BARON and LINDOGlobal algorithms achieved the best solution for the 7 x 7 test NDTP with function D which indicates the objective function value of 480.
For the 10x10 test NDTP with cost function D, the objective function value of the discrete solution found by BARON was smaller than those gained by AlphaECP (-6.
However, the non-convex cost functions with valleys and peaks defined inside the NDTP model may cause difficulties for the ECP method to find high quality result in reasonable solution time.
However, the non-convexities, within the NDTP model, may sometimes also cause difficulties for the SBB method to achieve the high quality solution fast enough, as it can be seen from the gained results for test problems with continuous arc-tangent approximations of a step piece-wise linear cost functions and those with peak cost functions.
The gained solutions were compared and a correlative evaluation of the considered MINLP methods was shown to demonstrate their suitability for solving the NDTPs.
The ECP method (Westerlund, Pettersson 1995) within the computer implementation AlphaECP by Westerlund and Porn (2002) was the first MINLP technique applied to solve the test NDTPs.
The applied set of the test NDTPs was solved on a 64-bit operating system using the personal computer: Intel Core i7, 2.
The discrete solutions of the test NDTPs with cost function A were achieved only by AlphaECP, DICOPT, LINDOGlobal and SBB since BARON could not handle the trigonometric function arctan(x) within the MINLP model.
The calculated objective function values for the test NDTPs with cost function B are shown in Fig.
The attained best solutions for the 7x7 and 10x10 test NDTPs with cost function B are shown in Tables 6 and 7.
The discrete solutions for the test NDTPs with cost function C were obtained by Alpha ECP, BARON, DICOPT, LINDOGlobal and SBB algorithms, see Fig.
The objective function values of the test NDTPs with cost function D found by AlphaECP, BARON, DICOPT, LINDOGlobal and SBB are presented in Fig.