Sentence examples for solutions of the examples from inspiring English sources

In order to test the accuracy and efficiency of our method, the solutions of the examples presented are introduced in the form of tables to make a comparison with those obtained by other methods and with the exact solutions easy.

Numerical solutions of the example are given in Table 2 and Figure 2.

Moreover, Fig. 3 illustrates the optimal solution of the examples after the grand coalition (i.e. S 15 = {1, 2, 3, 4}) and demonstrates that each customer is allocated to which depots.

Figure 2 Exact and approximate solution of the example.

The respective exact solution of the example is found using a commercial solver (CPLEX).

This prevents the learner from merely duplicating the characters and symbols that compose the text and solution of the example.

In addition, our Theorem helps to explain why the solution of the example above satisfies the standard conditions (11)–(13) despite not being piecewise differentiable.

Figure 2 shows a graphical representation of the exact solution and, for m = n = 15, the approximate solution of the example.

A nonlinear limit-state function example was provided to validate the accuracy and efficiency of the hybrid algorithm by comparing the algorithm's solution with the exact solution of the example.

We can see that the solutions of this example are δ-independent.

Open image in new window Figure 3 The all of efficient solutions of the MOLP example.