Using Landscape Topology to Compare Continuous Metaheuristics: A Framework and Case Study on EDAs and Ridge Structure

Morgan, Rachael; Gallagher, Marcus

doi:10.1162/evco_a_00070

Cited by 10 publications

(8 citation statements)

References 26 publications

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“…The aforementioned studies focus on developing benchmark problems, there are also many studies that focus on developing methods for analyzing existing benchmark problems based on features of the fitness landscape. A length scale was introduced to measure the ratio of changes in the objective function value to steps between points in the search space [41]. A random increasing walk method was proposed to measure the ruggedness of the fitness landscape [38].…”

Section: ) Summary and Discussionmentioning

confidence: 99%

An Open Framework for Constructing Continuous Optimization Problems

Nguyễn

Zeng

et al. 2019

IEEE Trans. Cybern.

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Many artificial benchmark problems have been proposed for different kinds of continuous optimization, e.g., global optimization, multimodal optimization, multiobjective optimization, dynamic optimization, and constrained optimization. However, there is no unified framework for constructing these types of problems and possible properties of many problems are not fully tunable. This will cause difficulties for researchers to analyze strengths and weaknesses of an algorithm. To address these issues, this paper proposes a simple and intuitive framework, which is able to construct different kinds of problems for continuous optimization. The framework utilizes the k-d tree to partition the search space and sets a certain number of simple functions in each subspace. The framework is implemented into global/multimodal optimization, dynamic single objective optimization, multiobjective optimization, and dynamic multiobjective optimization, respectively. Properties of the proposed framework are discussed and verified with traditional evolutionary algorithms.

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Section: ) Summary and Discussionmentioning

confidence: 99%

An Open Framework for Constructing Continuous Optimization Problems

Nguyễn

Zeng

et al. 2019

IEEE Trans. Cybern.

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show abstract

“…The only user-parameters to be specified are the population size and selection threshold. The algorithm has been studied theoretically [67,68,162,163] as well as experimentally [102,60,116,117]. The updates to the factorized model parameters are efficient and implementation is straightforward.…”

Section: Univariate Marginal Distribution Algorithmmentioning

confidence: 99%

“…Specifically, variable dependencies can be captured via pairwise covariance parameters. Experimentally, EMNA global has been shown to give improved performance over UMDA c on at least some specific problems where significant dependencies are known to exist [102,60,116,117]. However, these results also show that the relative success of EMNA global is related to several factors, such as the "nature" of the dependencies between variables as well as the algorithm parameters chosen.…”

Section: )mentioning

confidence: 99%

Data-driven analysis of variables and dependencies in continuous optimization problems and estimation of distribution algorithms

Mishra¹

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Optimization problems occur widely in various domains and are of great practical importance. Better solutions to optimization problems translate into increased production or efficiency, or less waste or error. As a result, the development of optimization algorithms is a large and active area of research. Although there is a large amount of theory and techniques for solving optimization problems, there are also many open issues and questions in understanding the relationship between optimization algorithms and the problems that they are applied to.In any optimization problem, the influence of each solution variable on the objective function, as well as the interactions between variables are very important. For example, if the variables in a problem are independent, then it might be efficiently solved by decomposition. If important dependencies exist between variables, an algorithm that is able to capture these dependencies may be able to exploit them to find good solutions. Alternatively, if a variable has a strong influence on the objective function, then an algorithm may be better off focusing its search on this variable, compared with another variable that has very little influence on the objective function.Estimation of Distribution Algorithms (EDAs) are a class of black-box optimization algorithms that learn and sample from a probabilistic model over the solution variables to carry out the search process. The explicit model in an EDA clearly specifies how the algorithm handles problem variables during the search process. A major focus in EDA research has been the incorporation of dependency modeling using models of varying complexity (e.g. probabilistic graphical models). The intuition behind this work is that if the algorithm model is capable and successful at capturing the structure of the problem, it will produce good performance on that problem. Experimental results have confirmed this intuition, for example EDAs that model dependency information have outperformed EDAs that do not model dependencies on certain problems.While EDAs have shown good performance results, little work has analyzed the dynamics of EDA models in practice. In fact, it is not clear what kind of problem structure EDAs can successfully model, or to what extent it is necessary to successfully model problem structure in order to achieve good performance. To provide insight into these issues, a more detailed analysis of EDAs applied to specific problems is needed.In this thesis, an experimental methodology is proposed to analyze the features of variables in continuous optimization problems and continuous EDAs. The approach is based on sampling points from the problem fitness landscape and/or the history of points visited by an EDA during the search process. These samples are then analyzed in three different ways, to identify key structural variables, variable dependencies and important variables. The techniques are used to analyze a variety of test problems and EDAs optimizing the same problem set. The results confirm that the i...

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“…Algorithm performance has also been used to quantify and compare problem similarity [117]. In this approach, an algorithm (or suite of algorithms) is applied to each problem, and the similarity between problems is derived via the similarity in algorithm performance.…”

Section: Measuring Problem Similaritymentioning

confidence: 99%

“…Larger values of a yield functions with steeper, narrower contours, which have been shown to be a problematic landscape structure for certain Estimation of Distribution Algorithms [23,64,117]. Therefore, the elliptical function provides a simple and intuitive landscape from which the ability of the length scale analysis to capture varying levels of eccentricity can be assessed.…”

Section: Elliptical Functionmentioning

confidence: 99%

Analysing and comparing problem landscapes for black-box optimization via length scale

Morgan¹

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Optimization problems are of fundamental practical importance and can be found in almost every aspect of human endeavour. Yet remarkably, we have a very limited understanding of the nature of optimization problems and subsequently of how, why and when different algorithms perform well or poorly. The notion of a problem landscape captures the relationship between the objective function and the problem variables. It is clear that the structure of this landscape is vital in understanding optimization problems, however analysis of this structure presents major challenges. Apart from the often high-dimensionality of problem landscapes, information available in the black-box setting is limited to the solutions in the ii

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Using Landscape Topology to Compare Continuous Metaheuristics: A Framework and Case Study on EDAs and Ridge Structure

Cited by 10 publications

References 26 publications

An Open Framework for Constructing Continuous Optimization Problems

An Open Framework for Constructing Continuous Optimization Problems

Data-driven analysis of variables and dependencies in continuous optimization problems and estimation of distribution algorithms

Analysing and comparing problem landscapes for black-box optimization via length scale

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