Katherine Malan

A survey of techniques for characterising fitness landscapes and some possible ways forward

Real-world optimisation problems are often very complex. Metaheuristics have been successful in solving many of these problems, but the difficulty in choosing the best approach can be a huge challenge for practitioners. One approach to this dilemma is to use fitness landscape analysis to better understand problems before deciding on approaches to solving the problems. However, despite extensive research on fitness landscape analysis and a large number of developed techniques, very few techniques are used in practice. This could be because fitness landscape analysis in itself can be complex. In an attempt to make fitness landscape analysis techniques accessible, this paper provides an overview of techniques from the 1980s to the present. Attributes that are important for practical implementation are highlighted and ways of adapting techniques to be more feasible or appropriate are suggested. The survey reveals the wide range of factors that can influence problem difficulty, emphasising the need for a shift in focus away from predicting problem hardness towards measuring characteristics. It is hoped that this survey will invoke renewed interest in the field of understanding complex optimisation problems and ultimately lead to better decision making on the use of appropriate metaheuristics.

Quantifying ruggedness of continuous landscapes using entropy

A major unsolved problem in the field of optimisation and computational intelligence is how to determine which algorithms are best suited to solving which problems. This research aims to analytically characterise individual problems as a first step towards attempting to link problem types with the algorithms best suited to solving them. In particular, an information theoretic technique for analysing the ruggedness of a fitness landscape with respect to neutrality was adapted to work in continuous landscapes and to output a single measure of ruggedness. Experiments run on test functions with increasing ruggedness show that the proposed measure of ruggedness produced relative values consistent with a visual inspection of the problem landscapes. Combined with other measures of complexity, the proposed ruggedness measure could be used to more broadly characterise the complexity of fitness landscapes in continuous domains.

Adaptive Genetic Programming for dynamic classification problems

This paper investigates the feasibility of using Genetic Programming in dynamically changing environments to evolve decision trees for classification problems and proposes an new version of Genetic Programming called Adaptive Genetic Programming. It does so by comparing the performance or classification error of Genetic Programming and Adaptive Genetic Programming to that of Gradient Descent in abruptly and progressively changing environments. To cope with dynamic environments, Adaptive Genetic Programming incorporates adaptive control parameters, variable elitism and culling. Results show that both Genetic Programming and Adaptive Genetic Programming are viable algorithms for dynamic environments yielding a performance gain over Gradient Descent for lower dimensional problems even with severe environment changes. In addition, Adaptive Genetic Programming performs slightly better than Genetic Programming, due to faster recovery from changes in the environment.

Fitness Landscape Analysis for Metaheuristic Performance Prediction

Metaheuristics have become popular for solving complex optimisation problems where classical techniques are either infeasible or perform poorly. Despite many success stories, it is well known that metaheuristics sometimes fail and that researchers and practitioners frequently resort to trial and error to find an appropriate algorithm or setting to solve a given problem. Within the framework of the general algorithm selection problem, this chapter addresses the feasibility of predicting algorithm performance on unknown real-valued problems based on fitness landscape features. Normalized metrics are proposed for quantifying algorithm performance on known problems to generate suitable training data. Performance metrics are tested using a standard particle swarm optimisation algorithm and are investigated alongside three existing fitness landscape measures. This preliminary investigation highlights the need for a shift in focus away from predicting general problem hardness towards characterising problems where each fitness landscape technique has value as a part-predictor of algorithm performance.

Ruggedness, funnels and gradients in fitness landscapes and the effect on PSO performance

Fitness landscape analysis has focussed on many different aspects of optimisation problems such as ruggedness, neutrality, epistasis and evolvability. Although many techniques have been proposed, there are very few that have been shown to be practically useful as predictors of algorithm performance. This paper investigates three metrics related to the structure of fitness landscapes of continuous problems: a ruggedness measure based on entropy, a dispersion index measure for detecting the presence of funnels and a new proposed technique for estimating gradients. Results on a range of benchmark problems show that all proposed measures show some correlation to performance of a traditional particle swarm optimisation (PSO) algorithm on the same benchmark problems. The three metrics could therefore have value as part-predictors of PSO performance on unknown problems if used in conjunction with measures approximating other features that have been linked to problem difficulty for PSOs.

