Globally-biased Disimpl algorithm for expensive global optimization

Paulavičius, Remigijus; Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Žilinskas, Julius

doi:10.1007/s10898-014-0180-4

Cited by 115 publications

(62 citation statements)

References 44 publications

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“…During their work, these methods evaluate only the objective function f (x) from (1) (and do not evaluate f ′ (x) as the SmoothD method does), therefore the operation of executing a trial is less expensive in the DIRECT-type algorithms with respect to that of the new method. The balancing parameter ǫ of the DIRECT and DIRECTl methods (see [10,20]) was set equal to ǫ = 10 −4 , as recommended by many authors (see, e.g., the review of different techniques for setting this parameter in [33]). …”

Section: Operating Characteristics Of the Compared Methodsmentioning

confidence: 99%

“…Regarding the partition strategies (see partitioning operator P on Step 4 in Figure 1), the diagonal partition strategies (see the references in [36,44,45,46]) are taken into account in this paper, although other types of subdivisions are worth to be considered (see, e. g., simplicial partitions in [3,33,34]). In the diagonal approach, the hyperinterval D from (3) is subdivided into a set of smaller hyperintervals, the objective function (and its gradient) is (are) evaluated only at two vertices corresponding to the main diagonal of the generated hyperintervals (see, e. g., vertices a i and b i of a hyperinterval D i in Figure 2), and the results of these trials are used to choose a hyperinterval for subsequent subdivisions.…”

Section: Efficient Partition Strategymentioning

confidence: 99%

“…Since each evaluation of a real-life black-box objective function is usually a time-consuming operation (see, e. g., [19,34,36,45,48,51,54]), the maximal number of function trials executed by the methods until the satisfaction of the stopping criteria (19) was chosen as the main criterion of the comparison (other possible comparison indicators as the number of generated hyperintervals, the average number of trials, and so on can be also used, see, e. g., [33,44,45,48]). …”

Section: Classes Of Test Functions and Comparison Criteriamentioning

confidence: 99%

See 2 more Smart Citations

A deterministic global optimization using smooth diagonal auxiliary functions

Sergeyev

Kvasov

2015

Communications in Nonlinear Science and Numerical Simulation

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In many practical decision-making problems it happens that functions involved in optimization process are black-box with unknown analytical representations and hard to evaluate. In this paper, a global optimization problem is considered where both the goal function f (x) and its gradient f ′ (x) are black-box functions. It is supposed that f ′ (x) satisfies the Lipschitz condition over the search hyperinterval with an unknown Lipschitz constant K. A new deterministic 'Divide-the-Best' algorithm based on efficient diagonal partitions and smooth auxiliary functions is proposed in its basic version, its convergence conditions are studied and numerical experiments executed on eight hundred test functions are presented.

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Section: Operating Characteristics Of the Compared Methodsmentioning

confidence: 99%

Section: Efficient Partition Strategymentioning

confidence: 99%

Section: Classes Of Test Functions and Comparison Criteriamentioning

confidence: 99%

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A deterministic global optimization using smooth diagonal auxiliary functions

Sergeyev

Kvasov

2015

Communications in Nonlinear Science and Numerical Simulation

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“…First, it is slow in reaching the solution with high accuracy, and second, it spends an excessive number of evaluations exploring local minima. Some variants have been developed to improve these weaknesses [52][53][54][55].…”

Section: Global Optimization Approachesmentioning

confidence: 99%

A Direct Search Algorithm for Global Optimization

2016

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Abstract:A direct search algorithm is proposed for minimizing an arbitrary real valued function. The algorithm uses a new function transformation and three simplex-based operations. The function transformation provides global exploration features, while the simplex-based operations guarantees the termination of the algorithm and provides global convergence to a stationary point if the cost function is differentiable and its gradient is Lipschitz continuous. The algorithm's performance has been extensively tested using benchmark functions and compared to some well-known global optimization algorithms. The results of the computational study show that the algorithm combines both simplicity and efficiency and is competitive with the heuristics-based strategies presently used for global optimization.

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“…In order to address this problem, a globally-biased version Gb-DISIMPL [31] with an adaptive balancing of local and global information during the search have been introduced, implemented and experimentally investigated. Extensive numerical experiments executed on 800 multidimensional multiextremal test functions had showed a promising performance of the new acceleration technique with respect to competitors.…”

Section: Modifications and Applications Of The Direct Algorithmmentioning

confidence: 99%

Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization

et al. 2015

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In this paper, a recently proposed global Lipschitz optimization algorithm PLOR (Pareto-Lipschitzian Optimization with Reduced-set) is further developed, investigated and applied to truss optimization problems. Partition patterns of the PLOR algorithm are similar to those of DIRECT (DIviding RECTangles), which was widely applied to different real-life problems. However here a set of all Lipschitz constants is reduced to just two: the maximal and the minimal ones. In such a way the PLOR approach is independent of any user-defined parameters and balances equally local and global search during the optimization process. An expanded list of other well-known DIRECT-type algorithms is used in investigation and experimental comparison using the standard test problems and truss optimization problems. The experimental investigation shows that the PLOR algorithm gives very competitive results to other DIRECT-type algorithms using standard test problems and performs pretty well on real truss optimization problems.

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Globally-biased Disimpl algorithm for expensive global optimization

Cited by 115 publications

References 44 publications

A deterministic global optimization using smooth diagonal auxiliary functions

A deterministic global optimization using smooth diagonal auxiliary functions

A Direct Search Algorithm for Global Optimization

Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization

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