Gabriela Ochoa

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 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 an overview of previous categorisations of hyper-heuristics and provide a unified classification and definition, which capture 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 goals are to clarify the mainfeatures of existing techniques and to suggest new directions for hyper-heuristic research.

Exploring Hyper-heuristic Methodologies with Genetic Programming

Hyper-heuristics represent a novel search methodology that is motivated by the goal of automating the process of selecting or combining simpler heuristics in order to solve hard computational search problems. An extension of the original hyper-heuristic idea is to generate new heuristics which are not currently known. These approaches operate on a search space of heuristics rather than directly on a search space of solutions to the underlying problem which is the case with most meta-heuristics implementations. In the majority of hyper-heuristic studies so far, a framework is provided with a set of human designed heuristics, taken from the literature, and with good measures of performance in practice. A less well studied approach aims to generate new heuristics from a set of potential heuristic components. The purpose of this chapter is to discuss this class of hyper-heuristics, in which Genetic Programming is the most widely used methodology. A detailed discussion is presented including the steps needed to apply this technique, some representative case studies, a literature review of related work, and a discussion of relevant issues. Our aim is to convey the exciting potential of this innovative approach for automating the heuristic design process.

HyFlex: a benchmark framework for cross-domain heuristic search

This paper presents HyFlex, a software framework for the development of cross-domain search methodologies. The framework features a common software interface for dealing with different combinatorial optimisation problems and provides the algorithm components that are problem specific. In this way, the algorithm designer does not require a detailed knowledge of the problem domains and thus can concentrate his/her efforts on designing adaptive general-purpose optimisation algorithms. Six hard combinatorial problems are fully implemented: maximum satisfiability, one dimensional bin packing, permutation flow shop, personnel scheduling, traveling salesman and vehicle routing. Each domain contains a varied set of instances, including real-world industrial data and an extensive set of state-of-the-art problem specific heuristics and search operators. HyFlex represents a valuable new benchmark of heuristic search generality, with which adaptive cross-domain algorithms are being easily developed and reliably compared.This article serves both as a tutorial and a as survey of the research achievements and publications so far using HyFlex.

A Reinforcement Learning-Great-Deluge Hyper-Heuristic for Examination Timetabling

Hyper-heuristics can be identified as methodologies that search the space generated by a finite set of low level heuristics for solving search problems. An iterative hyper-heuristic framework can be thought of as requiring a single candidate solution and multiple perturbation low level heuristics. An initially generated complete solution goes through two successive processes heuristic selection and move acceptance until a set of termination criteria is satisfied. A motivating goal of hyper-heuristic research is to create automated techniques that are applicable to a wide range of problems with different characteristics. Some previous studies show that different combinations of heuristic selection and move acceptance as hyper-heuristic components might yield different performances. This study investigates whether learning heuristic selection can improve the performance of a great deluge based hyper-heuristic using an examination timetabling problem as a case study.

Local Optima Networks of NK Landscapes With Neutrality

In previous work, we have introduced a network based model that abstracts many details of the underlying landscape and compresses the landscape information into a weighted, oriented graph which we call the local optima network. The vertices of this graph are the local optima of the given fitness landscape, while the arcs are transition probabilities between local optima basins. Here, we extend this formalism to neutral fitness landscapes, which are common in difficult combinatorial search spaces. The study is based on two neutral variants of the well-known NK family of landscapes (where N stands for the chromosome length, and K for the number of gene epistatic interactions within the chromosome). By using these two NK variants, probabilistic (NKp), and quantified NK (NKq), in which the amount of neutrality can be tuned by a parameter, we show that our new definitions of the optima networks and the associated basins are consistent with the previous definitions for the non-neutral case. Moreover, our empirical study and statistical analysis show that the features of neutral landscapes interpolate smoothly between landscapes with maximum neutrality and non-neutral ones. We found some unknown structural differences between the two studied families of neutral landscapes. But overall, the network features studied confirmed that neutrality, in landscapes with percolating neutral networks, may enhance heuristic search. Our current methodology requires the exhaustive enumeration of the underlying search space. Therefore, sampling techniques should be developed before this analysis can have practical implications. We argue, however, that the proposed model offers a new perspective into the problem difficulty of combinatorial optimization problems and may inspire the design of more effective search heuristics.

