Sentence examples for benchmark problems are presented from inspiring English sources

Numerical results for typical benchmark problems are presented and analyzed.

Three new benchmark problems are presented and an upper bound is provided.

Two instructive numerical benchmark problems are presented to test the performance of numerical FSI schemes involving composite structures.

An overview of the collection of benchmark problems is presented in Table 1.

Furthermore, the experimental results for a well-known RAP benchmark problem are presented to demonstrate the approximating error of the previous reliability function for a standby redundant system and the usefulness of the current research.

An economic optimization methodology for the pulp mill benchmark problem is presented.

A benchmark problem is presented to illustrate the accuracy and effectiveness of the method; the detailed results are compared with various heuristic methods.

Experiments using three benchmark function and three engineering design problems are presented and compared with the best known solutions reported in the literature.

An example using the learning basis IRIS, which is a benchmark for classification problems, is presented showing the performances of this classifier.

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

Thirteen solutions proposed to solve the benchmark problem are briefly presented and classified in terms of methodology and compared with respect to their complexity and performance.