourhood selection process in an iterative approach that uses multiple heuristics is not a trivial task. Hyper-heuristics are search methodologies that not only aim to provide a general framework for solving problem instances at different difficulty levels in a given domain, but a key goal is also to extend the level of generality so that different problems from different domains can also be solved. Indeed, a major challenge is to explore how the heuristic design process might be automated. Almost all existing iterative selection hyper-heuristics performing single point search contain two successive stages; heuristic selection and move acceptance. Different operators can be used in either of the stages. Recent studies explore ways of introducing learning mechanisms into the search process for improving the performance of hyper-heuristics. In this study, a broad empirical analysis is performed comparing Monte Carlo based hyper-heuristics for solving capacitated examination timetabling problems. One of these hyper-heuristics is an approach that overlaps two stages and presents them in a single algorithmic body. A learning heuristic selection method (L) operates in harmony with a simulated annealing move acceptance method using reheating (SA) based on some shared variables. Yet, the heuristic selection and move acceptance methods can be separated as the proposed approach respects the common selection hyper-heuristic framework. The experimental results show that simulated annealing with reheating as a hyper-heuristic move acceptance method has significant potential. On the other hand, the learning hyper-heuristic using simulated annealing with reheating move acceptance (L?CSA) performs poorly due to certain weaknesses, such as the choice of rewarding mechanism and the evaluation of utility values for heuristic selection as compared to some other hyper-heuristics in examination timetabling. Trials with other heuristic selection methods confirm that the best alternative for the simulated annealing with reheating move acceptance for examination timetabling is a previously proposed strategy known as the choice function.     

Generalized hyper-heuristics for solving 2D Regular and Irregular Packing Problems

The idea behind hyper-heuristics is to discover some combination of straightforward heuristics to solve a wide range of problems. To be worthwhile, such a combination should outperform the single heuristics. This article presents a GA-based method that produces general hyper-heuristics that solve two-dimensional regular (rectangular) and irregular (convex polygonal) bin-packing problems. A hyper-heuristic is used to define a high-level heuristic that controls low-level heuristics. The hyper-heuristic should decide when and where to apply each single low-level heuristic, depending on the given problem state. In this investigation two kinds of heuristics were considered: for selecting the figures (pieces) and objects (bins), and for placing the figures into the objects. Some of the heuristics were taken from the literature, others were adapted, and some other variations developed by us. We chose the most representative heuristics of their type, considering their individual performance in various studies and also in an initial experimentation on a collection of benchmark problems. The GA included in the proposed model uses a variable-length representation, which evolves combinations of condition-action rules producing hyper-heuristics after going through a learning process which includes training and testing phases. Such hyper-heuristics, when tested with a large set of benchmark problems, produce outstanding results for most of the cases. The testbed is composed of problems used in other similar studies in the literature. Some additional instances for the testbed were randomly generated.     

Hyper-heuristics: a survey of the state of the art

Hyper-heuristics comprise a set of approaches that are motivated (at least in part) by the goal of automating the design of heuristic methods to solve hard computational search problems. An underlying strategic research challenge is to develop more generally applicable search methodologies. The term hyper-heuristic is relatively new; it was first used in 2000 to describe heuristics to choose heuristics in the context of combinatorial optimisation. However, the idea of automating the design of heuristics is not new; it can be traced back to the 1960s. The definition of hyper-heuristics has been recently extended to refer to a search method or learning mechanism for selecting or generating heuristics to solve computational search problems. Two main hyper-heuristic categories can be considered: heuristic selection and heuristic generation. The distinguishing feature of hyper-heuristics is that they operate on a search space of heuristics (or heuristic components) rather than directly on the search space of solutions to the underlying problem that is being addressed. This paper presents a critical discussion of the scientific literature on hyper-heuristics including their origin and intellectual roots, a detailed account of the main types of approaches, and an overview of some related areas. Current research trends and directions for future research are also discussed.     

