Abstract
AbstractAdvanced optimization algorithms with a variety of configurable parameters become increasingly difficult to apply effectively to solving optimization problems. Appropriate algorithm configuration becomes highly relevant, still remaining a computationally expensive operation. Development of machine learning methods allows to model and predict the efficiency of different solving strategies and algorithm configurations depending on properties of optimization problem to be solved. The paper suggests the Dependency Decomposition approach to reduce computational complexity of modeling the efficiency of optimization algorithm, also considering the amount of computational resources available for optimization problem solving. The approach requires development of explicit Exploratory Landscape Analysis methods to assess a variety of significant characteristic features of optimization problems. The results of feature assessment depend on the number of sample points analyzed and their location in the design space, on top of that some of methods require additional evaluations of objective function. The paper proposes new landscape analysis methods based on given points without the need of any additional objective function evaluations. An algorithm of building a so-called Full Variability Map is suggested based on informativeness criteria formulated for groups of sample points. The paper suggests Generalized Information Content method for analysis of Full Variability Map which allows to get accurate and stable estimations of objective function features. The Sectorization method of Variability Map analysis is proposed to assess characteristic features reflecting such properties of objective function that are critical for optimization algorithm efficiency. The resulting features are invariant to the scale of objective function gradients which positively affects the generalizing ability of problems classification algorithm. The procedure of the comparative study of effectiveness of landscape analysis algorithms is introduced. The results of computational experiments indicate reliability of applying the suggested landscape analysis methods to optimization problem characterization and classification.
Highlights
Modern systems of automated design and engineering analysis include programs that implement advanced algorithms of continuous global optimization
Characterization algorithms are produced on the basis of Full Variability Map (FVM) analysis method by setting values of the corresponding characterizing function that will be used as components of C vector
The general template of methods of assessing optimization problem features based on the results of FVM analysis has the following steps: 1. collect the landscape sample points Xi, i ∈ [1 : n] and calculate the corresponding objective values fi, 2. build a FVM for the landscape sample using the algorithm provided in section 3.3, 3. according to the chosen characterization algorithm calculate the required values of the characterizing function, 4. compose the resulting vector C of problem’s features based of the values obtained
Summary
Modern systems of automated design and engineering analysis include programs that implement advanced algorithms of continuous global optimization. Characteristic features are assessed according to characterization algorithm by an expert and/or automatically, based on landscape sample, which is the result of f (X) function evaluations at some points of the search domain DX. The landscape sample points after being processed for the assessment of problem features can be used at the initialization stage of optimization algorithm, for example, to build an initial approximating model of an objective function in the case of Surrogate Based Optimization [7]. The strategy can include simple continuous, integer or categorical parameters as well as complex control parameters, for example, the rule of adaptive changing of simple parameters values during the problem solving process [8]. It presents a new approach to optimization algorithm configuration with characteristic features assessment powered by Variability Map based methods of exploratory landscape analysis. In the last part of this work, the procedure of assessing efficiency of landscape analysis algorithms is proposed and the computational experiment results are presented
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