Sentence examples for many test problems from inspiring English sources

In Table 4, the best results are obtained for many test problems from the normalization based on all solutions with (varepsilon =1).

Computational results are reported for many standard test problems.

Through many numerical test problems, it is shown that the use of GODRP schemes can broaden the application area of conventional DRP schemes to aeroacoustic phenomena, enhancing both the speed and accuracy of the computation using nonuniform Cartesian or curvilinear grids.

In addition to the frequently used many-objective test problems DTLZ and WFG, we use their minus versions.

In this section, we propose new many-objective test problems to further examine the effect of the normalization.

The minus version of DTLZ and WFG was proposed as many-objective test problems with inverted triangular Pareto fronts in [13].

Let us examine the performance of MOEA/D with and without the simple normalization mechanism through computation experiments on frequently used many-objective test problems in the literature: DTLZ1-4 [7] and WFG4-9 [9] with 3, 5, 8, and 10 objectives.

However, in many applied testing problems, the p-values could be under-estimated or over-estimated for many known or unknown reasons.

It is difficult for MOEA/D without normalization to find a set of uniformly distributed solutions over the entire Pareto front for such a many-objective test problem.

However, in many practical testing problems such as in genomics, the p-values could be under-estimated or over-estimated for many known or unknown reasons.

More recently, GBTG has been applied to many other testing problems, including the generation of eXtensible Markup Language (XML) documents and the generation of packets for testing communications protocols.