A hyper-heuristic approach to sequencing by hybridization of DNA sequences

In this paper we investigate the use of hyper-heuristic methodologies for predicting DNA sequences. In particular, we utilize Sequencing by Hybridization. We believe that this is the first time that hyper-heuristics have been investigated in this domain. A hyper-heuristic is provided with a set of low-level heuristics and the aim is to decide which heuristic to call at each decision point. We investigate three types of hyper-heuristics. Two of these (simulated annealing and tabu search) draw their inspiration from meta-heuristics. The choice function hyper-heuristic draws its inspiration from reinforcement learning. We utilize two independent sets of low-level heuristics. The first set is based on a previous tabu search method, with the second set being a significant extension to this basic set, including utilizing a different representation and introducing the definition of clusters. The datasets we use comprises two randomly generated datasets and also a publicly available biological dataset. In total, we carried out experiments using 70 different combinations of heuristics, using the three datasets mentioned above and investigating six different hyper-heuristic algorithms. Our results demonstrate the effectiveness of a hyper-heuristic approach to this problem domain. It is necessary to provide a good set of low-level heuristics, which are able to both intensify and diversify the search but this approach has demonstrated very encouraging results on this extremely difficult and important problem domain.     

Adaptive automated construction of hybrid heuristics for exam timetabling and graph colouring problems

In this paper, we present a random iterative graph based hyper-heuristic to produce a collection of heuristic sequences to construct solutions of different quality. These heuristic sequences can be seen as dynamic hybridisations of different graph colouring heuristics that construct solutions step by step. Based on these sequences, we statistically analyse the way in which graph colouring heuristics are automatically hybridised. This, to our knowledge, represents a new direction in hyper-heuristic research. It is observed that spending the search effort on hybridising Largest Weighted Degree with Saturation Degree at the early stage of solution construction tends to generate high quality solutions. Based on these observations, an iterative hybrid approach is developed to adaptively hybridise these two graph colouring heuristics at different stages of solution construction. The overall aim here is to automate the heuristic design process, which draws upon an emerging research theme on developing computer methods to design and adapt heuristics automatically. Experimental results on benchmark exam timetabling and graph colouring problems demonstrate the effectiveness and generality of this adaptive hybrid approach compared with previous methods on automatically generating and adapting heuristics. Indeed, we also show that the approach is competitive with the state of the art human produced methods.     

A graph-based hyper-heuristic for educational timetabling problems

This paper presents an investigation of a simple generic hyper-heuristic approach upon a set of widely used constructive heuristics (graph coloring heuristics) in timetabling. Within the hyper-heuristic framework, a tabu search approach is employed to search for permutations of graph heuristics which are used for constructing timetables in exam and course timetabling problems. This underpins a multi-stage hyper-heuristic where the tabu search employs permutations upon a different number of graph heuristics in two stages. We study this graph-based hyper-heuristic approach within the context of exploring fundamental issues concerning the search space of the hyper-heuristic (the heuristic space) and the solution space. Such issues have not been addressed in other hyper-heuristic research. These approaches are tested on both exam and course benchmark timetabling problems and are compared with the fine-tuned bespoke state-of-the-art approaches. The results are within the range of the best results reported in the literature. The approach described here represents a significantly more generally applicable approach than the current state of the art in the literature. Future work will extend this hyper-heuristic framework by employing methodologies which are applicable on a wider range of timetabling and scheduling problems.     

Hybridizations within a graph-based hyper-heuristic framework for university timetabling problems

A significant body of recent literature has explored various research directions in hyper-heuristics (which can be thought as heuristics to choose heuristics). In this paper, we extend our previous work to construct a unified graph-based hyper-heuristic (GHH) framework, under which a number of local search-based algorithms (as the high level heuristics) are studied to search upon sequences of low-level graph colouring heuristics. To gain an in-depth understanding on this new framework, we address some fundamental issues concerning neighbourhood structures and characteristics of the two search spaces (namely, the search spaces of the heuristics and the actual solutions). Furthermore, we investigate efficient hybridizations in GHH with local search methods and address issues concerning the exploration of the high-level search and the exploitation ability of the local search. These, to our knowledge, represent entirely novel directions in hyper-heuristics. The efficient hybrid GHH obtained competitive results compared with the best published results for both benchmark course and exam timetabling problems, demonstrating its efficiency and generality across different problem domains. Possible extensions upon this simple, yet general, GHH framework are also discussed.     

