Adaptive nested optimization scheme for multidimensional global search

Gergel, Victor; Grishagin, Vladimir A.; Gergel, Alexander

doi:10.1007/s10898-015-0355-7

Cited by 48 publications

(11 citation statements)

References 28 publications

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“…In this work, we will use another method based on the nested optimization scheme [34][35][36][37] and its generalization [38,39]. The nested optimization scheme, on the one hand, does not worsen the properties of the objective function (unlike reduction using Peano curves), and, on the other hand, does not require the use of complex data structures to support simplex or diagonal partitions of the feasible region.…”

Section: Problem Statementmentioning

confidence: 99%

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Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning

Barkalov

Lebedev

Kozinov

2021

Entropy

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This paper features the study of global optimization problems and numerical methods of their solution. Such problems are computationally expensive since the objective function can be multi-extremal, nondifferentiable, and, as a rule, given in the form of a “black box”. This study used a deterministic algorithm for finding the global extremum. This algorithm is based neither on the concept of multistart, nor nature-inspired algorithms. The article provides computational rules of the one-dimensional algorithm and the nested optimization scheme which could be applied for solving multidimensional problems. Please note that the solution complexity of global optimization problems essentially depends on the presence of multiple local extrema. In this paper, we apply machine learning methods to identify regions of attraction of local minima. The use of local optimization algorithms in the selected regions can significantly accelerate the convergence of global search as it could reduce the number of search trials in the vicinity of local minima. The results of computational experiments carried out on several hundred global optimization problems of different dimensionalities presented in the paper confirm the effect of accelerated convergence (in terms of the number of search trials required to solve a problem with a given accuracy).

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Section: Problem Statementmentioning

confidence: 99%

“…Another approach is an adaptive scheme, in which all subtasks are solved simultaneously, which allows taking into account much more information about a multidimensional problem, thereby speeding up the process of its solution. This approach was theoretically substantiated and tested in [38,39,42].…”

Section: Adaptive Dimension Reduction Schemementioning

confidence: 99%

Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning

Barkalov

Lebedev

Kozinov

2021

Entropy

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“…Using built-in tools, such as AutoCAD, SolidWorks, FlowVision, ANSYS CFX, etc. in conjunction with the multidimensional optimization methods [7][8] allows manufacturers of pumping equipment to reach a qualitatively new level.…”

Section: Introductionmentioning

confidence: 99%

Optimization Methods to Improve Energy Efficiency of Centrifugal Pumps at Thermal Power Plants

Vikhlyantsev*,

Naumov,

Volkov

et al. 2019

IJRTE

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This article considers the application of engineering optimization methods as a way to improve the energy efficiency of centrifugal pumps operated in thermal power plants taking into account the pump load diagram. The authors present an algorithm of engineering optimization of the wetted part of impeller being an individual working body of a centrifugal pump, as well as the results of approbation of the proposed approach for the centrifugal pump KM 65-50-160 designed in two optimized versions taking into account various options of the pump load diagram. It is revealed that the application of engineering optimization methods allows achieving higher energy efficiency indicators even in a significantly simplified formulation of the problem under consideration. According to the calculation results, when the pump operation condition is met, the KM 65-50-160 pump with an optimized wetted part of the impeller designed in two versions has higher average integral efficiency in comparison with its counterpart designed according to classical methods, namely, 52.24% vs. 49.18%, and 57.9% vs. 57.02%, respectively.

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“…A vast literature is dedicated to the problem (2), (3) and algorithms for its solving (see, e.g., [8,10,11,15,18,29,30,31,34,36,39]). In particular, in practice it can be useful to optimize a scaled function g(x) from (1) instead of the original objective function f (x) (see, e.g., [7,35,41]).…”

Section: Introductionmentioning

confidence: 99%

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

Sergeyev

Kvasov

Mukhametzhanov

2018

Communications in Nonlinear Science and Numerical Simulation

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The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is strong homogeneity meaning that a method produces the same sequences of points where the objective function is evaluated independently both of multiplication of the function by a scaling constant and of adding a shifting constant. In this paper, several aspects of global optimization using strongly homogeneous methods are considered. First, it is shown that even if a method possesses this property theoretically, numerically very small and large scaling constants can lead to illconditioning of the scaled problem. Second, a new class of global optimization problems where the objective function can have not only finite but also infinite or infinitesimal Lipschitz constants is introduced. Third, the strong homogeneity of several Lipschitz global optimization algorithms is studied in the framework of the Infinity Computing paradigm allowing one to work numerically with a variety of infinities and infinitesimals. Fourth, it is proved that a class of efficient univariate methods enjoys this property for finite, infinite and infinitesimal scaling and shifting constants. Finally, it is shown that in certain cases the usage of numerical infinities and infinitesimals can avoid ill-conditioning produced by scaling. Numerical experiments illustrating theoretical results are described.

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Adaptive nested optimization scheme for multidimensional global search

Cited by 48 publications

References 28 publications

Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning

Acceleration of Global Optimization Algorithm by Detecting Local Extrema Based on Machine Learning

Optimization Methods to Improve Energy Efficiency of Centrifugal Pumps at Thermal Power Plants

On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales

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