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Table showing the ERT in number of function evaluations divided by the best ERT measured during BBOB-2009

Last dimension | Dimension = 2 | Next dimension

Δ fopt
f1, 2-D		 1e1
2.0		 1e0
6.0		 1e-1
6.0		 1e-2
6.0		 1e-3
6.0		 1e-5
6.0		 1e-7
6.0		 #succ
15/15
CMA-ES-2019 Hansen 2.2 (3)2.6 (2)6.4 (6)12 (7)17 (4)27 (9)35 (10)15/15
HE-ES Glasmachers 2.7 (5)3.2 (2)7.5 (5)13 (9)21 (6)35 (6)49 (12)15/15
SLSQP+lq-CMA-ES Hansen 2.1 (2)1.1 (0.2)1.2 (0)1.2 (0)1.2 (0)1.2 (0)1.2 (0)15/15
SLSQP-11-scipy Hansen 2.1 (2)1.1 (0.2)1.2 (0)1.2 (0)1.2 (0)1.2 (0)1.2 (0)15/15
lq-CMA-ES Hansen 1.2 (1)1.4 (0.8)1.9 (0.3)2.7 (0.9)3.3 (1.0)4.6 (0.8)5.5 (1)15/15

Δ fopt
f2, 2-D		 1e1
16		 1e0
19		 1e-1
25		 1e-2
25		 1e-3
26		 1e-5
28		 1e-7
29		 #succ
15/15
CMA-ES-2019 Hansen 9.5 (7)12 (4)11 (3)12 (3)13 (3)14 (3)15 (3)15/15
HE-ES Glasmachers 8.6 (9)14 (6)13 (4)16 (3)17 (3)19 (3)20 (2)15/15
SLSQP+lq-CMA-ES Hansen 1.4 (0.3)1.4 (0.6)1.2 (0.4)1.4 (0.5)1.5 (0.3)1.6 (0.5)1.8 (0.5)15/15
SLSQP-11-scipy Hansen 1.4 (0.3)1.4 (0.6)1.2 (0.5)1.4 (0.5)1.5 (0.4)1.6 (0.4)1.8 (0.6)15/15
lq-CMA-ES Hansen 1.7 (0.5)1.9 (0.8)1.8 (0.4)2.0 (0.4)2.2 (0.2)2.4 (0.4)2.7 (0.5)15/15

Δ fopt
f3, 2-D		 1e1
15		 1e0
271		 1e-1
445		 1e-2
446		 1e-3
450		 1e-5
454		 1e-7
464		 #succ
15/15
CMA-ES-2019 Hansen 2.5 (1)3.7 (4)6.3 (6)6.5 (7)6.6 (7)6.9 (6)7.0 (7)15/15
HE-ES Glasmachers 2.6 (2)2.6 (2)8.2 (22)9.0 (23)11 (23)12 (25)12 (33)15/15
SLSQP+lq-CMA-ES Hansen 2.5 (2)2.3 (2)5.4 (3)5.7 (6)5.8 (6)6.0 (6)6.2 (6)15/15
SLSQP-11-scipy Hansen 3.9 (5)2.6 (2)10 (11)10 (11)10 (11)10 (9)10 (7)15/15
lq-CMA-ES Hansen 1.5 (1)2.0 (3)3.5 (2)3.9 (2)4.0 (4)4.1 (6)4.0 (6)15/15

Δ fopt
f4, 2-D		 1e1
22		 1e0
344		 1e-1
459		 1e-2
496		 1e-3
523		 1e-5
544		 1e-7
566		 #succ
15/15
CMA-ES-2019 Hansen 3.2 (2)5.3 (2)42 (57)96 (158)108 (170)112 (191)114 (129)15/15
HE-ES Glasmachers 2.2 (1)8.4 (14)157 (207)1277 (746)6198 (9452)1.5e4 (2e4)1.4e4 (2e4)3/15
SLSQP+lq-CMA-ES Hansen 2.0 (2)5.6 (7)43 (53)64 (105)69 (89)72 (122)75 (82)15/15
SLSQP-11-scipy Hansen 4.4 (6)3.1 (3)10 (17)9.4 (17)9.0 (6)8.6 (6)8.3 (15)15/15
lq-CMA-ES Hansen 1.7 (2)2.0 (3)30 (28)123 (120)126 (227)134 (140)137 (251)14/15

Δ fopt
f5, 2-D		 1e1
4.0		 1e0
4.0		 1e-1
4.0		 1e-2
4.0		 1e-3
4.0		 1e-5
4.0		 1e-7
4.0		 #succ
15/15
CMA-ES-2019 Hansen 3.4 (2)6.9 (7)7.7 (2)7.7 (2)7.7 (7)7.7 (7)7.7 (7)15/15
HE-ES Glasmachers 3.2 (2)5.6 (2)6.0 (2)6.0 (2)6.0 (3)6.0 (3)6.0 (2)15/15
SLSQP+lq-CMA-ES Hansen 1.5 (0)3.5 (0)3.5 (0)3.5 (0)3.5 (0)3.5 (0)3.5 (0)15/15
SLSQP-11-scipy Hansen 1.5 (0)3.5 (0)3.5 (0)3.5 (0)3.5 (0)3.5 (0)3.5 (0)15/15
lq-CMA-ES Hansen 1.8 (0.4)2.9 (1)★3.0 (0.7)★3.0 (2)★3.0 (2)★3.0 (1)★3.0 (1)★15/15

Δ fopt
f6, 2-D		 1e1
13		 1e0
23		 1e-1
41		 1e-2
54		 1e-3
67		 1e-5
95		 1e-7
124		 #succ
15/15
CMA-ES-2019 Hansen 2.0 (2)3.3 (2)3.3 (2)3.5 (1)3.7 (0.8)3.8 (0.6)4.0 (0.6)15/15
HE-ES Glasmachers 2.2 (3)5.3 (3)5.3 (2)5.3 (2)5.7 (2)6.3 (2)6.5 (2)15/15
SLSQP+lq-CMA-ES Hansen 5.1 (5)3.9 (4)2.5 (2)2.1 (1)2.1 (2)1.9 (1)2.0 (2)15/15
SLSQP-11-scipy Hansen 5.2 (5)4.1 (4)2.6 (2)2.2 (2)2.1 (1)1.8 (0.9)2.0 (2)15/15
lq-CMA-ES Hansen 1.7 (2)2.1 (1)2.4 (0.9)2.8 (0.7)3.0 (0.6)3.0 (0.5)3.2 (0.4)15/15

Δ fopt
f7, 2-D		 1e1
3.0		 1e0
21		 1e-1
60		 1e-2
193		 1e-3
217		 1e-5
217		 1e-7
241		 #succ
15/15
CMA-ES-2019 Hansen 3.0 (4)1.0 (1)2.5 (3)0.95 (0.8)0.93 (0.5)0.93 (0.6)0.95 (0.7)15/15
HE-ES Glasmachers 2.8 (3)2.5 (6)2.1 (2)0.89 (0.6)0.99 (0.6)0.99 (0.7)1.1 (0.7)15/15
SLSQP+lq-CMA-ES Hansen 2.8 (4)2.0 (1)1.8 (2)0.76 (0.4)0.76 (0.3)0.76 (0.2)0.80 (0.6)15/15
SLSQP-11-scipy Hansen 17 (24)24 (28)89 (90)241 (558)571 (800)571 (870)514 (1048)4/15
lq-CMA-ES Hansen 1.6 (2)0.74 (0.4)1.2 (2)0.58 (0.8)0.68 (0.9)0.68 (1)0.77 (1.0)15/15

Δ fopt
f8, 2-D		 1e1
5.0		 1e0
12		 1e-1
37		 1e-2
46		 1e-3
86		 1e-5
94		 1e-7
112		 #succ
15/15
CMA-ES-2019 Hansen 3.8 (3)5.6 (10)5.2 (3)6.2 (4)3.9 (3)4.2 (1)4.1 (2)15/15
HE-ES Glasmachers 4.8 (5)7.3 (12)7.8 (6)9.0 (6)5.4 (2)5.9 (3)5.8 (2)15/15
SLSQP+lq-CMA-ES Hansen 3.2 (3)3.2 (4)2.0 (1)2.1 (2)1.2 (0.6)1.2 (0.6)1.1 (0.5)15/15
SLSQP-11-scipy Hansen 3.2 (2)3.2 (4)2.0 (2)2.1 (0.8)1.2 (0.9)1.2 (0.8)1.1 (0.7)15/15
lq-CMA-ES Hansen 2.4 (3)3.5 (5)2.2 (2)2.6 (1)1.5 (0.9)1.5 (0.5)1.4 (0.6)15/15

Δ fopt
f9, 2-D		 1e1
1		 1e0
18		 1e-1
30		 1e-2
44		 1e-3
68		 1e-5
81		 1e-7
92		 #succ
15/15
CMA-ES-2019 Hansen 1 (0)2.9 (3)6.2 (5)6.1 (3)4.6 (3)4.8 (2)4.8 (2)15/15
HE-ES Glasmachers 1 (0)3.8 (2)7.7 (4)8.0 (3)6.0 (2)6.1 (2)6.2 (2)15/15
SLSQP+lq-CMA-ES Hansen 1 (0)0.50 (0)0.63 (0)0.98 (0)0.78 (0)0.80 (0)0.75 (0)15/15
SLSQP-11-scipy Hansen 1 (0)0.50 (0)0.63 (0)0.98 (0)0.78 (0)0.80 (0)0.75 (0)15/15
lq-CMA-ES Hansen 1 (0)2.1 (1)2.7 (2)2.9 (2)2.1 (1)1.9 (1)1.8 (1)15/15

