A filled function method for finding a global minimizer on global integer optimization

A critical review of discrete filled function methods in solving nonlinear discrete optimization problems

“…Remark 2 Some methods in the literature, such as [32,33,44], replace N (x * ) in Step 3 with M = {w 1 , w 2 , . .…”

“…Remark 1 Note that some methods in the literature, such as [32,46] Choose an initial starting point x 0 ∈ X.…”

“…A third exponential filled function is suggested in [32]. Let x * be the current local minimizer and choose any x 0 such that f (x 0 ) ≥ f (x * ).…”

“…This adjustment of the parameters continues until the parameters reach their predetermined bounds; the best solution obtained so far is then taken as the global minimizer. Note that some filled functions have one parameter (such as those in [16,32,43]), while the rest are equipped with two parameters. The latter filled functions often have one parameter which is partially dependent on the other and this requires additional steps when tuning the parameters in order to satisfy the required convergence criteria.…”

“…However, the filled function proposed by Zhu contains an exponential term, which consequently makes it difficult to determine a point in a lower basin [26,27]. Since then, several types of discrete filled functions with improved theoretical properties have been proposed in [16,27,28,32,33,[42][43][44] to enhance computational efficiency.…”