DVRP: a hard dynamic combinatorial optimisation problem tackled by an evolutionary hyper-heuristic

In this paper we propose and evaluate an evolutionary-based hyper-heuristic approach, called EH-DVRP, for solving hard instances of the dynamic vehicle routing problem. A hyper-heuristic is a high-level algorithm, which generates or chooses a set of low-level heuristics in a common framework, to solve the problem at hand. In our collaborative framework, we have included three different types of low-level heuristics: constructive, perturbative, and noise heuristics. Basically, the hyper-heuristic manages and evolves a sophisticated sequence of combinations of these low-level heuristics, which are sequentially applied in order to construct and improve partial solutions, i.e., partial routes. In presenting some design considerations, we have taken into account the allowance of a proper cooperation and communication among low-level heuristics, and as a result, find the most promising sequence to tackle partial states of the (dynamic) problem. Our approach has been evaluated using the Kilby’s benchmarks, which comprise a large number of instances with different topologies and degrees of dynamism, and we have compared it with some well-known methods proposed in the literature. The experimental results have shown that, due to the dynamic nature of the hyper-heuristic, our proposed approach is able to adapt to dynamic scenarios more naturally than low-level heuristics. Furthermore, the hyper-heuristic can obtain high-quality solutions when compared with other (meta) heuristic-based methods. Therefore, the findings of this contribution justify the employment of hyper-heuristic techniques in such changing environments, and we believe that further contributions could be successfully proposed in related dynamic problems.     

Hyper-heuristic approaches for the response time variability problem

We propose two classes for the implementation of hyper-heuristic algorithms. The first is based on constructive heuristics, whereas the second uses improvement methods. Within the latter class, a general framework is designed for the use of local search procedures and metaheuristics as low-level heuristics. A dynamic scheme to guide the use of these approaches is also devised. These ideas are tested on an NP-hard scheduling problem known as the response time variability problem (RTVP). An intensive computational experiment shows, especially in the second class where the new best results are found, the effectiveness of the proposed hyper-heuristics.     

Competitive travelling salesmen problem: A hyper-heuristic approach

We introduce a novel variant of the travelling salesmen problem and propose a hyper-heuristic methodology in order to solve it. In a competitive travelling salesmen problem (CTSP), m travelling salesmen are to visit n cities and the relationship between the travelling salesmen is non-cooperative. The salesmen will receive a payoff if they are the first one to visit a city and they pay a cost for any distance travelled. The objective of each salesman is to visit as many unvisited cities as possible, with a minimum travelling distance. Due to the competitive element, each salesman needs to consider the tours of other salesman when planning their own tour. Since equilibrium analysis is difficult in the CTSP, a hyper-heuristic methodology is developed. The model assumes that each agent adopts a heuristic (or set of heuristics) to choose their moves (or tour) and each agent knows that the moves/tours of all agents are not necessarily optimal. The hyper-heuristic consists of a number of low-level heuristics, each of which can be used to create a move/tour given the heuristics of the other agents, together with a high-level heuristic that is used to select from the low-level heuristics at each decision point. Several computational examples are given to illustrate the effectiveness of the proposed approach.     

Adaptive selection of heuristics for improving exam timetables

This paper presents a hyper-heuristic approach which hybridises low-level heuristic moves to improve timetables. Exams which cause a soft-constraint violation in the timetable are ordered and rescheduled to produce a better timetable. It is observed that both the order in which exams are rescheduled and the heuristic moves used to reschedule the exams and improve the timetable affect the quality of the solution produced. After testing different combinations in a hybrid hyper-heuristic approach, the Kempe chain move heuristic and time-slot swapping heuristic proved to be the best heuristic moves to use in a hybridisation. Similarly, it was shown that ordering the exams using Saturation Degree and breaking any ties using Largest Weighted Degree produce the best results. Based on these observations, a methodology is developed to adaptively hybridise the Kempe chain move and timeslot swapping heuristics in two stages. In the first stage, random heuristic sequences are generated and automatically analysed. The heuristics repeated in the best sequences are fixed while the rest are kept empty. In the second stage, sequences are generated by randomly assigning heuristics to the empty positions in an attempt to find the best heuristic sequence. Finally, the generated sequences are applied to the problem. The approach is tested on the Toronto benchmark and the exam timetabling track of the second International Timetabling Competition, to evaluate its generality. The hyper-heuristic with low-level improvement heuristics approach was found to generalise well over the two different datasets and performed comparably to the state of the art approaches.     

