When Does Dependency Modelling Help? Using a Randomized Landscape Generator to Compare Algorithms in Terms of Problem Structure

Morgan, Rachael; Gallagher, Marcus

doi:10.1007/978-3-642-15844-5_10

Cited by 5 publications

(15 citation statements)

References 14 publications

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“…Counter to our assumption and intuition, the results show no obvious trend between the angle of component rotation and the fitness difference between the two algorithms. This lack of trend was also evident in the results in Morgan and Gallagher (2010). However, the distribution of the results in Figure 4 shows that the majority of points have fitness differences concentrated between 0 and -0.05 and skewed in favor of EMNA (negative values), indicating that EMNA tends to slightly outperform UMDA c on average.…”

Section: Algorithm Performance With Respect To Degree Of Landscape Comentioning

confidence: 47%

“…Each algorithm used a population size of 50, a selection threshold of 0.8, and was run for 50 generations. Note that this repeats the set of experiments described in Morgan and Gallagher (2010), but while analyzing these previous results, we discovered an error in the implementation of the EMNA algorithm. The effect of this error was that EMNA was being initialized in [−3, 1] 2 while UMDA c was (correctly) initialized in [−1, 1] 2 .…”

Section: Algorithm Performance With Respect To Degree Of Landscape Comentioning

confidence: 57%

“…Section 6 concludes the paper. This paper is based in part on the work presented in Morgan and Gallagher (2010) but contains significant revisions and extensions.…”

Section: Introductionmentioning

confidence: 98%

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

Morgan

Gallagher

2012

Evolutionary Computation

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In this paper we extend a previously proposed randomized landscape generator in combination with a comparative experimental methodology to study the behavior of continuous metaheuristic optimization algorithms. In particular, we generate two-dimensional landscapes with parameterized, linear ridge structure, and perform pairwise comparisons of algorithms to gain insight into what kind of problems are easy and difficult for one algorithm instance relative to another. We apply this methodology to investigate the specific issue of explicit dependency modeling in simple continuous estimation of distribution algorithms. Experimental results reveal specific examples of landscapes (with certain identifiable features) where dependency modeling is useful, harmful, or has little impact on mean algorithm performance. Heat maps are used to compare algorithm performance over a large number of landscape instances and algorithm trials. Finally, we perform a meta-search in the landscape parameter space to find landscapes which maximize the performance between algorithms. The results are related to some previous intuition about the behavior of these algorithms, but at the same time lead to new insights into the relationship between dependency modeling in EDAs and the structure of the problem landscape. The landscape generator and overall methodology are quite general and extendable and can be used to examine specific features of other algorithms.

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Section: Algorithm Performance With Respect To Degree Of Landscape Comentioning

confidence: 47%

Section: Algorithm Performance With Respect To Degree Of Landscape Comentioning

confidence: 57%

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

Morgan

Gallagher

2012

Evolutionary Computation

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“…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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Fitness Landscape-Based Characterisation of Nature-Inspired Algorithms

Crossley

Nisbet

Amos

2013

Adaptive and Natural Computing Algorithms

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A significant challenge in nature-inspired algorithmics is the identification of specific characteristics of problems that make them harder (or easier) to solve using specific methods. The hope is that, by identifying these characteristics, we may more easily predict which algorithms are best-suited to problems sharing certain features. Here, we approach this problem using fitness landscape analysis. Techniques already exist for measuring the "difficulty" of specific landscapes, but these are often designed solely with evolutionary algorithms in mind, and are generally specific to discrete optimisation. In this paper we develop an approach for comparing a wide range of continuous optimisation algorithms. Using a fitness landscape generation technique, we compare six different nature-inspired algorithms and identify which methods perform best on landscapes exhibiting specific features.Comment: 10 pages, 1 figure, submitted to the 11th International Conference on Adaptive and Natural Computing Algorithm

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When Does Dependency Modelling Help? Using a Randomized Landscape Generator to Compare Algorithms in Terms of Problem Structure

Cited by 5 publications

References 14 publications

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

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

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

Fitness Landscape-Based Characterisation of Nature-Inspired Algorithms

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