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 final findings are related to the MINLP solution of the convex NDTP.
The aim of this paper was to present the suitability of five different state-of-the-art MINLP methods, specifically for the exact optimum solution of the NDTP.
Based on the presented results, the most performed tests show that each MINLP method was able to solve a specific NDTP within determined solution time to a better solution than the other considered MINLP techniques.
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.
Cost function E is rarely applied in the objective functions of practical NDTPs, see Fig.