A study of heuristic combinations for hyper-heuristic systems for the uncapacitated examination timetabling problem

Research in the domain of examination timetabling is moving towards developing methods that generalise well over a range of problems. This is achieved by implementing hyper-heuristic systems to find the best heuristic or heuristic combination to allocate examinations when constructing a timetable for a problem. Heuristic combinations usually take the form of a list of low-level heuristics that are applied sequentially. This study proposes an alternative representation for heuristic combinations, namely, a hierarchical combination of heuristics. Furthermore, the heuristics in each combination are applied simultaneously rather than sequentially. The study also introduces a new low-level heuristic, namely, highest cost. A set of heuristic combinations of this format have been tested on the 13 Carter benchmarks. The quality of the examination timetables induced using these combinations are comparable to, and in some cases better than, those produced by hyper-heuristic systems combining and applying heuristic combinations sequentially.     

A stochastic local search algorithm with adaptive acceptance for high-school timetabling

Automating high school timetabling is a challenging task. This problem is a well known hard computational problem which has been of interest to practitioners as well as researchers. High schools need to timetable their regular activities once per year, or even more frequently. The exact solvers might fail to find a solution for a given instance of the problem. A selection hyper-heuristic can be defined as an easy-to-implement, easy-to-maintain and effective ‘heuristic to choose heuristics’ to solve such computationally hard problems. This paper describes the approach of the team hyper-heuristic search strategies and timetabling (HySST) to high school timetabling which competed in all three rounds of the third international timetabling competition. HySST generated the best new solutions for three given instances in Round 1 and gained the second place in Rounds 2 and 3. It achieved this by using a fairly standard stochastic search method but significantly enhanced by a selection hyper-heuristic with an adaptive acceptance mechanism.     

An empirical study of hyperheuristics for managing very large sets of low level heuristics

Hyperheuristics give us the appealing possibility of abstracting the solution method from the problem, since our hyperheuristic, at each decision point, chooses between different low level heuristics rather than different solutions as is usually the case for metaheuristics. By assembling low level heuristics from parameterised components we may create hundreds or thousands of low level heuristics, and there is increasing evidence that this is effective in dealing with every eventuality that may arise when solving different combinatorial optimisation problem instances since at each iteration the solution landscape is amenable to at least one of the low level heuristics. However, the large number of low level heuristics means that the hyperheuristic has to intelligently select the correct low level heuristic to use, to make best use of available CPU time. This paper empirically investigates several hyperheuristics designed for large collections of low level heuristics and adapts other hyperheuristics from the literature to cope with these large sets of low level heuristics on a difficult real-world workforce scheduling problem. In the process we empirically investigate a wide range of approaches for setting tabu tenure in hyperheuristic methods, for a complex real-world problem. The results show that the hyperheuristic methods described provide a good way to trade off CPU time and solution quality.     

Coalition-based metaheuristic: a self-adaptive metaheuristic using reinforcement learning and mimetism

We present a self-adaptive and distributed metaheuristic called Coalition-Based Metaheuristic (CBM). This method is based on the Agent Metaheuristic Framework (AMF) and hyper-heuristic approach. In CBM, several agents, grouped in a coalition, concurrently explore the search space of a given problem instance. Each agent modifies a solution with a set of operators. The selection of these operators is determined by heuristic rules dynamically adapted by individual and collective learning mechanisms. The intention of this study is to exploit AMF and hyper-heuristic approaches to conceive an efficient, flexible and modular metaheuristic. AMF provides a generic model of metaheuristic that encourages modularity, and hyper-heuristic approach gives some guidelines to design flexible search methods. The performance of CBM is assessed by computational experiments on the vehicle routing problem.     

Unified encoding for hyper-heuristics with application to bioinformatics

This paper introduces a new approach to applying hyper-heuristic algorithms to solve combinatorial problems with less effort, taking into account the modelling and algorithm construction process. We propose a unified encoding of a solution and a set of low level heuristics which are domain-independent and which change the solution itself. This approach enables us to address NP-hard problems and generate good approximate solutions in a reasonable time without a large amount of additional work required to tailor search methodologies for the problem in hand. In particular, we focused on solving DNA sequencing by hybrydization with errors, which is known to be strongly NP-hard. The approach was extensively tested by solving multiple instances of well-known combinatorial problems and compared with results generated by meta heuristics that have been tailored for specific problem domains.     

