From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

Table 3

Mean fitness values of F1–F25 with 10D. The fitness values in bold and italic font are the best and worst optimization results among the five chaotic evolution algorithms, respectively. The (†) and () marks mean that they are significantly better than or as the same as DE/best/1/bin and DE/rand/1/bin, respectively, by Wilcoxon sign-ranked test ().

Function	DE-best	DE-rand	CE-logistic	CE-tent	CE-Gauss	CE-Hénon-rand	CE-Hénon-attrac.
F1	−449.998	−414.47	2998.806	5171.277	1925.366	1768.834	1661.428
F2	−440.516	−421.736	4219.061	7585.492		3855.883	3568.253
F3	1583.076	215058.7	3624018	26036921		4846787	3973677
F4	−283.931	−402.19	6487.652	8960.625		4723.953	5358.734
F5	−310	−309.972	3775.085	9448.24	3986.86	4148.611
F6	446.6181	35496.74	287017050.30	628335744.87	272134693.96	78198866
F7	−177.747	−177.865	−97.4097	−22.6933		−105.609	−121.71
F8	−119.992	−119.893	−119.635	−119.38	−119.62	−119.604
F9	−308.575	−306.239		−269.758	−282.345	−284.484	−282.21
F10	−291.876	−282.316	−254.408	−232.193	−261.758	−258.089
F11	98.34748	94.5809		99.94741			97.52258
F12	321.4523	4968.164	20706.57	53091.15	33802.12	28609.12
F13	−126.975	−126.213	−125.596	−123.459		−124.246
F14	−296.159	−296.567		−295.874
F15	476.4005	557.9363		746.0844
F16	302.9829	337.3688	378.9592	452.6815	377.3656	391.311
F17	323.7027	326.4775	409.4423	474.5775	401.6362	426.4379
F18	869.8405	578.9428				910.1011
F19	869.4931	591.2802	910	910		910.5839	910
F20	866.7625	610.5591	910	910		910.5858	910
F21	1079.758	929.7804	1623.005	1691.75		1657.526	1574.536
F22	1222.383	1164.546	1320.278	1406.045	1307.327	1309.518
F23	1066.17	970.7627	1647.835	1701.935		1649.8	1563.626
F24	824.7887	494.8996	1450.171	1498.591	1376.52	1398.889
F25	1989.595	2001.341	2010.443		2018.292	2021.227	2014.102