Δ fopt
f10, 2-D		 1e1
30		 1e0
46		 1e-1
54		 1e-2
61		 1e-3
68		 1e-5
82		 1e-7
98		 #succ
15/15
CMA-ES-2019 Hansen 4.5 (3)4.5 (2)4.6 (2)4.8 (1.0)4.6 (0.6)4.6 (0.7)4.4 (0.5)15/15
HE-ES Glasmachers 5.9 (5)6.4 (3)6.8 (0.9)6.7 (1)6.6 (1)6.5 (1)6.1 (0.8)15/15
SLSQP+lq-CMA-ES Hansen 0.82 (0.3)0.65 (0.2)0.61 (0.2)0.60 (0.2)0.60 (0.2)1.5 (2)8.2 (17)15/15
SLSQP-11-scipy Hansen 0.82 (0.3)0.65 (0.2)0.61 (0.2)0.59 (0.2)0.57 (0.2)38 (130)166 (217)8/15
lq-CMA-ES Hansen 0.98 (0.7)0.97 (0.5)0.96 (0.3)1.00 (0.3)0.97 (0.2)0.95 (0.2)1.1 (0.3)15/15

Δ fopt
f11, 2-D		 1e1
35		 1e0
45		 1e-1
50		 1e-2
62		 1e-3
67		 1e-5
81		 1e-7
97		 #succ
15/15
CMA-ES-2019 Hansen 3.4 (2)4.5 (2)5.0 (2)4.4 (1)4.8 (1)4.6 (0.9)4.4 (0.9)15/15
HE-ES Glasmachers 6.1 (4)6.9 (2)7.5 (2)6.7 (0.6)6.9 (0.8)6.5 (1.0)6.5 (0.6)15/15
SLSQP+lq-CMA-ES Hansen 0.67 (0.3)0.61 (0.2)0.63 (0.2)0.59 (0.2)0.63 (0.1)8.6 (15)19 (23)15/15
SLSQP-11-scipy Hansen 0.67 (0.2)0.61 (0.2)0.63 (0.2)0.59 (0.2)0.63 (0.2)83 (120)288 (563)8/15
lq-CMA-ES Hansen 0.78 (0.2)0.97 (0.4)1.0 (0.4)0.96 (0.2)0.94 (0.2)0.91 (0.2)1.1 (0.3)15/15

Δ fopt
f12, 2-D		 1e1
35		 1e0
46		 1e-1
75		 1e-2
94		 1e-3
105		 1e-5
153		 1e-7
195		 #succ
15/15
CMA-ES-2019 Hansen 4.2 (2)4.3 (2)3.7 (2)4.0 (1.0)4.0 (4)3.8 (4)3.8 (4)15/15
HE-ES Glasmachers 5.2 (4)6.6 (4)7.0 (3)7.3 (6)7.7 (7)7.4 (7)7.1 (4)15/15
SLSQP+lq-CMA-ES Hansen 1.1 (0.7)1.0 (0.6)0.64 (0.3)0.52 (0.3)0.48 (0.3)0.37 (0.3)1.2 (2)15/15
SLSQP-11-scipy Hansen 1.1 (0.8)1.0 (0.5)0.64 (0.3)0.52 (0.3)0.48 (0.2)0.37 (0.3)1.5 (3)15/15
lq-CMA-ES Hansen 1.0 (0.4)1.9 (2)2.0 (5)2.3 (3)2.3 (5)1.9 (2)1.8 (3)15/15

Δ fopt
f13, 2-D		 1e1
23		 1e0
35		 1e-1
46		 1e-2
60		 1e-3
71		 1e-5
95		 1e-7
122		 #succ
15/15
CMA-ES-2019 Hansen 2.9 (2)3.4 (1)3.8 (1)4.1 (1)4.3 (0.7)4.4 (0.7)4.3 (0.4)15/15
HE-ES Glasmachers 3.1 (2)4.6 (4)6.0 (2)6.1 (2)6.6 (1.0)6.9 (1)6.8 (0.8)15/15
SLSQP+lq-CMA-ES Hansen 0.90 (0.3)0.79 (0.2)0.82 (0.2)0.76 (0.1)0.75 (0.1)1.4 (1)5.0 (11)15/15
SLSQP-11-scipy Hansen 0.90 (0.3)0.79 (0.2)0.82 (0.2)0.76 (0.1)0.75 (0.1)0.87 (0.7)56 (172)9/15
lq-CMA-ES Hansen 1.0 (0.6)1.1 (0.4)1.1 (0.4)1.1 (0.3)1.1 (0.3)1.3 (0.3)2.1 (0.5)15/15

Δ fopt
f14, 2-D		 1e1
1		 1e0
7.0		 1e-1
16		 1e-2
24		 1e-3
38		 1e-5
67		 1e-7
90		 #succ
15/15
CMA-ES-2019 Hansen 3.3 (4)2.1 (3)3.2 (2)4.6 (2)4.1 (1)4.2 (1)4.6 (1)15/15
HE-ES Glasmachers 3.8 (5)2.2 (2)2.6 (1)4.1 (1)4.9 (2)5.6 (2)7.0 (1)15/15
SLSQP+lq-CMA-ES Hansen 3.8 (3)1.6 (0.9)1.3 (0.6)1.4 (0.4)1.1 (0.4)0.97 (0.2)3.8 (2)15/15
SLSQP-11-scipy Hansen 3.8 (3)1.6 (1)1.3 (0.4)1.4 (0.4)1.1 (0.3)0.97 (0.1)3.5 (4)14/15
lq-CMA-ES Hansen 2.3 (2)1.6 (2)1.5 (0.9)1.6 (0.6)1.5 (0.4)1.3 (0.3)1.6 (0.4)15/15

Δ fopt
f15, 2-D		 1e1
37		 1e0
291		 1e-1
1033		 1e-2
1066		 1e-3
1113		 1e-5
1231		 1e-7
1412		 #succ
15/15
CMA-ES-2019 Hansen 1.1 (2)1.5 (1)2.5 (3)3.2 (5)3.2 (5)3.0 (5)2.7 (4)15/15
HE-ES Glasmachers 1.1 (1.0)2.4 (2)3.7 (4)4.4 (4)6.0 (11)6.3 (13)5.9 (12)15/15
SLSQP+lq-CMA-ES Hansen 1.5 (1)2.5 (2)2.0 (1)2.2 (1)2.1 (0.9)2.0 (1)1.8 (1)15/15
SLSQP-11-scipy Hansen 2.9 (5)2.7 (4)2.4 (3)2.4 (3)2.3 (3)2.1 (1)1.8 (1)15/15
lq-CMA-ES Hansen 0.71 (0.6)1.4 (2)1.6 (1)1.7 (1)1.7 (2)1.6 (2)1.4 (1)15/15

Δ fopt
f16, 2-D		 1e1
9.0		 1e0
50		 1e-1
174		 1e-2
326		 1e-3
358		 1e-5
409		 1e-7
538		 #succ
15/15
CMA-ES-2019 Hansen 1.7 (2)4.8 (11)2.3 (2)1.4 (2)1.4 (0.9)1.4 (1)1.2 (1)15/15
HE-ES Glasmachers 2.8 (2)4.3 (8)5.1 (9)3.4 (2)3.2 (4)3.2 (4)2.7 (3)15/15
SLSQP+lq-CMA-ES Hansen 13 (10)11 (15)4.8 (6)2.7 (3)2.6 (2)2.9 (3)2.4 (2)15/15
SLSQP-11-scipy Hansen 430 (39)513 (695)457 (423)599 (671)1850 (2072)∞∞4e40/15
lq-CMA-ES Hansen 3.1 (4)4.0 (2)4.3 (6)2.7 (3)2.9 (2)2.6 (2)2.1 (3)15/15

Δ fopt
f17, 2-D		 1e1
3.0		 1e0
61		 1e-1
133		 1e-2
275		 1e-3
396		 1e-5
1086		 1e-7
1657		 #succ
15/15
CMA-ES-2019 Hansen 1.6 (1)0.62 (0.2)1.0 (0.5)0.90 (1.0)1.2 (1)1.1 (0.8)1.0 (0.8)15/15
HE-ES Glasmachers 2.2 (2)0.77 (0.5)1.3 (0.5)1.0 (0.3)1.1 (0.4)1.2 (0.7)1.3 (1.0)15/15
SLSQP+lq-CMA-ES Hansen 6.6 (7)2.5 (5)1.7 (1)1.1 (1)1.2 (0.7)1.5 (1)1.3 (1.0)15/15
SLSQP-11-scipy Hansen 11 (13)14 (16)72 (52)2121 (2867)∞∞∞4e40/15
lq-CMA-ES Hansen 2.3 (2)0.82 (0.3)1.3 (2)1.3 (2)1.2 (1)1.6 (2)1.4 (0.9)15/15

Δ fopt
f18, 2-D		 1e1
19		 1e0
134		 1e-1
666		 1e-2
1249		 1e-3
1708		 1e-5
2438		 1e-7
2858		 #succ
15/15
CMA-ES-2019 Hansen 1.6 (1)2.4 (3)1.1 (0.9)0.78 (0.7)0.75 (0.5)1.00 (0.7)0.95 (0.6)15/15
HE-ES Glasmachers 1.4 (0.9)1.0 (0.4)0.61 (0.5)0.42 (0.3)0.57 (0.3)0.81 (0.6)1.00 (0.8)15/15
SLSQP+lq-CMA-ES Hansen 5.2 (4)4.9 (5)1.3 (1)0.94 (0.6)0.80 (0.5)0.99 (0.4)1.1 (0.4)15/15
SLSQP-11-scipy Hansen 10 (14)59 (63)103 (182)501 (480)366 (279)∞∞4e40/15
lq-CMA-ES Hansen 1.2 (0.9)1.4 (1)0.75 (1.0)0.61 (0.6)0.62 (0.5)0.96 (0.3)1.0 (0.5)15/15

