Metaheuristic vs. deterministic global optimization algorithms: The univariate case

Kvasov, Dmitri E.; Mukhametzhanov, Marat S.

doi:10.1016/j.amc.2017.05.014

Cited by 91 publications

(72 citation statements)

References 34 publications

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“…For example, consider the comparison of a deterministic and a non-deterministic method [GK17,KM17]. If the multiple repeats of the non-deterministic method are considered, is it fair to compare the average quality to the single run of the deterministic method.…”

Section: Some Final Insights and Remarks From The Refereesmentioning

confidence: 99%

Best practices for comparing optimization algorithms

2017

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The final publication is available at Springer via http://dx.doi.org/10.1007/s11081-017-9366-1 Comparing, or benchmarking, of optimization algorithms is a complicated task that involves many subtle considerations to yield a fair and unbiased evaluation. In this paper, we systematically review the benchmarking process of optimization algorithms, and discuss the challenges of fair comparison. We provide suggestions for each step of the comparison process and highlight the pitfalls to avoid when evaluating the performance of optimization algorithms. We also discuss various methods of reporting the benchmarking results. Finally, some suggestions for future research are presented to improve the current benchmarking process.

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Section: Some Final Insights and Remarks From The Refereesmentioning

confidence: 99%

Best practices for comparing optimization algorithms

2017

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“…The algorithms Geom-AL, Inf-GL, and Geom-LTM have been tested on 20 global optimization problems from [12,15] and on the respective scaled functions g(x) and h(x) constructed from them. It has been obtained that on all 20 test problems with infinite and infinitesimal constants (α 1 , β 1 ) and (α 2 , β 2 ) the results on the original functions f (x) from [12,15] and on scaled functions g(x) and h(x) coincide.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

“…In algorithms Geom-LTM and Inf-GL, the Lipschitz constant is estimated during the search and the reliability parameter r is used. In this work, the values of the Lipschitz constant of the functions f (x) for the algorithm Geom-AL have been taken from [15] (and multiplied by α for the function g(x)). The values of the parameter r for the algorithms Geom-LTM and Inf-GL have been set to 1.1 and 1.5, respectively.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

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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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“…For example, [5] introduces a methodology allowing one to compare stochastic and deterministic methods. The article [6] is dedicated to a comparison between nature-inspired metaheuristic and deterministic algorithms. The systematic review of the benchmarking process of optimization algorithms is given in [7].…”

Section: Introductionmentioning

confidence: 99%

Implementation and verification of global optimization benchmark problems

Posypkin

Usov

2017

Open Engineering

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Abstract:The paper considers the implementation and verification of a test suite containing 150 benchmarks for global deterministic box-constrained optimization. A C++ library for describing standard mathematical expressions was developed for this purpose. The library automate the process of generating the value of a function and its' gradient at a given point and the interval estimates of a function and its' gradient on a given box using a single description. Based on this functionality, we have developed a collection of tests for an automatic verification of the proposed benchmarks. The verification has shown that literary sources contain mistakes in the benchmarks description. The library and the test suite are available for download and can be used freely.

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Metaheuristic vs. deterministic global optimization algorithms: The univariate case

Cited by 91 publications

References 34 publications

Best practices for comparing optimization algorithms

Best practices for comparing optimization algorithms

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

Implementation and verification of global optimization benchmark problems

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