Hyperheuristics can be defined to be heuristics which choose between heuristics in order to solve a given optimisation problem. The main motivation behind the development of such approaches is the goal of developing automated scheduling methods which are not restricted to one problem. In this paper we report the investigation of a hyperheuristic approach and evaluate it on various instances of two distinct timetabling and rostering problems. In the framework of our hyperheuristic approach, heuristics compete using rules based on the principles of reinforcement learning. A tabu list of heuristics is also maintained which prevents certain heuristics from being chosen at certain times during the search. We demonstrate that this tabu-search hyperheuristic is an easily re-usable method which can produce solutions of at least acceptable quality across a variety of problems and instances. In effect the proposed method is capable of producing solutions that are competitive with those obtained using stateof -the-art problem-specific techniques for the problems studied here, but is fundamentally more general than those techniques.

This chapter introduces and overviews an emerging methodology in search and optimisation. One of the key aims of these new approaches, which have been termed hyper-heuristics, is to raise the level of generality at which optimisation systems can operate. An objective is that hyper-heuristics will lead to more general systems that are able to handle a wide range of problem domains rather than current meta-heuristic technology which tends to be customised to a particular problem or a narrow class of problems. Hyperheuristics are broadly concerned with intelligently choosing the right heuristic or algorithm in a given situation. Of course, a hyper-heuristic can be (often is) a (meta-)heuristic and it can operate on (meta-)heuristics. In a certain sense, a hyper-heuristic works at a higher level when compared with the typical application of meta-heuristics to optimisation problems i.e. a hyper-heuristic could be thought of as a (meta)-heuristic which operates on lower level (meta- )heuristics. In this chapter we will introduce the idea and give a brief history of this emerging area. In addition, we will review some of the latest work to be published in the field.

The combination of Evolutionary algorithms with local search was named "Memetic Algorithms" (MAs) in [1]. These methods are inspired by models of natural systems that combine the evolutionary adaptation of a population with individual learning within the lifetimes of its members. Additionally, MAs are inspired by Richard Dawkin's concept of a meme, which represents a unit of cultural evolution that can exhibit local refinement [2]. In the case of MAs "memes" refer to the strategies (e.g. local refinement, perturbation or constructive methods, etc) that are employed to improve individuals. In this paper we review some works on the application of MAs to well known combinatorial optimisation problems, and place them in a framework defined by a general syntactic model. This model provides us with a classification scheme based on a computable index D, which facilitates algorithmic comparisons and suggests areas for future research. Also, by having an abstract model for this class of meta-heuristics it is possible to explore their design space and better understand their behaviour from a theoretical standpoint. We illustrate the theoretical and practical relevance of this model and taxonomy for MAs in the context of a discussion of important design issues that must be addressed to produce effective and efficient Memetic Algorithms.

Abstract-This paper investigates a genetic algorithm based hyperheuristic (hyper-GA) for scheduling geographically distributed training staff and courses. The aim of the hyper-GA is to evolve a good-quality heuristic for each given instance of the problem and use this to find a solution by applying a suitable ordering from a set of low-level heuristics. Since the user only supplies a number of low-level problem-specific heuristics and an evaluation function, the hyperheuristic can easily be reimplemented for a different type of problem, and we would expect it to be robust across a wide range of problem instances. We show that the problem can be solved successfully by a hyper-GA, presenting results for four versions of the hyper-GA as well as a range of simpler heuristics and applying them to five test data set 1.

We consider a simplification of a typical university course timetabling problem involving three types of hard and three types of soft constraints. A MAX-MIN Ant System, which makes use of a separate local search routine, is proposed for tackling this problem. We devise an appropriate construction graph and pheromone matrix representation after considering alternatives. The resulting algorithm is tested over a set of eleven instances from three classes of the problem. The results demonstrate that the ant system is able to construct significantly better timetables than an algorithm that iterates the local search procedure from random starting solutions.