Δ fopt
f19, 2-D		 1e1
1		 1e0
1		 1e-1
26		 1e-2
216		 1e-3
227		 1e-5
252		 1e-7
276		 #succ
15/15
CMA-ES-2019 Hansen 1 (0)1 (0)12 (25)17 (16)18 (15)17 (14)16 (19)15/15
HE-ES Glasmachers 1 (0)1 (0)7.3 (6)7.9 (14)10 (13)12 (17)12 (16)15/15
SLSQP+lq-CMA-ES Hansen 1 (0)1 (0)0.54 (0)15 (25)17 (23)18 (25)17 (14)15/15
SLSQP-11-scipy Hansen 1 (0)1 (0)0.54 (0)∞∞∞∞4e40/15
lq-CMA-ES Hansen 1 (0)1 (0)6.2 (10)10 (16)10 (16)11 (19)10 (10)15/15

Δ fopt
f20, 2-D		 1e1
4.0		 1e0
61		 1e-1
365		 1e-2
366		 1e-3
366		 1e-5
370		 1e-7
375		 #succ
15/15
CMA-ES-2019 Hansen 2.3 (4)13 (12)5.0 (3)7.3 (9)7.6 (7)8.0 (5)8.2 (10)15/15
HE-ES Glasmachers 2.0 (2)5.4 (5)6.2 (4)14 (24)15 (22)15 (26)16 (25)15/15
SLSQP+lq-CMA-ES Hansen 2.5 (0)17 (29)6.1 (6)7.4 (8)7.7 (5)8.0 (8)8.2 (8)15/15
SLSQP-11-scipy Hansen 2.5 (0)4.7 (7)21 (27)21 (36)21 (28)21 (36)21 (34)15/15
lq-CMA-ES Hansen 1.1 (0.9)3.2 (4)6.5 (13)8.3 (15)9.3 (15)9.3 (15)9.3 (11)15/15

Δ fopt
f21, 2-D		 1e1
2.0		 1e0
51		 1e-1
174		 1e-2
276		 1e-3
290		 1e-5
324		 1e-7
330		 #succ
15/15
CMA-ES-2019 Hansen 1.1 (0.4)6.4 (12)2.8 (2)2.0 (2)2.0 (2)1.9 (2)2.0 (1)15/15
HE-ES Glasmachers 1.1 (1)4.0 (5)4.0 (9)5.1 (15)13 (44)192 (34)330 (36)14/15
SLSQP+lq-CMA-ES Hansen 2.5 (2)8.1 (11)4.4 (9)2.9 (6)2.9 (6)2.7 (2)2.8 (6)15/15
SLSQP-11-scipy Hansen 2.5 (2)3.2 (3)1.3 (1.0)0.88 (0.7)0.86 (0.8)0.83 (0.6)0.89 (0.6)15/15
lq-CMA-ES Hansen 1.3 (0.4)3.5 (5)3.4 (5)2.3 (4)2.9 (6)2.7 (2)2.8 (5)15/15

Δ fopt
f22, 2-D		 1e1
5.0		 1e0
27		 1e-1
168		 1e-2
218		 1e-3
249		 1e-5
289		 1e-7
306		 #succ
15/15
CMA-ES-2019 Hansen 1.4 (2)6.8 (13)8.9 (17)16 (38)33 (101)107 (183)157 (279)12/15
HE-ES Glasmachers 0.87 (0.6)6.3 (19)6.8 (6)6.7 (12)35 (65)278 (88)1464 (1996)11/15
SLSQP+lq-CMA-ES Hansen 2.1 (2)3.8 (7)6.3 (12)13 (37)12 (9)49 (8)46 (8)14/15
SLSQP-11-scipy Hansen 2.1 (2)4.2 (5)1.5 (0.8)1.2 (2)1.1 (2)1.0 (0.5)1.0 (1)15/15
lq-CMA-ES Hansen 1.0 (2)5.6 (16)2.8 (3)4.8 (3)6.1 (12)31 (29)39 (103)13/15

Δ fopt
f23, 2-D		 1e1
8.0		 1e0
193		 1e-1
234		 1e-2
263		 1e-3
299		 1e-5
348		 1e-7
379		 #succ
15/15
CMA-ES-2019 Hansen 1.9 (2)4.3 (5)6.1 (9)5.8 (8)5.3 (7)5.0 (6)5.0 (6)15/15
HE-ES Glasmachers 3.4 (5)6.5 (7)13 (18)12 (16)11 (15)10 (6)10 (12)15/15
SLSQP+lq-CMA-ES Hansen 16 (8)6.3 (10)10 (13)10 (4)9.2 (11)8.2 (7)8.1 (7)15/15
SLSQP-11-scipy Hansen 9.2 (13)10 (12)16 (17)23 (19)31 (51)111 (159)∞4e40/15
lq-CMA-ES Hansen 1.5 (2)5.0 (6)9.3 (18)8.7 (17)8.3 (15)7.5 (13)7.4 (12)15/15

Δ fopt
f24, 2-D		 1e1
18		 1e0
857		 1e-1
8515		 1e-2
23399		 1e-3
24113		 1e-5
24721		 1e-7
24721		 #succ
5/15
CMA-ES-2019 Hansen 2.0 (2)6.5 (6)189 (293)∞∞∞∞6e50/15
HE-ES Glasmachers 1.4 (1)202 (253)3379 (2467)∞∞∞∞2e60/15
SLSQP+lq-CMA-ES Hansen 2.8 (2)99 (238)133 (83)67 (53)65 (126)63 (80)63 (51)4/15
SLSQP-11-scipy Hansen 4.2 (6)1.7 (1)1.5 (1)3.4 (6)3.3 (2)3.3 (3)3.3 (4)6/15
lq-CMA-ES Hansen 1.3 (2)64 (51)77 (120)99 (116)96 (109)93 (99)93 (165)3/15

Previous dimension | Dimension = 3 | Next dimension

Δ fopt
f1, 3-D		 1e1
4.0		 1e0
8.0		 1e-1
8.0		 1e-2
8.0		 1e-3
8.0		 1e-5
8.0		 1e-7
8.0		 #succ
15/15
CMA-ES-2019 Hansen 2.1 (1)4.9 (3)11 (3)16 (4)21 (6)32 (6)43 (8)15/15
HE-ES Glasmachers 2.2 (3)3.8 (2)8.1 (3)14 (4)19 (5)30 (3)41 (5)15/15
SLSQP+lq-CMA-ES Hansen 1.6 (0.9)1 (0)1 (0)1 (0)1 (0)1 (0)1 (0)15/15
SLSQP-11-scipy Hansen 1.6 (0.4)1 (0)1 (0)1 (0)1 (0)1 (0)1 (0)15/15
lq-CMA-ES Hansen 1.2 (1)1.8 (0.3)2.1 (0.4)3.0 (0.8)3.7 (0.7)4.9 (0.8)6.2 (0.7)15/15

Δ fopt
f2, 3-D		 1e1
38		 1e0
42		 1e-1
43		 1e-2
44		 1e-3
45		 1e-5
47		 1e-7
48		 #succ
15/15
CMA-ES-2019 Hansen 7.0 (3)9.0 (3)10 (2)11 (1)12 (2)13 (2)15 (2)15/15
HE-ES Glasmachers 5.2 (3)7.0 (2)7.8 (1)8.5 (1)9.2 (1)11 (2)12 (2)15/15
SLSQP+lq-CMA-ES Hansen 0.98 (0.2)1.1 (0.3)1.2 (0.4)1.3 (0.4)1.4 (0.4)1.6 (0.5)1.7 (0.5)15/15
SLSQP-11-scipy Hansen 0.98 (0.3)1.1 (0.3)1.2 (0.4)1.3 (0.4)1.4 (0.4)1.6 (0.3)1.8 (0.5)15/15
lq-CMA-ES Hansen 1.1 (0.2)1.3 (0.4)1.4 (0.4)1.6 (0.4)1.6 (0.3)1.8 (0.4)2.0 (0.3)15/15

Δ fopt
f3, 3-D		 1e1
38		 1e0
822		 1e-1
830		 1e-2
835		 1e-3
842		 1e-5
847		 1e-7
853		 #succ
15/15
CMA-ES-2019 Hansen 3.7 (3)3.7 (4)23 (35)66 (141)69 (208)71 (78)73 (217)15/15
HE-ES Glasmachers 2.8 (0.8)4.2 (8)162 (185)1841 (3430)2447 (8915)2438 (1899)2425 (7040)9/15
SLSQP+lq-CMA-ES Hansen 4.0 (2)2.1 (2)25 (22)27 (24)47 (155)50 (29)51 (30)15/15
SLSQP-11-scipy Hansen 15 (9)6.8 (7)47 (47)47 (43)47 (84)46 (49)46 (58)12/15
lq-CMA-ES Hansen 2.4 (1)2.6 (3)13 (22)22 (9)23 (62)23 (8)23 (63)15/15

