Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants

Sergeyev, Yaroslav D.; Kvasov, Dmitri E.

doi:10.1137/040621132

Cited by 158 publications

(119 citation statements)

References 27 publications

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“…Moreover, if stopping tests are internalized within a method, it may not be possible to ensure all algorithms use the same stopping conditions [SS00,SK06]. However, if a fixed-cost or fixed-target approach (see Subsection 4.3) is employed, then other stopping conditions can be turned off, thereby ensuring all algorithms use the same stopping conditions.…”

Section: Parameter Tuning and Stopping Conditionsmentioning

confidence: 99%

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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: Parameter Tuning and Stopping Conditionsmentioning

confidence: 99%

“…Summary tables can be employed as a first step [SK06]. For example, in [BDF97] optimization methods were rated by the percentage of problems for which a method's time is termed competitive or very competitive.…”

Section: Tablesmentioning

confidence: 99%

Best practices for comparing optimization algorithms

2017

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“…For the S-H. Camel B. and Hartman-6 test problems PLOR performs close to the best results obtained with the DIRECT-l and only for the Shekel-5 problem PLOR took much higher amount of function evaluations comparing with the other DIRECT-type algorithms. However, it was shown in [37], that for these standard test functions DIRECT executes a very small number of trials until it generates a point in the neighborhood of the global minimizer. Moreover, the initial feasible region can also have a significant impact on this.…”

Section: Optimization Of Traditional Test Functionsmentioning

confidence: 99%

“…DIRECT ideas were also generalized in the framework of diagonal partitions [37], space-filling curves [18] and derivatives [16,17].…”

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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“…The review of principal methods are presented in [2]. Efficient diagonal partitions are discussed in [6]. In [4] the interval method is used to compute global optimum.…”

Section: Introductionmentioning

confidence: 99%