Sentence examples for benchmark problems are compared from inspiring English sources

Numerical examples are given for the full Boltzmann equation and results for some benchmark problems are compared with analytical or prior solutions.

For the evaluation of minor actinide isotopes for which there was no experiment, calculation results of benchmark problems were compared with MCNP4c2 results.

The performance of the proposed framework on properly designed benchmark problems is compared with effective GA and ACO approaches taken as algorithm components.

Three benchmark problems are first solved to compare the performance of these adaptations with the earlier JG adaptations of NSGA-II.

In this contribution these two different strategies are applied to a benchmark problem and are compared with each other.

Computational results comparing the models on a set of benchmark problems are also presented.

To compare the performances of multi-modal optimization algorithms, multi-modal benchmark problems are always required.

Several numerical benchmark problems are analyzed.

Some benchmark problems are solved to support our discussion.

Several benchmark problems are solved using the proposed method.

Implementations of the benchmark problems are provided as Additional files 2 and 3.