Δ fopt
f4, 3-D		 1e1
40		 1e0
808		 1e-1
866		 1e-2
921		 1e-3
952		 1e-5
1015		 1e-7
1044		 #succ
15/15
CMA-ES-2019 Hansen 9.0 (14)576 (565)4402 (5262)4140 (6219)4005 (3698)3757 (2786)3652 (7182)2/15
HE-ES Glasmachers 3.9 (3)133 (313)1.1e4 (1e4)2.1e4 (2e4)2.0e4 (2e4)1.9e4 (3e4)1.9e4 (2e4)2/15
SLSQP+lq-CMA-ES Hansen 5.6 (4)775 (1881)9766 (1e4)∞∞∞∞6e50/15
SLSQP-11-scipy Hansen 21 (31)39 (42)328 (192)309 (229)299 (256)280 (314)272 (187)3/15
lq-CMA-ES Hansen 4.4 (2)232 (454)3730 (2791)3507 (6356)3393 (4941)3182 (4980)3094 (3498)2/15

Δ fopt
f5, 3-D		 1e1
7.0		 1e0
7.0		 1e-1
7.0		 1e-2
7.0		 1e-3
7.0		 1e-5
7.0		 1e-7
7.0		 #succ
15/15
CMA-ES-2019 Hansen 3.4 (2)5.9 (3)6.2 (3)6.4 (3)6.4 (3)6.4 (2)6.4 (3)15/15
HE-ES Glasmachers 3.3 (1)4.3 (2)4.7 (1)4.8 (2)4.8 (2)4.8 (1)4.8 (2)15/15
SLSQP+lq-CMA-ES Hansen 1 (0)3.1 (0)3.1 (0)3.1 (0)3.1 (0)3.1 (0)3.1 (0)15/15
SLSQP-11-scipy Hansen 1 (0)3.1 (0)3.1 (0)3.1 (0)3.1 (0)3.1 (0)3.1 (0)15/15
lq-CMA-ES Hansen 1.4 (0.5)2.4 (1)★2.6 (1)2.6 (1)2.6 (1)2.6 (1)2.6 (1)15/15

Δ fopt
f6, 3-D		 1e1
34		 1e0
56		 1e-1
90		 1e-2
117		 1e-3
149		 1e-5
215		 1e-7
265		 #succ
15/15
CMA-ES-2019 Hansen 1.8 (1)2.9 (1)3.0 (0.8)3.1 (0.9)3.0 (0.5)2.9 (0.7)3.1 (0.5)15/15
HE-ES Glasmachers 2.8 (2)3.8 (1)3.4 (1)3.5 (0.7)3.6 (0.8)3.5 (0.6)3.6 (0.4)15/15
SLSQP+lq-CMA-ES Hansen 4.7 (4)3.5 (2)2.6 (1)2.3 (1)2.2 (1)2.1 (1)2.7 (2)15/15
SLSQP-11-scipy Hansen 4.4 (2)3.3 (2)2.6 (1)2.4 (1)2.3 (1)2.0 (0.8)2.4 (2)15/15
lq-CMA-ES Hansen 1.6 (0.7)2.1 (0.7)2.1 (0.8)2.2 (0.3)2.3 (0.4)2.3 (0.2)2.5 (0.2)15/15

Δ fopt
f7, 3-D		 1e1
11		 1e0
65		 1e-1
342		 1e-2
464		 1e-3
482		 1e-5
482		 1e-7
535		 #succ
15/15
CMA-ES-2019 Hansen 2.4 (2)2.0 (0.7)0.69 (0.9)0.65 (0.5)0.72 (0.6)0.72 (0.5)0.69 (0.3)15/15
HE-ES Glasmachers 2.2 (2)0.99 (0.6)0.47 (0.3)0.49 (0.2)0.50 (0.2)0.50 (0.3)0.49 (0.1)15/15
SLSQP+lq-CMA-ES Hansen 3.6 (3)1.7 (2)0.86 (0.7)0.92 (0.6)0.94 (0.6)0.94 (0.6)0.88 (0.5)15/15
SLSQP-11-scipy Hansen 16 (22)190 (358)324 (540)1846 (2090)1777 (1258)1777 (3270)1601 (2918)1/15
lq-CMA-ES Hansen 1.2 (0.8)0.38 (0.3)★20.38 (0.6)0.34 (0.4)0.40 (0.5)0.40 (0.5)0.39 (0.4)15/15

Δ fopt
f8, 3-D		 1e1
27		 1e0
45		 1e-1
152		 1e-2
179		 1e-3
188		 1e-5
198		 1e-7
208		 #succ
15/15
CMA-ES-2019 Hansen 2.3 (1)5.3 (4)3.0 (1)3.1 (1)3.3 (1)3.6 (0.9)3.9 (1)15/15
HE-ES Glasmachers 2.9 (2)5.1 (3)2.7 (0.6)2.8 (0.6)2.9 (0.8)3.2 (0.7)3.4 (0.6)15/15
SLSQP+lq-CMA-ES Hansen 1.3 (0.4)2.2 (2)0.95 (0.7)0.92 (0.7)0.94 (0.2)0.95 (0.4)0.94 (0.6)15/15
SLSQP-11-scipy Hansen 1.3 (0.4)2.2 (1)0.95 (0.7)0.94 (0.7)0.96 (0.4)0.96 (0.6)0.95 (0.6)15/15
lq-CMA-ES Hansen 1.4 (0.8)2.3 (1)1.00 (0.5)0.96 (0.6)0.98 (0.6)1.00 (0.5)1.00 (0.5)15/15

Δ fopt
f9, 3-D		 1e1
21		 1e0
65		 1e-1
127		 1e-2
149		 1e-3
159		 1e-5
169		 1e-7
178		 #succ
15/15
CMA-ES-2019 Hansen 2.8 (2)4.0 (3)3.6 (2)3.9 (2)4.0 (1)4.3 (1)4.6 (1)15/15
HE-ES Glasmachers 2.8 (2)3.8 (3)3.3 (1)3.5 (0.7)3.6 (1)3.8 (0.9)4.1 (0.8)15/15
SLSQP+lq-CMA-ES Hansen 0.48 (0)0.15 (0)0.44 (0)0.48 (0)0.55 (0)0.57 (0)0.57 (0)15/15
SLSQP-11-scipy Hansen 0.48 (0)0.15 (0)0.44 (0)0.48 (0)0.55 (0)0.57 (0)0.57 (0)15/15
lq-CMA-ES Hansen 1.6 (0.9)1.3 (0.7)1.1 (0.3)1.1 (0.3)1.0 (0.3)1.1 (0.3)1.1 (0.2)15/15

Δ fopt
f10, 3-D		 1e1
114		 1e0
152		 1e-1
168		 1e-2
180		 1e-3
194		 1e-5
218		 1e-7
242		 #succ
15/15
CMA-ES-2019 Hansen 2.2 (0.8)2.3 (0.5)2.5 (0.4)2.5 (0.2)2.6 (0.2)2.7 (0.1)2.8 (0.3)15/15
HE-ES Glasmachers 2.3 (0.8)2.2 (0.4)2.2 (0.3)2.3 (0.4)2.4 (0.3)2.5 (0.3)2.7 (0.2)15/15
SLSQP+lq-CMA-ES Hansen 0.33 (0.1)0.28 (0.1)0.29 (0.1)0.31 (0.1)0.31 (0.1)0.93 (2)5.3 (7)15/15
SLSQP-11-scipy Hansen 0.33 (0.1)0.29 (0.1)0.30 (0.1)0.31 (0.1)0.32 (0.1)0.41 (0.3)108 (38)9/15
lq-CMA-ES Hansen 0.41 (0.1)0.40 (0.1)0.40 (0.1)0.41 (0.1)0.41 (0.1)0.41 (0.0)0.53 (0.1)15/15

Δ fopt
f11, 3-D		 1e1
67		 1e0
105		 1e-1
227		 1e-2
263		 1e-3
277		 1e-5
302		 1e-7
327		 #succ
15/15
CMA-ES-2019 Hansen 4.0 (2)3.4 (1)1.8 (0.4)1.7 (0.5)1.8 (0.5)1.9 (0.4)2.1 (0.3)15/15
HE-ES Glasmachers 2.7 (2)2.7 (0.8)1.5 (0.2)1.5 (0.2)1.5 (0.2)1.7 (0.2)1.8 (0.1)15/15
SLSQP+lq-CMA-ES Hansen 0.44 (0.2)0.34 (0.1)0.19 (0.0)0.19 (0.1)0.21 (0.1)1.5 (5)6.3 (8)15/15
SLSQP-11-scipy Hansen 0.44 (0.1)0.34 (0.1)0.19 (0.0)0.19 (0.1)0.21 (0.0)33 (111)169 (149)5/15
lq-CMA-ES Hansen 0.68 (0.2)0.54 (0.1)0.28 (0.0)0.27 (0.0)0.27 (0.0)0.29 (0.0)0.40 (0.2)★15/15

Δ fopt
f12, 3-D		 1e1
65		 1e0
168		 1e-1
338		 1e-2
401		 1e-3
445		 1e-5
696		 1e-7
790		 #succ
15/15
CMA-ES-2019 Hansen 6.8 (12)5.1 (8)4.0 (6)4.0 (5)4.0 (5)3.2 (3)4.1 (5)15/15
HE-ES Glasmachers 4.2 (1)3.7 (2)2.8 (2)2.9 (2)2.9 (2)2.3 (2)2.4 (1)15/15
SLSQP+lq-CMA-ES Hansen 2.3 (3)1.5 (2)1.0 (0.9)1.0 (1)1.0 (1.0)2.2 (4)3.9 (3)15/15
SLSQP-11-scipy Hansen 2.3 (2)1.5 (2)1.0 (1)1.0 (0.9)1.0 (1)1.2 (1)4.6 (4)9/15
lq-CMA-ES Hansen 1.2 (2)0.81 (2)0.61 (1)0.66 (0.3)0.71 (0.4)0.74 (0.9)1.6 (1.0)15/15

