Glowworm Swarm Optimization by Krishnanand N. Kaipa & Debasish Ghose

Author:Krishnanand N. Kaipa & Debasish Ghose
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

4.3.3 Tests on the Staircase Function

The Staircase function (Fig. 4.3c) has connected local maxima at different levels with discontinuity in the function. It contains 16 regions at 7 different heights in the square . The initial locations of the glowworms, the trajectories followed by the glowworms, and the final solution are shown in Fig. 4.19a, b and c, respectively. Different square regions are marked according to the increasing order of their function values. Note that regions marked with the same number have equal function values. All the glowworms initially located in region 7 remain stationary as they are located in the flat region of global maxima. Note that glowworms in the interior locations (except those that are very close to or on the edges) of all other regions move toward and settle on the edges of the next higher peak-regions. Refer to Fig. 4.19c to observe this pattern.

Even though the Staircase function has step discontinuities, it provides an uphill direction toward the highest level in discrete steps whose size is equal to the width of each stair. Therefore, if the values of the sensor range and of the number of glowworms n are such that there is sufficient connectivity among the swarm members, all the glowworms will reach the highest level. However, the values of and n can be tuned (as is the case in the above simulation result) so that the glowworms detect the presence of other stairs. From a global optimization point of view (i.e., when the goal is to compute only the global peak), it appears that GSO does not perform well for optimization with . However, in the context of this book, since multiple local peaks are being sought, GSO’s performance on the function is indeed good.

Fig. 4.19Test results on the Staircase function. a Initial placement of glowworms. b Emergence of the solution after 250 iterations. c Final co-location of groups of glowworms

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.