The sale of spectacles and contact lenses in the old days subsidised the sight

test function, but these sales are now being eroded by the internet.

From tables 3-4, it is stated that the proposed algorithm is an effective and efficient algorithm for solving bench mark

test function and this algorithms also provides more stable results in comparison to other algorithms being compared.

Let us choose now [phi] = [[(1 + [absolute value of [u.sub.n]].sup.m-1] - 1] sgn([u.sub.n]) as a

test function in (16), and we obtain

In order to reduce the influence of random disturbance, the independent operating for each

test function is carried out 10 times.

A multigroup

test function is used for comparison with the IEPSO.

Moreover, the coefficient of power function will change in a certain range for different types of benchmark

test functions. The coefficient h ranges between -1.3 to -1.1 when the benchmark

test function is unimodal function, the coefficient h ranges between -0.8 to -0.5 when the benchmark

test function is multimodal function and the coefficient h ranges between -1.4 to -1.2 when the benchmark

test function is composite function.

From now on, there will be no need to create test groups for each type of device and manually add the

test function for each individual device to the relevant test group.

In Tables 2-4, the algorithm that produced the lowest final function value of a

test function was ranked 1 and for the equal final function values the algorithm utilizing smaller number of function evaluations was ranked 1.

For each

test function, the MFOA method is used to find the optimal solutions at h = [0.1, 0.3, 0.5, 0.7, 0.9, 1, 1.1, 1.3, 1.5, 2] and the algorithm runs for 20 times for each h.

Caption: Figure 2: Graphs of the extended functions [??.sub.L](x) and [??.sub.R](x) with m = 40 for the

test function [f.sub.1](x).

holds for any

test function [phi] [member of] D([0, T) x [PHI]) and any b such that

If 1 < p < q < [infinity], 1/Q < 1/p-1/q < 2/Q, w [member of] [A.sub.p,q], and Lu [member of] [L.sup.p,p/q] ([w.sup.p], [w.sup.q], G), then there exists c > 0 such that, for any

test function u and every x, z [member of] G, x [not equal to] z,