Δ fopt
f13, 3-D		 1e1
49		 1e0
85		 1e-1
108		 1e-2
136		 1e-3
215		 1e-5
281		 1e-7
365		 #succ
15/15
CMA-ES-2019 Hansen 2.8 (1)2.9 (0.8)3.3 (0.6)3.4 (0.5)2.7 (0.4)2.8 (0.3)2.6 (0.3)15/15
HE-ES Glasmachers 2.2 (0.7)2.3 (0.7)2.8 (0.5)2.8 (0.3)2.2 (0.2)2.3 (0.2)2.3 (0.2)15/15
SLSQP+lq-CMA-ES Hansen 0.89 (0.2)0.77 (0.1)0.79 (0.1)0.77 (0.1)3.6 (11)12 (8)12 (5)15/15
SLSQP-11-scipy Hansen 0.89 (0.2)0.77 (0.1)0.79 (0.1)0.77 (0.1)41 (52)287 (245)∞9e40/15
lq-CMA-ES Hansen 0.71 (0.1)★0.64 (0.1)★0.64 (0.2)★20.64 (0.1)★20.47 (0.1)★30.67 (0.2)★31.2 (0.3)★415/15

Δ fopt
f14, 3-D		 1e1
2.0		 1e0
17		 1e-1
28		 1e-2
43		 1e-3
71		 1e-5
110		 1e-7
194		 #succ
15/15
CMA-ES-2019 Hansen 1.7 (1)2.6 (2)3.5 (1)4.1 (0.7)3.6 (0.6)3.9 (0.4)3.2 (0.4)15/15
HE-ES Glasmachers 2.5 (3)1.7 (2)2.5 (1)3.5 (0.8)3.1 (0.8)3.5 (0.4)2.8 (0.5)15/15
SLSQP+lq-CMA-ES Hansen 2.6 (2)0.90 (0.6)0.83 (0.3)0.85 (0.3)0.74 (0.3)0.75 (0.2)7.4 (12)15/15
SLSQP-11-scipy Hansen 2.6 (2)0.90 (0.4)0.83 (0.4)0.85 (0.4)0.74 (0.2)0.75 (0.2)38 (109)11/15
lq-CMA-ES Hansen 2.2 (2)1.2 (0.5)1.2 (0.5)1.1 (0.3)0.90 (0.2)0.90 (0.1)1.0 (0.4)★215/15

Δ fopt
f15, 3-D		 1e1
121		 1e0
1372		 1e-1
6285		 1e-2
8282		 1e-3
8429		 1e-5
8787		 1e-7
9041		 #succ
15/15
CMA-ES-2019 Hansen 1.3 (0.5)1.2 (0.8)0.99 (0.9)0.78 (0.6)0.80 (0.7)0.79 (0.6)0.81 (0.6)15/15
HE-ES Glasmachers 0.70 (0.5)1.2 (0.8)2.2 (3)1.8 (2)1.8 (2)1.8 (2)1.8 (2)15/15
SLSQP+lq-CMA-ES Hansen 1.5 (0.9)1.1 (0.4)1.1 (0.8)0.84 (0.7)0.84 (0.6)0.84 (0.6)0.85 (0.6)15/15
SLSQP-11-scipy Hansen 5.0 (4)6.4 (6)9.2 (6)7.0 (9)6.8 (11)6.6 (5)6.4 (10)10/15
lq-CMA-ES Hansen 1.2 (1)0.87 (0.9)0.58 (0.6)0.45 (0.3)0.45 (0.6)0.44 (0.6)0.43 (0.3)15/15

Δ fopt
f16, 3-D		 1e1
41		 1e0
319		 1e-1
582		 1e-2
789		 1e-3
1864		 1e-5
3204		 1e-7
3361		 #succ
15/15
CMA-ES-2019 Hansen 1.6 (2)2.4 (2)4.1 (5)3.9 (5)1.7 (2)1.1 (1)1.1 (1)15/15
HE-ES Glasmachers 0.92 (0.8)1.9 (4)1.6 (2)1.3 (1)0.75 (1)0.59 (1)0.61 (0.8)15/15
SLSQP+lq-CMA-ES Hansen 19 (36)3.6 (4)4.1 (3)4.0 (3)1.8 (1)1.1 (0.7)1.1 (0.7)15/15
SLSQP-11-scipy Hansen 66 (54)367 (320)1750 (1901)∞∞∞∞7e40/15
lq-CMA-ES Hansen 1.1 (1.0)1.3 (2)2.6 (5)2.4 (3)1.0 (1)0.68 (0.7)0.67 (0.9)15/15

Δ fopt
f17, 3-D		 1e1
4.0		 1e0
78		 1e-1
282		 1e-2
491		 1e-3
1134		 1e-5
2347		 1e-7
3469		 #succ
15/15
CMA-ES-2019 Hansen 0.95 (1)1.5 (1)1.2 (0.3)1.3 (0.8)1.1 (1)1.0 (0.9)0.96 (0.4)15/15
HE-ES Glasmachers 1.7 (0.9)0.92 (0.8)0.77 (0.2)0.72 (0.2)0.46 (0.1)0.69 (0.4)0.56 (0.3)15/15
SLSQP+lq-CMA-ES Hansen 2.7 (6)3.1 (5)1.5 (2)1.3 (2)0.95 (0.8)0.95 (0.4)0.86 (0.5)15/15
SLSQP-11-scipy Hansen 2.1 (1)46 (51)∞∞∞∞∞6e40/15
lq-CMA-ES Hansen 1.3 (0.7)1.2 (0.5)0.96 (1)0.82 (0.4)0.75 (0.5)0.74 (0.3)0.60 (0.4)15/15

Δ fopt
f18, 3-D		 1e1
40		 1e0
145		 1e-1
1289		 1e-2
3084		 1e-3
3523		 1e-5
4738		 1e-7
5527		 #succ
15/15
CMA-ES-2019 Hansen 2.6 (7)2.3 (3)0.90 (1)0.47 (0.5)0.46 (0.4)0.57 (0.4)0.66 (0.4)15/15
HE-ES Glasmachers 0.70 (0.6)1.0 (0.4)0.23 (0.1)0.17 (0.1)0.24 (0.1)0.41 (0.2)0.42 (0.2)15/15
SLSQP+lq-CMA-ES Hansen 4.8 (4)3.8 (4)0.65 (0.6)0.65 (0.6)0.68 (0.5)0.74 (0.4)0.81 (0.3)15/15
SLSQP-11-scipy Hansen 18 (33)582 (446)∞∞∞∞∞6e40/15
lq-CMA-ES Hansen 0.87 (0.6)3.4 (5)0.94 (0.6)0.56 (0.4)0.55 (0.2)0.58 (0.2)0.66 (0.3)15/15

Δ fopt
f19, 3-D		 1e1
1		 1e0
1		 1e-1
109		 1e-2
6764		 1e-3
7367		 1e-5
7399		 1e-7
7441		 #succ
15/15
CMA-ES-2019 Hansen 1 (0)1 (0)42 (68)2.7 (3)2.6 (4)2.6 (4)2.6 (4)15/15
HE-ES Glasmachers 1 (0)1 (0)47 (59)5.3 (7)5.2 (7)5.3 (7)5.3 (7)15/15
SLSQP+lq-CMA-ES Hansen 1 (0)1 (0)0.14 (0)1.7 (2)2.6 (4)2.6 (3)2.6 (4)15/15
SLSQP-11-scipy Hansen 1 (0)1 (0)0.14 (0)∞∞∞∞9e40/15
lq-CMA-ES Hansen 1 (0)1 (0)36 (39)2.2 (3)2.6 (3)2.6 (3)2.6 (3)15/15

Δ fopt
f20, 3-D		 1e1
8.0		 1e0
385		 1e-1
2291		 1e-2
2398		 1e-3
2481		 1e-5
2573		 1e-7
2776		 #succ
15/15
CMA-ES-2019 Hansen 0.72 (0.6)3.8 (6)4.0 (4)4.1 (4)4.0 (4)4.0 (4)3.9 (4)15/15
HE-ES Glasmachers 2.2 (2)3.5 (3)6.6 (8)9.5 (18)9.2 (15)9.0 (13)8.5 (15)15/15
SLSQP+lq-CMA-ES Hansen 1.4 (0)5.0 (6)5.5 (4)5.8 (4)5.8 (4)5.8 (4)5.5 (4)15/15
SLSQP-11-scipy Hansen 1.4 (0)4.1 (5)11 (18)10 (8)10 (9)10 (5)8.9 (8)14/15
lq-CMA-ES Hansen 1.2 (0.7)3.1 (3)3.5 (3)3.6 (3)3.7 (3)3.6 (3)3.3 (3)15/15

Δ fopt
f21, 3-D		 1e1
6.0		 1e0
184		 1e-1
425		 1e-2
439		 1e-3
458		 1e-5
469		 1e-7
482		 #succ
14/15
CMA-ES-2019 Hansen 1.5 (2)7.1 (18)12 (27)12 (10)12 (9)13 (11)13 (32)15/15
HE-ES Glasmachers 1.3 (2)6.3 (2)7.3 (17)22 (4)415 (1547)987 (1600)961 (3114)13/15
SLSQP+lq-CMA-ES Hansen 2.7 (3)4.9 (10)10 (20)27 (76)27 (83)34 (108)34 (109)15/15
SLSQP-11-scipy Hansen 2.7 (3)1.8 (2)1.7 (2)1.6 (1)1.6 (2)1.6 (2)2.3 (4)15/15
lq-CMA-ES Hansen 1.7 (2)2.0 (3)1.9 (3)2.0 (2)2.0 (3)2.1 (3)2.1 (3)15/15

