Solving a set of global optimization problems by the parallel technique with uniform convergence

Barkalov, Konstantin; Strongin, Roman G.

doi:10.1007/s10898-017-0555-4

Cited by 21 publications

(9 citation statements)

References 21 publications

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“…There exist a lot of algorithms for solving global optimization problems (see, e.g., [1,2,14] for parallel optimization, [9,13] for dimensionality reduction schemes, [10,11,25] for numerical solution of real-life optimization problems, [21] for simplicial optimization methods, [15,35,36] for stochastic optimization methods, [16,17,22,32] for univariate Lipschitz global optimization, [23] for interval branch-and-bound methods, etc. Among them, there can be distinguished two groups of algorithms: nature-inspired metaheuristic algorithms (as, for instance, genetic algorithm, firefly algorithm, particle swarm optimization, etc.…”

Section: Statement Of the Optimization Problemmentioning

confidence: 99%

An Experimental Study of Univariate Global Optimization Algorithms for Finding the Shape Parameter in Radial Basis Functions

Mukhametzhanov

Cavoretto²,

Rossi³

2020

Communications in Computer and Information Science

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In this contribution, an interpolation problem using radial basis functions is considered. A recently proposed approach for the search of the optimal value of the shape parameter is studied. The approach consists of using global optimization algorithms to minimize the error function obtained using a leave-one-out cross validation (LOOCV) technique, which is commonly used for solving machine learning problems. In this paper, the proposed approach is studied experimentally on classes of randomly generated test problems using the GKLS-generator, which is widely used for testing global optimization algorithms. The experimental study on classes of randomly generated test problems is very important from the practical point of view, since results show the behavior of the algorithms for solving not a single test problem, but the whole class with controllable difficulty, which is the main property of the GKLS-generator. The obtained results are relevant, since the experiments have been carried out on 200 randomized test problems, and show that the algorithms are efficient for solving difficult real-life problems demonstrating a promising behavior.

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Section: Statement Of the Optimization Problemmentioning

confidence: 99%

An Experimental Study of Univariate Global Optimization Algorithms for Finding the Shape Parameter in Radial Basis Functions

Mukhametzhanov

Cavoretto²,

Rossi³

2020

Communications in Computer and Information Science

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“…a currently available solution obtained by engineers using practical reasons, global optimization problems are considered (see [1,10,13,17,18,28,34,40,42,43,44]). Unfortunately, very often a practical global optimization process is performed under a limited budget, i.e., the number of allowed evaluations of the objective function f (x) is fixed a priori and is not very high (see a detailed discussion in [37]) requiring so an accurate development of fast global optimization methods (see, e.g., [2,3,15,23,27,34,40,44]).…”

Section: Introductionmentioning

confidence: 99%

“…Since Lipschitz continuity is a quite natural assumption for applied problems (specifically for technical systems, see, e.g., [14,17,21,28,34,40]), we consider here objective functions that satisfy the Lipschitz condition over the search domain D. Thus, our problem becomes Lipschitz global optimization problem broadly studied in the literature (see, e.g., [2,12,14,15,18,21,28,33,34,40] and references given therein). In this paper, we propose a new Lipschitz-based safe global optimization algorithm, specifically designed to work in the noisy setting.…”

Section: Introductionmentioning

confidence: 99%

Safe global optimization of expensive noisy black-box functions in the $δ$-Lipschitz framework

Sergeyev,

Candelieri,

Kvasov

et al. 2019

Preprint

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In this paper, the problem of safe global maximization (it should not be confused with robust optimization) of expensive noisy black-box functions satisfying the Lipschitz condition is considered. The notion "safe" means that the objective function f (x) during optimization should not violate a "safety" threshold, for instance, a certain a priori given value h in a maximization problem. Thus, any new function evaluation must be performed at "safe points" only, namely, at points y for which it is known that the objective function f (y) > h. The main difficulty here consists in the fact that the used optimization algorithm should ensure that the safety constraint will be satisfied at a point y before evaluation of f (y) will be executed. Thus, it is required both to determine the safe region Ω within the search domain D and to find the global maximum within Ω. An additional difficulty consists in the fact that these problems should be solved in the presence of the noise. This paper starts with a theoretical study of the problem and it is shown that even though the objective function f (x) satisfies the Lipschitz condition, traditional Lipschitz minorants and majorants cannot be used due to the presence of the noise. Then, a δ -Lipschitz framework and two algorithms using it are proposed to solve the safe global maximization problem. The first method determines the safe area within the search domain and the second one executes the global maximization over the found safe region. For both methods a number of theoretical results related to their functioning and convergence is established. Finally, numerical experiments confirming the reliability of the proposed procedures are performed.

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“…• In the article [2], the authors consider solving a set of global optimization problems in parallel. It is shown that the algorithm they propose provides a uniform convergence to the set of solutions for all problems treated simultaneously.…”

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confidence: 99%

Guest editors’ preface to the special issue devoted to the 2nd International Conference “Numerical Computations: Theory and Algorithms”, June 19–25, 2016, Pizzo Calabro, Italy

2018

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Solving a set of global optimization problems by the parallel technique with uniform convergence

Cited by 21 publications

References 21 publications

An Experimental Study of Univariate Global Optimization Algorithms for Finding the Shape Parameter in Radial Basis Functions

An Experimental Study of Univariate Global Optimization Algorithms for Finding the Shape Parameter in Radial Basis Functions

Safe global optimization of expensive noisy black-box functions in the $δ$-Lipschitz framework

Guest editors’ preface to the special issue devoted to the 2nd International Conference “Numerical Computations: Theory and Algorithms”, June 19–25, 2016, Pizzo Calabro, Italy

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