Towards the Design of Heuristics by Means of Self-Assembly

The current investigations on hyper-heuristics design have sprung up in two different flavours: heuristics that choose heuristics and heuristics that generate heuristics. In the latter, the goal is to develop a problem-domain independent strategy to automatically generate a good performing heuristic for the problem at hand. This can be done, for example, by automatically selecting and combining different low-level heuristics into a problem specific and effective strategy. Hyper-heuristics raise the level of generality on automated problem solving by attempting to select and/or generate tailored heuristics for the problem at hand. Some approaches like genetic programming have been proposed for this. In this paper, we explore an elegant nature-inspired alternative based on self-assembly construction processes, in which structures emerge out of local interactions between autonomous components. This idea arises from previous works in which computational models of self-assembly were subject to evolutionary design in order to perform the automatic construction of user-defined structures. Then, the aim of this paper is to present a novel methodology for the automated design of heuristics by means of self-assembly

An iterated multi-stage selection hyper-heuristic

There is a growing interest towards the design of reusable general purpose search methods that are applicable to different problems instead of tailored solutions to a single particular problem. Hyper-heuristics have emerged as such high level methods that explore the space formed by a set of heuristics (move operators) or heuristic components for solving computationally hard problems. A selection hyper-heuristic mixes and controls a predefined set of low level heuristics with the goal of improving an initially generated solution by choosing and applying an appropriate heuristic to a solution in hand and deciding whether to accept or reject the new solution at each step under an iterative framework. Designing an adaptive control mechanism for the heuristic selection and combining it with a suitable acceptance method is a major challenge, because both components can influence the overall performance of a selection hyper-heuristic. In this study, we describe a novel iterated multi-stage hyper-heuristic approach which cycles through two interacting hyper-heuristics and operates based on the principle that not all low level heuristics for a problem domain would be useful at any point of the search process. The empirical results on a hyper-heuristic benchmark indicate the success of the proposed selection hyper-heuristic across six problem domains beating the state-of-the-art approach

Solving high school timetabling problems worldwide using selection hyper-heuristics

High school timetabling is one of those recurring NP-hard real-world combinatorial optimisation problems that has to be dealt with by many educational institutions periodically, and so has been of interest to practitioners and researchers. Solving a high school timetabling problem requires scheduling of resources and events into time slots subject to a set of constraints. Recently, an international competition, referred to as ITC 2011 was organised to determine the state-of-the-art approach for high school timetabling. The problem instances, obtained from eight different countries across the world used in this competition became a benchmark for further research in the field. Selection hyper-heuristics are general-purpose improvement methodologies that control/mix a given set of low level heuristics during the search process. In this study, we evaluate the performance of a range of selection hyper-heuristics combining different reusable components for high school timetabling. The empirical results show the success of the approach which embeds an adaptive great-deluge move acceptance method on the ITC 2011 benchmark instances. This selection hyper-heuristic ranks the second among the previously proposed approaches including the ones competed at ITC 2011

A case study of controlling crossover in a selection hyper-heuristic framework using the multidimensional knapsack problem

Hyper-heuristics are high-level methodologies for solving complex problems that operate on a search space of heuristics. In a selection hyper-heuristic framework, a heuristic is chosen from an existing set of low-level heuristics and applied to the current solution to produce a new solution at each point in the search. The use of crossover low-level heuristics is possible in an increasing number of general-purpose hyper-heuristic tools such as HyFlex and Hyperion. However, little work has been undertaken to assess how best to utilise it. Since a single-point search hyper-heuristic operates on a single candidate solution, and two candidate solutions are required for crossover, a mechanism is required to control the choice of the other solution. The frameworks we propose maintain a list of potential solutions for use in crossover. We investigate the use of such lists at two conceptual levels. First, crossover is controlled at the hyper-heuristic level where no problem-specific information is required. Second, it is controlled at the problem domain level where problem-specific information is used to produce good-quality solutions to use in crossover. A number of selection hyper-heuristics are compared using these frameworks over three benchmark libraries with varying properties for an NP-hard optimisation problem: the multidimensional 0-1 knapsack problem. It is shown that allowing crossover to be managed at the domain level outperforms managing crossover at the hyper-heuristic level in this problem domain. © 2016 Massachusetts Institute of Technolog

A tensor-based selection hyper-heuristic for cross-domain heuristic search

Hyper-heuristics have emerged as automated high level search methodologies that manage a set of low level heuristics for solving computationally hard problems. A generic selection hyper-heuristic combines heuristic selection and move acceptance methods under an iterative single point-based search framework. At each step, the solution in hand is modified after applying a selected heuristic and a decision is made whether the new solution is accepted or not. In this study, we represent the trail of a hyper-heuristic as a third order tensor. Factorization of such a tensor reveals the latent relationships between the low level heuristics and the hyper-heuristic itself. The proposed learning approach partitions the set of low level heuristics into two subsets where heuristics in each subset are associated with a separate move acceptance method. Then a multi-stage hyper-heuristic is formed and while solving a given problem instance, heuristics are allowed to operate only in conjunction with the associated acceptance method at each stage. To the best of our knowledge, this is the first time tensor analysis of the space of heuristics is used as a data science approach to improve the performance of a hyper-heuristic in the prescribed manner. The empirical results across six different problem domains from a benchmark indeed indicate the success of the proposed approach

A Classification of Hyper-heuristic Approaches

The current state of the art in hyper-heuristic research comprises a set of approaches that share the common goal of automating the design and adaptation of heuristic methods to solve hard computational search problems. The main goal is to produce more generally applicable search methodologies. In this chapter we present and overview of previous categorisations of hyper-heuristics and provide a unified classification and definition which captures the work that is being undertaken in this field. We distinguish between two main hyper-heuristic categories: heuristic selection and heuristic generation. Some representative examples of each category are discussed in detail. Our goal is to both clarify the main features of existing techniques and to suggest new directions for hyper-heuristic research