Δ fopt
f22, 3-D		 1e1
18		 1e0
170		 1e-1
354		 1e-2
362		 1e-3
384		 1e-5
401		 1e-7
414		 #succ
15/15
CMA-ES-2019 Hansen 1.4 (1)5.0 (12)24 (62)87 (126)160 (547)259 (497)252 (695)11/15
HE-ES Glasmachers 3.2 (8)4.6 (7)38 (29)102 (180)617 (1775)5230 (1e4)8310 (9070)7/15
SLSQP+lq-CMA-ES Hansen 1.9 (2)4.5 (5)10 (9)13 (14)56 (173)54 (156)53 (161)14/15
SLSQP-11-scipy Hansen 2.2 (3)2.4 (3)2.1 (2)2.1 (3)2.0 (2)2.0 (2)2.1 (2)15/15
lq-CMA-ES Hansen 2.5 (6)2.1 (2)8.0 (19)34 (86)33 (101)50 (6)48 (76)13/15

Δ fopt
f23, 3-D		 1e1
3.0		 1e0
407		 1e-1
906		 1e-2
1215		 1e-3
2214		 1e-5
2293		 1e-7
2393		 #succ
15/15
CMA-ES-2019 Hansen 3.2 (4)6.8 (11)5.7 (7)4.5 (4)3.6 (5)3.7 (3)3.6 (4)15/15
HE-ES Glasmachers 3.5 (3)13 (10)18 (15)14 (13)8.0 (7)7.9 (6)7.7 (7)15/15
SLSQP+lq-CMA-ES Hansen 19 (43)5.3 (7)10 (8)8.1 (9)4.6 (5)4.6 (3)4.5 (5)15/15
SLSQP-11-scipy Hansen 21 (37)6.6 (5)21 (25)22 (30)15 (27)83 (158)∞6e40/15
lq-CMA-ES Hansen 3.2 (6)4.6 (3)4.5 (6)3.5 (5)1.9 (1.0)2.0 (2)2.0 (2)15/15

Δ fopt
f24, 3-D		 1e1
97		 1e0
10391		 1e-1
1.0e5		 1e-2
3.6e5		 1e-3
3.6e5		 1e-5
3.6e5		 1e-7
3.6e5		 #succ
2/15
CMA-ES-2019 Hansen 1.6 (2)37 (110)106 (181)31 (34)31 (27)31 (47)31 (52)1/15
HE-ES Glasmachers 0.98 (0.7)1156 (2600)∞∞∞∞∞3e60/15
SLSQP+lq-CMA-ES Hansen 2.6 (2)63 (92)100 (206)29 (26)29 (40)29 (18)29 (36)1/15
SLSQP-11-scipy Hansen 8.2 (9)3.2 (4)8.4 (10)∞∞∞∞6e40/15
lq-CMA-ES Hansen 1.5 (1)986 (1747)∞∞∞∞∞7e50/15

Previous dimension | Dimension = 5 | Next dimension

Δ fopt
f1, 5-D		 1e1
11		 1e0
12		 1e-1
12		 1e-2
12		 1e-3
12		 1e-5
12		 1e-7
12		 #succ
15/15
CMA-ES-2019 Hansen 2.1 (2)7.3 (3)14 (4)19 (4)26 (2)37 (5)51 (4)15/15
HE-ES Glasmachers 2.0 (1)4.8 (3)11 (4)17 (3)22 (3)33 (5)44 (5)15/15
SLSQP+lq-CMA-ES Hansen 0.91 (0)0.83 (0)0.83 (0)0.83 (0)0.83 (0)0.83 (0)0.83 (0)15/15
SLSQP-11-scipy Hansen 0.91 (0)0.83 (0)0.83 (0)0.83 (0)0.83 (0)0.83 (0)0.83 (0)15/15
lq-CMA-ES Hansen 1.2 (0.5)1.8 (0.3)2.3 (0.4)2.8 (0.5)3.5 (0.6)4.6 (0.9)5.5 (0.7)15/15

Δ fopt
f2, 5-D		 1e1
83		 1e0
87		 1e-1
88		 1e-2
89		 1e-3
90		 1e-5
92		 1e-7
94		 #succ
15/15
CMA-ES-2019 Hansen 7.5 (3)9.2 (2)10 (2)11 (2)12 (2)13 (2)15 (1)15/15
HE-ES Glasmachers 6.9 (2)7.9 (1)8.5 (1)9.0 (1)10 (1)11 (1)12 (1)15/15
SLSQP+lq-CMA-ES Hansen 1.1 (0.6)1.2 (0.5)1.3 (0.6)1.4 (0.5)1.6 (0.5)1.8 (0.5)2.1 (1)15/15
SLSQP-11-scipy Hansen 1.1 (0.2)1.2 (0.3)1.3 (0.3)1.4 (0.6)1.5 (0.8)1.8 (0.5)1.9 (0.4)15/15
lq-CMA-ES Hansen 1.1 (0.4)1.2 (0.3)1.4 (0.3)1.5 (0.3)1.6 (0.3)1.8 (0.3)2.0 (0.4)15/15

Δ fopt
f3, 5-D		 1e1
716		 1e0
1622		 1e-1
1637		 1e-2
1642		 1e-3
1646		 1e-5
1650		 1e-7
1654		 #succ
15/15
CMA-ES-2019 Hansen 1.5 (1)67 (172)721 (2502)719 (1303)717 (971)716 (832)714 (1417)6/15
HE-ES Glasmachers 0.89 (0.4)5093 (5215)4.3e4 (5e4)4.3e4 (4e4)4.3e4 (3e4)4.2e4 (4e4)4.2e4 (7e4)1/15
SLSQP+lq-CMA-ES Hansen 1.7 (1)9.2 (13)942 (1289)940 (1163)938 (2633)936 (1250)934 (1276)5/15
SLSQP-11-scipy Hansen 17 (24)879 (1231)∞∞∞∞∞1e50/15
lq-CMA-ES Hansen 0.50 (0.4)54 (74)765 (944)763 (1128)761 (1641)759 (1051)757 (1223)5/15

Δ fopt
f4, 5-D		 1e1
809		 1e0
1633		 1e-1
1688		 1e-2
1758		 1e-3
1817		 1e-5
1886		 1e-7
1903		 #succ
15/15
CMA-ES-2019 Hansen 0.77 (0.2)7196 (7724)∞∞∞∞∞8e50/15
HE-ES Glasmachers 0.76 (0.6)∞∞∞∞∞∞5e60/15
SLSQP+lq-CMA-ES Hansen 1.8 (1)∞∞∞∞∞∞8e50/15
SLSQP-11-scipy Hansen 59 (39)∞∞∞∞∞∞1e50/15
lq-CMA-ES Hansen 1.4 (2)∞∞∞∞∞∞8e50/15

Δ fopt
f5, 5-D		 1e1
10		 1e0
10		 1e-1
10		 1e-2
10		 1e-3
10		 1e-5
10		 1e-7
10		 #succ
15/15
CMA-ES-2019 Hansen 4.6 (2)6.2 (3)6.4 (2)6.5 (2)6.5 (2)6.5 (2)6.5 (2)15/15
HE-ES Glasmachers 4.0 (2)5.5 (1)5.8 (2)5.8 (2)5.8 (2)5.8 (2)5.8 (2)15/15
SLSQP+lq-CMA-ES Hansen 1.6 (0)2.3 (0)3.0 (0)3.0 (0)3.0 (0)3.0 (0)3.0 (0)15/15
SLSQP-11-scipy Hansen 1.6 (0)2.3 (0)3.0 (0)3.0 (0)3.0 (0)3.0 (0)3.0 (0)15/15
lq-CMA-ES Hansen 1.5 (0.6)2.2 (0.8)2.3 (0.8)★22.3 (0.8)★22.3 (0.9)★22.3 (0.8)★22.3 (0.8)★215/15

Δ fopt
f6, 5-D		 1e1
114		 1e0
214		 1e-1
281		 1e-2
404		 1e-3
580		 1e-5
1038		 1e-7
1332		 #succ
15/15
CMA-ES-2019 Hansen 1.8 (0.7)1.7 (0.4)1.8 (0.5)1.7 (0.3)1.5 (0.2)1.1 (0.2)1.1 (0.1)15/15
HE-ES Glasmachers 2.1 (1)2.0 (0.6)2.2 (0.4)1.9 (0.4)1.7 (0.3)1.3 (0.2)1.3 (0.1)15/15
SLSQP+lq-CMA-ES Hansen 2.9 (2)1.9 (1)2.0 (0.9)1.6 (0.7)1.4 (0.6)1.0 (0.5)1.4 (0.9)15/15
SLSQP-11-scipy Hansen 2.9 (2)2.1 (1)2.2 (1)1.7 (1)1.4 (0.7)0.99 (0.5)2.2 (1)15/15
lq-CMA-ES Hansen 1.5 (0.6)1.5 (0.6)1.7 (0.2)1.5 (0.2)1.4 (0.2)1.1 (0.1)1.1 (0.1)15/15