In this paper we introduce a Monte Carlo based hyper-heuristic. The Monte Carlo hyper-heuristic manages a set of low level heuristics (in this case just simple 2-opt swaps but they could be any other heuristics). Each of the low level heuristics is responsible for creating a unique neighbour that may be impossible to create by the other low level heuristics. On each iteration, the Monte Carlo hyper heuristic randomly calls a low level heuristic. The new solution returned by the low level heuristic will be accepted based on the Monte Carlo acceptance criteria. The Monte Carlo acceptance criteria always accept an improved solution. Worse solutions will be accepted with a certain probability, which decreases with worse solutions, in order to escape local minima. We develop three hyper-heuristics based on a Monte Carlo method, these being Linear Monte Carlo Exponential Monte Carlo and Exponential Monte Carlo with counter. We also investigate four other hyperheuristics to examine their performance and for comparative purposes. To demonstrate our approach we employ these hyper-heuristics to optimise component placement sequencing in order to improve the efficiency of the multi head placement machine. Experimental results show that the Exponential Monte Carlo hyperheuristic is superior to the other hyper-heuristics and is superior to a choice function hyper-heuristic reported in earlier work.

Abstract 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

The bin-packing problem is a well known NP-Hard optimisation problem, and, over the years, many heuristics have been developed to generate good quality solutions. This paper outlines a genetic programming system which evolves a heuristic that decides whether to put a piece in a bin when presented with the sum of the pieces already in the bin and the size of the piece that is about to be packed. This heuristic operates in a fixed framework that iterates through the open bins, applying the heuristic to each one, before deciding which bin to use. The best evolved programs emulate the functionality of the human designed `first-fit' heuristic. Thus, the contribution of this paper is to demonstrate that genetic programming can be employed to automatically evolve bin packing heuristics which are the same as high quality heuristics which have been designed by humans.

This paper is concerned with the d2 elopment of a mechanism for automatically setting the parameters as well as refining the choice function. Tod o so we apply the hyperheuristic to a real-world personnel sched5qUW problem, that of schedUEI: a sales summit. The remaind5 of the paper is structured as follows. We firstd escribe and formulate the sales summit schedI/Eq problem. This is followed by thed25H iption of our parameter-free hyperheuristic approach in section 3. Section 4 is d2 oted to experimental resultsand section 5concludx the paper. 2 The Sales Summit Scheduling Problem The sales summit sched uling problem is that of a commercial company that organises sales summits which involve two groups of company representatives: suppliers, who want to sell prodfifi/ or services, delegates who are representatives of companies that are potentially interested in purchasing the prod:qH and services. Suppliers pay a registration fee to have a stand at the sales summit and provid a list of thed2qIUUfi2 that they would like to meet. A meeting (between oned elegate and one supplier) is classified as Priority or Non-Priority d2 endEE on how strongly the supplier would like to meet thed elegate. Delegates pay no fee but instead cost money to the commercial company who pays for their travelling and hotel expenses. Besid2 meetings, seminars are organised whered elegates may meet otherd elegates. Eachd elegate providE a list of the seminars that he/she would like to attend and (if he/she is invited to the summit) is guaranteed attend nce to all seminars. In this instance of the sales summit schedI//H problem there are 4 meeting timeslots available for both seminars and meetings, where each seminar lasts three times as long as a supplier/d55W ate meeting. There are 43 suppliers, 99 ...

It is possible to argue that online bin packing heuristics should be evaluated by using metrics based on their performance over the set of all bin packing problems, such as the worst case or average case performance. However, this method of assessing a heuristic would only be relevant to a user who employs the heuristic over a set of problems which is actually representative of the set of all possible bin packing problems. On the other hand, a real world user will often only deal with packing problems that are representative of a particular sub-set. Their piece sizes will all belong to a particular distribution. The contribution of this paper is to show that a Genetic Programming system can automate the process of heuristic generation and produce heuristics that are human-competitive over a range of sets of problems, or which excel on a particular sub-set. We also show that the choice of training instances is vital in the area of automatic heuristic generation, due to the trade-off between the performance and generality of the heuristics generated and their applicability to new problems.