A greedy gradient-simulated annealing selection hyper-heuristic

Educational timetabling problem is a challenging real world problem which has been of interest to many researchers and practitioners. There are many variants of this problem which mainly require scheduling of events and resources under various constraints. In this study, a curriculum based course timetabling problem at Yeditepe University is described and an iterative selection hyper-heuristic is presented as a solution method. A selection hyper-heuristic as a high level methodology operates on the space formed by a fixed set of low level heuristics which operate directly on the space of solutions. The move acceptance and heuristic selection methods are the main components of a selection hyper-heuristic. The proposed hyper-heuristic in this study combines a simulated annealing move acceptance method with a learning heuristic selection method and manages a set of low level constraint oriented heuristics. A key goal in hyper-heuristic research is to build low cost methods which are general and can be reused on unseen problem instances as well as other problem domains desirably with no additional human expert intervention. Hence, the proposed method is additionally applied to a high school timetabling problem, as well as six other problem domains from a hyper-heuristic benchmark to test its level of generality. The empirical results show that our easy-to-implement hyper-heuristic is effective in solving the Yeditepe course timetabling problem. Moreover, being sufficiently general, it delivers a reasonable performance across different problem domains

Hyper-heuristic decision tree induction

A hyper-heuristic is any algorithm that searches or operates in the space of heuristics as opposed to the space of solutions. Hyper-heuristics are increasingly used in function and combinatorial optimization. Rather than attempt to solve a problem using a fixed heuristic, a hyper-heuristic approach attempts to find a combination of heuristics that solve a problem (and in turn may be directly suitable for a class of problem instances). Hyper-heuristics have been little explored in data mining. This work presents novel hyper-heuristic approaches to data mining, by searching a space of attribute selection criteria for decision tree building algorithm. The search is conducted by a genetic algorithm. The result of the hyper-heuristic search in this case is a strategy for selecting attributes while building decision trees. Most hyper-heuristics work by trying to adapt the heuristic to the state of the problem being solved. Our hyper-heuristic is no different. It employs a strategy for adapting the heuristic used to build decision tree nodes according to some set of features of the training set it is working on. We introduce, explore and evaluate five different ways in which this problem state can be represented for a hyper-heuristic that operates within a decisiontree building algorithm. In each case, the hyper-heuristic is guided by a rule set that tries to map features of the data set to be split by the decision tree building algorithm to a heuristic to be used for splitting the same data set. We also explore and evaluate three different sets of low-level heuristics that could be employed by such a hyper-heuristic. This work also makes a distinction between specialist hyper-heuristics and generalist hyper-heuristics. The main difference between these two hyperheuristcs is the number of training sets used by the hyper-heuristic genetic algorithm. Specialist hyper-heuristics are created using a single data set from a particular domain for evolving the hyper-heurisic rule set. Such algorithms are expected to outperform standard algorithms on the kind of data set used by the hyper-heuristic genetic algorithm. Generalist hyper-heuristics are trained on multiple data sets from different domains and are expected to deliver a robust and competitive performance over these data sets when compared to standard algorithms. We evaluate both approaches for each kind of hyper-heuristic presented in this thesis. We use both real data sets as well as synthetic data sets. Our results suggest that none of the hyper-heuristics presented in this work are suited for specialization – in most cases, the hyper-heuristic’s performance on the data set it was specialized for was not significantly better than that of the best performing standard algorithm. On the other hand, the generalist hyper-heuristics delivered results that were very competitive to the best standard methods. In some cases we even achieved a significantly better overall performance than all of the standard methods

Multi-stage hyper-heuristics for optimisation problems

There is a growing interest towards self configuring/tuning automated general-purpose reusable heuristic approaches for combinatorial optimisation, such as, hyper-heuristics. Hyper-heuristics are search methodologies which explore the space of heuristics rather than the solutions to solve a broad range of hard computational problems without requiring any expert intervention. There are two common types of hyper-heuristics in the literature: selection and generation methodologies. This work focuses on the former type of hyper-heuristics. Almost all selection hyper-heuristics perform a single point based iterative search over the space of heuristics by selecting and applying a suitable heuristic to the solution in hand at each decision point. Then the newly generated solution is either accepted or rejected using an acceptance method. This improvement process is repeated starting from an initial solution until a set of termination criteria is satisfied. The number of studies on the design of hyper-heuristic methodologies has been rapidly increasing and currently, we already have a variety of approaches, each with their own strengths and weaknesses. It has been observed that different hyper-heuristics perform differently on a given subset of problem instances and more importantly, a hyper-heuristic performs differently as the set of low level heuristics vary. This thesis introduces a general "multi-stage" hyper-heuristic framework enabling the use and exploitation of multiple selection hyper-heuristics at different stages during the search process. The goal is designing an approach utilising multiple hyper-heuristics for a more effective and efficient overall performance when compared to the performance of each constituent selection hyper-heuristic. The level of generality that a hyper-heuristic can achieve has always been of interest to the hyper-heuristic researchers. Hence, a variety of multi-stage hyper-heuristics based on the framework are not only applied to the real-world combinatorial optimisation problems of high school timetabling, multi-mode resource-constrained multi-project scheduling and construction of magic squares, but also tested on the well known hyper-heuristic benchmark of CHeSC 2011. The empirical results show that the multi-stage hyper-heuristics designed based on the proposed framework are still inherently general, easy-to-implement, adaptive and reusable. They can be extremely effective solvers considering their success in the competitions of ITC 2011 and MISTA 2013. Moreover, a particular multi-stage hyper-heuristic outperformed the state-of-the-art selection hyper-heuristic from CHeSC 2011