Δ fopt
f7, 5-D		 1e1
24		 1e0
324		 1e-1
1171		 1e-2
1451		 1e-3
1572		 1e-5
1572		 1e-7
1597		 #succ
15/15
CMA-ES-2019 Hansen 2.5 (1)0.69 (0.5)0.47 (0.4)0.49 (0.3)0.58 (0.3)0.58 (0.3)0.67 (0.3)15/15
HE-ES Glasmachers 2.6 (2)0.49 (0.2)0.33 (0.3)0.35 (0.2)0.34 (0.2)0.34 (0.1)0.41 (0.3)15/15
SLSQP+lq-CMA-ES Hansen 4.1 (3)0.86 (0.3)0.74 (0.6)0.68 (0.6)0.65 (0.4)0.65 (0.5)0.67 (0.5)15/15
SLSQP-11-scipy Hansen 286 (620)1064 (1105)∞∞∞∞∞1e50/15
lq-CMA-ES Hansen 1.5 (0.6)0.50 (0.5)0.45 (0.4)0.48 (0.3)0.47 (0.3)0.47 (0.2)0.51 (0.3)15/15

Δ fopt
f8, 5-D		 1e1
73		 1e0
273		 1e-1
336		 1e-2
372		 1e-3
391		 1e-5
410		 1e-7
422		 #succ
15/15
CMA-ES-2019 Hansen 2.5 (1)3.2 (2)3.7 (3)3.9 (2)4.0 (2)4.3 (2)4.6 (1)15/15
HE-ES Glasmachers 2.3 (0.9)2.9 (2)3.3 (2)3.4 (2)3.5 (2)3.7 (2)3.9 (0.4)15/15
SLSQP+lq-CMA-ES Hansen 1.3 (0.6)1.9 (3)2.0 (3)2.0 (0.4)2.0 (2)2.1 (3)2.1 (3)15/15
SLSQP-11-scipy Hansen 1.3 (0.5)1.1 (0.9)1.0 (0.8)1.0 (0.7)1.0 (0.5)1.0 (0.5)1.0 (0.7)15/15
lq-CMA-ES Hansen 1.3 (0.4)1.2 (1)1.2 (0.9)1.2 (0.8)1.1 (1)1.1 (1)1.1 (1.0)15/15

Δ fopt
f9, 5-D		 1e1
35		 1e0
127		 1e-1
214		 1e-2
263		 1e-3
300		 1e-5
335		 1e-7
369		 #succ
15/15
CMA-ES-2019 Hansen 4.1 (1)7.4 (9)6.1 (3)5.7 (3)5.4 (0.7)5.3 (3)5.2 (2)15/15
HE-ES Glasmachers 4.3 (0.8)5.1 (1)4.3 (0.6)4.2 (0.7)4.0 (0.5)4.0 (0.4)3.9 (0.4)15/15
SLSQP+lq-CMA-ES Hansen 0.63 (0)0.46 (0)0.54 (0)0.55 (0)0.53 (0)0.51 (0)0.50 (0)15/15
SLSQP-11-scipy Hansen 0.63 (0)0.46 (0)0.54 (0)0.55 (0)0.53 (0)0.51 (0)0.50 (0)15/15
lq-CMA-ES Hansen 2.5 (1)2.3 (3)1.7 (2)1.5 (0.9)1.4 (2)1.3 (0.7)1.2 (0.6)15/15

Δ fopt
f10, 5-D		 1e1
349		 1e0
500		 1e-1
574		 1e-2
607		 1e-3
626		 1e-5
829		 1e-7
880		 #succ
15/15
CMA-ES-2019 Hansen 2.0 (0.6)1.6 (0.4)1.6 (0.3)1.7 (0.3)1.7 (0.2)1.5 (0.2)1.6 (0.2)15/15
HE-ES Glasmachers 1.5 (0.4)1.3 (0.3)1.3 (0.2)1.3 (0.2)1.4 (0.2)1.2 (0.1)1.3 (0.1)15/15
SLSQP+lq-CMA-ES Hansen 0.25 (0.1)0.20 (0.0)0.19 (0.1)0.20 (0.1)0.22 (0.1)0.95 (0.5)2.9 (1)15/15
SLSQP-11-scipy Hansen 0.25 (0.1)0.20 (0.0)0.19 (0.0)0.19 (0.0)0.20 (0.0)0.22 (0.0)23 (30)10/15
lq-CMA-ES Hansen 0.34 (0.1)0.27 (0.1)0.25 (0.1)0.25 (0.1)0.26 (0.0)0.22 (0.0)0.28 (0.1)15/15

Δ fopt
f11, 5-D		 1e1
143		 1e0
202		 1e-1
763		 1e-2
977		 1e-3
1177		 1e-5
1467		 1e-7
1673		 #succ
15/15
CMA-ES-2019 Hansen 3.8 (0.8)3.2 (0.3)0.99 (0.1)0.85 (0.1)0.77 (0.1)0.72 (0.1)0.71 (0.0)15/15
HE-ES Glasmachers 3.6 (0.5)3.0 (0.3)0.87 (0.1)0.74 (0.1)0.68 (0.1)0.64 (0.1)0.64 (0.0)15/15
SLSQP+lq-CMA-ES Hansen 0.28 (0.1)0.28 (0.1)0.08 (0.0)0.08 (0.0)0.07 (0.0)1.1 (1)1.9 (1)15/15
SLSQP-11-scipy Hansen 0.28 (0.1)0.27 (0.1)0.08 (0.0)0.07 (0.0)0.07 (0.0)7.2 (17)195 (133)0/15
lq-CMA-ES Hansen 0.68 (0.2)0.63 (0.1)0.19 (0.0)0.16 (0.0)0.14 (0.0)0.13 (0.0)0.15 (0.0)★415/15

Δ fopt
f12, 5-D		 1e1
108		 1e0
268		 1e-1
371		 1e-2
413		 1e-3
461		 1e-5
1303		 1e-7
1494		 #succ
15/15
CMA-ES-2019 Hansen 6.4 (2)4.5 (6)5.2 (2)5.6 (3)5.9 (6)2.7 (1)2.8 (3)15/15
HE-ES Glasmachers 4.7 (2)3.1 (1)3.5 (3)3.8 (2)4.0 (3)2.0 (1)2.1 (1)15/15
SLSQP+lq-CMA-ES Hansen 2.8 (4)1.7 (2)1.6 (2)1.6 (2)1.5 (2)1.1 (0.6)3.3 (4)15/15
SLSQP-11-scipy Hansen 2.8 (4)1.7 (2)1.5 (2)1.5 (2)1.5 (2)0.88 (1)4.2 (11)11/15
lq-CMA-ES Hansen 1.2 (0.2)0.90 (0.9)1.0 (1)1.1 (1)1.2 (1)0.76 (0.7)1.1 (0.9)15/15

Δ fopt
f13, 5-D		 1e1
132		 1e0
195		 1e-1
250		 1e-2
319		 1e-3
1310		 1e-5
1752		 1e-7
2255		 #succ
15/15
CMA-ES-2019 Hansen 2.3 (0.6)3.1 (1)3.3 (0.9)3.3 (0.9)1.0 (0.2)1.0 (0.2)0.97 (0.1)15/15
HE-ES Glasmachers 1.7 (0.5)2.0 (0.2)2.6 (0.8)2.9 (0.5)0.84 (0.2)0.91 (0.1)0.88 (0.1)15/15
SLSQP+lq-CMA-ES Hansen 0.76 (0.1)0.74 (0.1)0.76 (0.1)0.73 (0.0)2.6 (2)3.5 (0.6)3.0 (0.6)15/15
SLSQP-11-scipy Hansen 0.76 (0.1)0.74 (0.1)0.76 (0.1)0.73 (0.0)35 (103)437 (633)∞1e50/15
lq-CMA-ES Hansen 0.64 (0.1)★0.63 (0.1)★0.67 (0.1)★0.65 (0.1)★0.19 (0.0)★30.30 (0.1)★40.45 (0.1)★415/15

Δ fopt
f14, 5-D		 1e1
10		 1e0
41		 1e-1
58		 1e-2
90		 1e-3
139		 1e-5
251		 1e-7
476		 #succ
15/15
CMA-ES-2019 Hansen 1.5 (3)2.2 (1)3.3 (2)3.6 (1)3.4 (0.8)3.2 (0.3)2.5 (0.2)15/15
HE-ES Glasmachers 0.61 (0.7)1.5 (0.9)2.4 (0.9)2.6 (0.8)2.5 (0.5)2.7 (0.5)2.2 (0.2)15/15
SLSQP+lq-CMA-ES Hansen 0.89 (0.8)0.58 (0.3)0.74 (0.3)0.77 (0.2)0.70 (0.2)0.59 (0.1)5.7 (5)15/15
SLSQP-11-scipy Hansen 0.89 (0.8)0.58 (0.2)0.74 (0.3)0.77 (0.2)0.70 (0.1)0.59 (0.1)512 (754)3/15
lq-CMA-ES Hansen 1.1 (1)1.1 (0.4)1.2 (0.3)1.1 (0.3)1.0 (0.1)0.85 (0.1)1.0 (0.2)★215/15

Δ fopt
f15, 5-D		 1e1
511		 1e0
9310		 1e-1
19369		 1e-2
19743		 1e-3
20073		 1e-5
20769		 1e-7
21359		 #succ
14/15
CMA-ES-2019 Hansen 1.3 (1)0.68 (0.7)0.76 (0.9)0.76 (1)0.76 (0.6)0.77 (0.9)0.78 (1.0)15/15
HE-ES Glasmachers 1.2 (0.4)0.49 (0.4)0.78 (0.8)0.79 (0.6)0.80 (0.7)0.81 (0.8)0.82 (0.7)15/15
SLSQP+lq-CMA-ES Hansen 1.7 (2)0.99 (0.5)1.1 (1)1.1 (0.7)1.1 (0.9)1.1 (1)1.2 (1)15/15
SLSQP-11-scipy Hansen 30 (19)153 (234)∞∞∞∞∞1e50/15
lq-CMA-ES Hansen 1.3 (1)0.62 (0.5)0.54 (0.5)0.54 (0.5)0.53 (0.5)0.52 (0.3)0.51 (0.5)15/15