Contrasting meta-learning and hyper-heuristic research: the role of evolutionary algorithms

The fields of machine meta-learning and hyper-heuristic optimisation have developed mostly independently of each other, although evolutionary algorithms (particularly genetic programming) have recently played an important role in the development of both fields. Recent work in both fields shares a common goal, that of automating as much of the algorithm design process as possible. In this paper we first provide a historical perspective on automated algorithm design, and then we discuss similarities and differences between meta-learning in the field of supervised machine learning (classification) and hyper-heuristics in the field of optimisation. This discussion focuses on the dimensions of the problem space, the algorithm space and the performance measure, as well as clarifying important issues related to different levels of automation and generality in both fields. We also discuss important research directions, challenges and foundational issues in meta-learning and hyper-heuristic research. It is important to emphasize that this paper is not a survey, as several surveys on the areas of meta-learning and hyper-heuristics (separately) have been previously published. The main contribution of the paper is to contrast meta-learning and hyper-heuristics methods and concepts, in order to promote awareness and cross-fertilisation of ideas across the (by and large, non-overlapping) different communities of meta-learning and hyper-heuristic researchers. We hope that this cross-fertilisation of ideas can inspire interesting new research in both fields and in the new emerging research area which consists of integrating those fields.

Iterated local search vs. hyper-heuristics: Towards general-purpose search algorithms

An important challenge within hyper-heuristic research is to design search methodologies that work well, not only across different instances of the same problem, but also across different problem domains. This article conducts an empirical study involving three different domains in combinatorial optimisation: bin packing, permutation flow shop and personnel scheduling. Using a common software interface (HyFlex), the same algorithms (high-level strategies or hyper-heuristics) can be readily run on all of them. The study is intended as a proof of concept of the proposed interface and domain modules, as a benchmark for testing the generalisation abilities of heuristic search algorithms. Several algorithms and variants from the literature were implemented and tested. From them, the implementation of iterated local search produced the best overall performance. Interestingly, this is one of the most conceptually simple competing algorithms, its advantage as a robust algorithm is probably due to two factors: (i) the simple yet powerful exploration/exploitation balance achieved by systematically combining a perturbation followed by local search; and (ii) its parameter-less nature. We believe that the challenge is still open for the design of robust algorithms that can learn and adapt to the available low-level heuristics, and thus select and apply them accordingly.

On Genetic Algorithms and Lindenmayer Systems

This paper describes a system for simulating the evolution of artificial 2D plant morphologies. Virtual plant genotypes are inspired by the mathematical formalism known as Lindenmayer systems (L-systems). The phenotypes are the branching structures resulting from the derivation and graphic interpretation of the genotypes. Evolution is simulated using a genetic algorithm with a fitness function inspired by current evolutionary hypotheses concerning the factors that have had the greatest effect on plant evolution. The system also provides interactive selection, allowing the user to direct simulated evolution towards preferred phenotypes. Simulation results demonstrate many interesting structures, suggesting that artificial evolution constitutes a powerful tool for (1) exploring the large, complex space of branching structures found in nature, and (2) generating novel ones. Finally, we emphasize that Lindenmayer systems constitute a highly suitable encoding for artificial evolution studies.

Complex-network analysis of combinatorial spaces: the NK landscape case.

We propose a network characterization of combinatorial fitness landscapes by adapting the notion of inherent networks proposed for energy surfaces. We use the well-known family of NK landscapes as an example. In our case the inherent network is the graph whose vertices represent the local maxima in the landscape, and the edges account for the transition probabilities between their corresponding basins of attraction. We exhaustively extracted such networks on representative NK landscape instances, and performed a statistical characterization of their properties. We found that most of these network properties are related to the search difficulty on the underlying NK landscapes with varying values of K .