4。2。2。Numerical results on basic multimodal functions and complex multimodal functions

For the multimodal functions, the global optimum is difficult to be located, especially for the complex multimodal func- tions。 In Table 3, the results for the basic multimodal functions are reported。 From this table, the proposed DFPSO algorithm can  produce  the  very  competitive  results  for  most  of  the  test  functions。  In  order  to  further  validate  the performance

Table 2

The function error values on the unimodal functions based on 50 runs。 The lowest values in each line for mean and best are highlighted in boldface。

Functions Index DFPSO PSO PSOw ALC-PSO SPSO2007 GPSO SPSO2011 CLPSO

f1 meana 4。17E—300 8。83E—17 1。44E—21 7。36E—70 7。15E—77 8。45E—191 9。09E—99 3。80E—12

bestb 2。54E—314 1。45E—78 8。29E—26 1。07E—89 3。56E—83 6。53E—205 2。64E—104 4。76E—13

stdc 0 4。39E—16 8。83E—21 5。15E—69 2。56e—76 0 3。50E—98 2。61E—12

p valued – 9。43E—14⁄  e 9。43E—14⁄ 9。43E—14⁄ 9。43E—14⁄ 9。43E—14⁄ 9。43E—14⁄ 9。43E—14⁄

f2 mean 7。92E—148 6。46E—32 9。42E—08 1。50E—31 4。33E—37 3。98E—67 3。01 3。20E—08

best 6。96E—153 1。64E—37 4。97E—16 4。49E—39 3。80E—46 3。26E—87 5。69E—01 1。14E—08

std 3。05E—147 2。02E—31