A progressive random walk algorithm for sampling continuous fitness landscapes

A number of fitness landscape analysis approaches are based on random walks through discrete search spaces. Applying these approaches to real-encoded problems requires the notion of a random walk in continuous space. This paper proposes a progressive random walk algorithm and the use of multiple walks to sample neighbourhood structure in continuous multi-dimensional spaces. It is shown that better coverage of a search space is provided by progressive random walks than simple unbiased random walks.

Particle swarm optimisation failure prediction based on fitness landscape characteristics

Particle swarm optimisation (PSO) algorithms have been successfully used to solve many complex real-world optimisation problems. Since their introduction in 1995, the focus of research in PSOs has largely been on the algorithmic side with many new variations proposed on the original PSO algorithm. Relatively little attention has been paid to the study of problems with respect to PSO performance. The aim of this study is to investigate whether a link can be found between problem characteristics and algorithm performance for PSOs. A range of benchmark problems are numerically characterised using fitness landscape analysis techniques. Decision tree induction is used to develop failure prediction models for seven different variations on the PSO algorithm. Results show that for most PSO models, failure could be predicted to a fairly high level of accuracy. The resulting prediction models are not only useful as predictors of failure, but also provide insight into the algorithms themselves, especially when expressed as fuzzy rules in terms of fitness landscape features.

Characterising the searchability of continuous optimisation problems for PSO

The focus of research in swarm intelligence has been largely on the algorithmic side with relatively little attention being paid to the study of problems and the behaviour of algorithms in relation to problems. When a new algorithm or variation on an existing algorithm is proposed in the literature, there is seldom any discussion or analysis of algorithm weaknesses and on what kinds of problems the algorithm is expected to fail. Fitness landscape analysis is an approach that can be used to analyse optimisation problems. By characterising problems in terms of fitness landscape features, the link between problem types and algorithm performance can be studied. This article investigates a number of measures for analysing the ability of a search process to improve fitness on a particular problem (called evolvability in literature but referred to as searchability in this study to broaden the scope to non-evolutionary-based search techniques). A number of existing fitness landscape analysis techniques originally proposed for discrete problems are adapted to work in continuous search spaces. For a range of benchmark problems, the proposed searchability measures are viewed alongside performance measures for a traditional global best particle swarm optimisation (PSO) algorithm. Empirical results show that no single measure can be used as a predictor of PSO performance, but that multiple measures of different fitness landscape features can be used together to predict PSO failure.

Analysis of stagnation behavior of vector evaluated particle swarm optimization

The vector evaluated particle swarm optimization (VEPSO) algorithm is a cooperative, multi-swarm algorithm. Each sub-swarm optimizes only a single objective of a multi-objective problem (MOP), and implements a knowledge transfer strategy (KTS) to share optimal positions of the different objectives among the sub-swarms, guiding the particles to different regions of the Pareto front. This paper shows that the stagnation problem that occurs in VEPSO can be addressed by using a different KTS. A comparison is made between the ring-based and random knowledge transfer strategies. Experimental results show that the random knowledge transfer strategy suffers less from stagnation than the ring-based KTS, making it the preferred KTS to use.

Steep gradients as a predictor of PSO failure

There are many features of optimisation problems that can influence the difficulty for search algorithms. This paper investigates the steepness of gradients in a fitness landscape as an additional feature that can be linked to difficulty for particle swarm optimisation (PSO) algorithms. The performances of different variations of PSO algorithms on a range of benchmark problems are considered against average estimations of gradients based on random walks. Results show that all variations of PSO failed to solve problems with estimated steep gradients in higher dimensions.