A scatter search based hyper-heuristic for sequencing a mixed-model assembly line

We address a mixed-model assembly-line sequencing problem with work overload minimization criteria. We consider time windows in work stations of the assembly line (closed stations) and different versions of a product to be assembled in the line, which require different processing time according to the work required in each work station. In a paced assembly line, products are feeded in the line at a predetermined constant rate (cycle time). Then, if many products with processing time greater than cycle time are feeded consecutively, work overload can be produced when the worker has insufficient time to finish his/her job. We propose a scatter search based hyper-heuristic for this NP-hard problem. In the low-level, the procedure makes use of priority rules through a constructive procedure. Computational experiments over a wide range of instances from the literature show the effectiveness of the proposed hyper-heuristics when compared to existing heuristics. The relevance of the priority rules was evaluated as well.     

Evolving timetabling heuristics using a grammar-based genetic programming hyper-heuristic framework

This paper introduces a Grammar-based Genetic Programming Hyper-Heuristic framework (GPHH) for evolving constructive heuristics for timetabling. In this application GP is used as an online learning method which evolves heuristics while solving the problem. In other words, the system keeps on evolving heuristics for a problem instance until a good solution is found. The framework is tested on some of the most widely used benchmarks in the field of exam timetabling and compared with the best state-of-the-art approaches. Results show that the framework is very competitive with other constructive techniques, and did outperform other hyper-heuristic frameworks on many occasions.     

A hybrid framework for optimizing beam angles in radiation therapy planning

The purpose of this paper is twofold: (1) to examine strengths and weaknesses of recently developed optimization methods for selecting radiation treatment beam angles and (2) to propose a simple and easy-to-use hybrid framework that overcomes some of the weaknesses observed with these methods. Six optimization methods—branch and bound (BB), simulated annealing (SA), genetic algorithms (GA), nested partitions (NP), branch and prune (BP), and local neighborhood search (LNS)—were evaluated. Our preliminary test results revealed that (1) one of the major drawbacks of the reported algorithms was the limited ability to find a good solution within a reasonable amount of time in a clinical setting, (2) all heuristic methods require selecting appropriate parameter values, which is a difficult chore, and (3) the LNS algorithm has the ability to identify good solutions only if provided with a good starting point. On the basis of these findings, we propose a unified beam angle selection framework that, through two sequential phases, consistently finds clinically relevant locally optimal solutions. Considering that different users may use different optimization approaches among those mentioned above, the first phase aims to quickly find a good feasible solution using SA, GA, NP, or BP. This solution is then used as a starting point for LNS to find a locally optimal solution. Experimental results using this unified method on five clinical cases show that it not only produces consistently good-quality treatment solutions but also alleviates the effort of selecting an initial set of appropriate parameter values that is required by all of the existing optimization methods.     

Roster evaluation based on classifiers for the nurse rostering problem

The personnel scheduling problem is a well-known NP-hard combinatorial problem. Due to the complexity of this problem and the size of the real-world instances, it is not possible to use exact methods, and thus heuristics, meta-heuristics, or hyper-heuristics must be employed. The majority of heuristic approaches are based on iterative search, where the quality of intermediate solutions must be calculated. Unfortunately, this is computationally highly expensive because these problems have many constraints and some are very complex. In this study, we propose a machine learning technique as a tool to accelerate the evaluation phase in heuristic approaches. The solution is based on a simple classifier, which is able to determine whether the changed solution (more precisely, the changed part of the solution) is better than the original or not. This decision is made much faster than a standard cost-oriented evaluation process. However, the classification process cannot guarantee 100 % correctness. Therefore, our approach, which is illustrated using a tabu search algorithm in this study, includes a filtering mechanism, where the classifier rejects the majority of the potentially bad solutions and the remaining solutions are then evaluated in a standard manner. We also show how the boosting algorithms can improve the quality of the final solution compared with a simple classifier. We verified our proposed approach and premises, based on standard and real-world benchmark instances, to demonstrate the significant speedup obtained with comparable solution quality.