LDIW-PSO is also more stable and robust compared with DLPSO2, because its standard deviation is comparatively GW572016 smaller in all the test problems. Besides, LDIW-PSO demonstrated better global search ability and getting out of local optima than DLPSO2.6. ConclusionMotivated by the superiority claims by some PSO variants over LDIW-PSO in terms of performance, a number of experiments were performed in this paper to empirically verify some of these claims. Firstly, an appropriate (approximate) percentage of the test problems search space limits were obtained to determine the particle velocity limits for LDIW-PSO. Secondly, these values were used in the implementation of LDIW-PSO for some benchmark optimization problems and the results obtained compared with that of some PSO variants that have previously claimed superiority in performance.

LDIW-PSO performed better than these variant. The performances of the two other recent PSO variants with different inertia weight strategies were also compared with LDIW-PSO on similar problems with the latter showing competitive advantage. This work has therefore showed that with good experimental setting, LDIW-PSO will perform competitively with similar variants. Precious claims of inferior performance might therefore be due to some unfavourable experimental settings. The Appendix provides further simulation results that can provide useful hints for deciding the setting velocity threshold for particles for LDIW-PSO.AcknowledgmentThanks are due to the College of Agricultural Science, Engineering and Sciences, University of Kwazulu-Natal, South Africa, for their support towards this work through financial grant.

AppendixTables Tables9,9, ,10,10, ,11,11, ,12,12, and and1313 show the results of LDIW-PSO in optimizing some benchmark problems so as to determine a suitable value for �� that was used to set the velocity limits for the particles. The experiments were repeated 500 times for each of the problems. Two different swarm sizes of 20 and 30 were used for each of the three different problem dimensions 10, 30, and 50. The respective number of iterations that was used with the dimensions is 1000, 1500, and 2000. The LDIW strategy was decreased from 0.9 to 0.4 in course of searching for solution to the problem [7, 10�C12, 27], the acceleration constants (c1 and c2) were set to 2.0, and Vmax = ��(Xmax ) and Vmin = ��(Xmin ).

In the tables, bold values represent the best mean fitness value.Table 9Different values of parameter �� and respective mean best fitness for Griewank test problem.Table 10Different values of parameter �� and respective mean best fitness for Rastrigin test problem.Table 11Different values of parameter �� and respective mean best fitness for Rosenbrock test problem.Table 12Different Dacomitinib values of parameter �� and respective mean best fitness for Sphere test problem.