Δ fopt
f16, 5-D		 1e1
120		 1e0
612		 1e-1
2662		 1e-2
10163		 1e-3
10449		 1e-5
11644		 1e-7
12095		 #succ
15/15
CMA-ES-2019 Hansen 2.3 (2)1.8 (3)1.7 (1)0.61 (0.6)0.69 (0.6)0.65 (0.6)0.65 (0.6)15/15
HE-ES Glasmachers 3.2 (2)3.2 (4)0.81 (1)0.29 (0.3)0.30 (0.4)0.33 (0.4)0.34 (0.4)15/15
SLSQP+lq-CMA-ES Hansen 7.0 (7)2.8 (3)1.4 (1)0.90 (1)1.1 (1)0.99 (1)0.99 (1)15/15
SLSQP-11-scipy Hansen 250 (406)∞∞∞∞∞∞1e50/15
lq-CMA-ES Hansen 2.0 (2)1.6 (2)1.2 (0.8)0.43 (0.5)0.47 (0.5)0.47 (0.5)0.47 (0.5)15/15

Δ fopt
f17, 5-D		 1e1
5.0		 1e0
215		 1e-1
899		 1e-2
2861		 1e-3
3669		 1e-5
6351		 1e-7
7934		 #succ
15/15
CMA-ES-2019 Hansen 1.9 (2)0.72 (0.3)0.48 (0.1)0.63 (0.7)0.75 (0.5)0.79 (0.4)1.2 (0.4)15/15
HE-ES Glasmachers 2.1 (2)0.66 (0.2)0.37 (0.1)0.20 (0.0)0.22 (0.0)★20.46 (0.2)0.51 (0.2)★215/15
SLSQP+lq-CMA-ES Hansen 13 (20)2.6 (0.8)1.3 (2)0.55 (0.5)0.60 (0.4)0.95 (0.6)1.0 (0.4)15/15
SLSQP-11-scipy Hansen 31 (73)300 (377)∞∞∞∞∞1e50/15
lq-CMA-ES Hansen 3.1 (7)5.0 (16)2.6 (4)0.95 (1)1.1 (1)1.3 (0.6)1.2 (0.8)15/15

Δ fopt
f18, 5-D		 1e1
103		 1e0
378		 1e-1
3968		 1e-2
8451		 1e-3
9280		 1e-5
10905		 1e-7
12469		 #succ
15/15
CMA-ES-2019 Hansen 0.82 (0.5)0.77 (0.3)0.36 (0.6)0.58 (0.6)0.66 (0.5)0.79 (0.5)0.93 (0.6)15/15
HE-ES Glasmachers 0.72 (0.6)0.73 (0.3)90 (315)50 (175)46 (135)39 (136)68 (101)13/15
SLSQP+lq-CMA-ES Hansen 2.1 (1.0)1.4 (0.5)0.78 (0.9)0.52 (0.4)0.69 (0.4)0.77 (0.4)0.85 (0.3)15/15
SLSQP-11-scipy Hansen 46 (31)∞∞∞∞∞∞1e50/15
lq-CMA-ES Hansen 6.0 (20)2.3 (6)0.80 (1.0)0.69 (0.3)0.73 (0.3)0.79 (0.3)0.82 (0.2)15/15

Δ fopt
f19, 5-D		 1e1
1		 1e0
1		 1e-1
242		 1e-2
1.0e5		 1e-3
1.2e5		 1e-5
1.2e5		 1e-7
1.2e5		 #succ
15/15
CMA-ES-2019 Hansen 1 (0)1 (0)171 (137)1.0 (0.4)1.0 (0.8)1.0 (0.9)1.0 (0.9)15/15
HE-ES Glasmachers 1 (0)1 (0)256 (375)1.2 (0.7)1.0 (0.8)1.1 (0.8)1.1 (0.8)15/15
SLSQP+lq-CMA-ES Hansen 1 (0)1 (0)0.12 (0)1.0 (0.8)1.0 (0.5)1.0 (0.7)1.1 (0.8)15/15
SLSQP-11-scipy Hansen 1 (0)1 (0)0.12 (0)∞∞∞∞1e50/15
lq-CMA-ES Hansen 1 (0)1 (0)72 (75)0.54 (0.3)0.55 (0.4)0.56 (0.4)0.57 (0.5)15/15

Δ fopt
f20, 5-D		 1e1
16		 1e0
851		 1e-1
38111		 1e-2
51362		 1e-3
54470		 1e-5
54861		 1e-7
55313		 #succ
14/15
CMA-ES-2019 Hansen 1.7 (1)4.3 (4)1.9 (2)1.5 (1)1.5 (1)1.5 (1)1.5 (1)15/15
HE-ES Glasmachers 1.4 (0.8)14 (30)21 (28)16 (35)15 (33)15 (19)15 (33)15/15
SLSQP+lq-CMA-ES Hansen 0.81 (0)7.9 (7)2.2 (2)1.9 (1)1.9 (1)1.9 (1)2.0 (1)15/15
SLSQP-11-scipy Hansen 0.81 (0)2.3 (2)∞∞∞∞∞1e50/15
lq-CMA-ES Hansen 1.4 (1)6.1 (3)1.4 (1)1.1 (0.9)1.0 (0.3)1.0 (0.9)1.0 (0.8)15/15

Δ fopt
f21, 5-D		 1e1
41		 1e0
1157		 1e-1
1674		 1e-2
1692		 1e-3
1705		 1e-5
1729		 1e-7
1757		 #succ
14/15
CMA-ES-2019 Hansen 1.5 (1)8.6 (4)15 (32)21 (51)21 (52)23 (59)23 (20)15/15
HE-ES Glasmachers 1.4 (2)4.2 (10)362 (36)1484 (2963)1473 (2940)1453 (2176)1430 (2848)10/15
SLSQP+lq-CMA-ES Hansen 1.3 (2)8.9 (25)38 (100)38 (52)38 (85)38 (98)38 (114)13/15
SLSQP-11-scipy Hansen 1.3 (2)0.81 (1)1.3 (2)1.2 (2)1.2 (0.7)1.3 (2)1.4 (3)15/15
lq-CMA-ES Hansen 1.5 (1)2.0 (3)10 (5)11 (5)11 (29)11 (28)11 (6)14/15

Δ fopt
f22, 5-D		 1e1
71		 1e0
386		 1e-1
938		 1e-2
980		 1e-3
1008		 1e-5
1040		 1e-7
1068		 #succ
14/15
CMA-ES-2019 Hansen 3.4 (5)10 (15)155 (183)332 (424)323 (709)315 (597)307 (179)8/15
HE-ES Glasmachers 2.4 (4)41 (38)872 (1270)8753 (1e4)2.0e4 (3e4)1.9e4 (3e4)1.9e4 (3e4)3/15
SLSQP+lq-CMA-ES Hansen 1.4 (1)7.5 (19)333 (458)319 (368)311 (515)302 (340)294 (407)8/15
SLSQP-11-scipy Hansen 1.8 (2)1.1 (2)1.8 (4)1.7 (4)1.7 (4)1.7 (4)2.0 (4)14/15
lq-CMA-ES Hansen 3.6 (6)7.0 (7)76 (86)170 (332)165 (321)161 (308)157 (139)8/15

Δ fopt
f23, 5-D		 1e1
3.0		 1e0
518		 1e-1
14249		 1e-2
27890		 1e-3
31654		 1e-5
33030		 1e-7
34256		 #succ
15/15
CMA-ES-2019 Hansen 2.9 (3)6.4 (7)1.9 (2)1.1 (1)1.0 (1)0.99 (0.8)0.98 (1)15/15
HE-ES Glasmachers 2.6 (1)25 (15)5.8 (6)4.8 (5)4.2 (6)4.1 (7)4.0 (4)15/15
SLSQP+lq-CMA-ES Hansen 96 (334)12 (17)2.3 (4)1.2 (1)1.1 (1)1.1 (0.7)1.1 (2)15/15
SLSQP-11-scipy Hansen 27 (7)13 (14)17 (48)25 (25)∞∞∞1e50/15
lq-CMA-ES Hansen 1.8 (2)3.3 (2)15 (33)7.9 (3)6.9 (6)10 (24)9.4 (14)13/15

Δ fopt
f24, 5-D		 1e1
1622		 1e0
2.2e5		 1e-1
6.4e6		 1e-2
9.6e6		 1e-3
9.6e6		 1e-5
1.3e7		 1e-7
1.3e7		 #succ
3/15
CMA-ES-2019 Hansen 1.2 (2)9.1 (8)2.8 (2)∞∞∞∞1e60/15
HE-ES Glasmachers 3.0 (3)∞∞∞∞∞∞5e60/15
SLSQP+lq-CMA-ES Hansen 1.5 (1)13 (14)1.4 (2)1.9 (2)1.9 (4)1.4 (2)1.4 (0.8)1/15
SLSQP-11-scipy Hansen 6.4 (6)∞∞∞∞∞∞1e50/15
lq-CMA-ES Hansen 1.2 (0.9)109 (104)3.7 (4)2.5 (3)2.5 (2)1.8 (2)1.8 (2)1/15

Previous dimension | Dimension = 10 | Next dimension

Δ fopt
f1, 10-D		 1e1
22		 1e0
23		 1e-1
23		 1e-2
23		 1e-3
23		 1e-5
23		 1e-7
23		 #succ
15/15
CMA-ES-2019 Hansen 3.6 (2)10 (2)17 (2)23 (4)30 (4)43 (4)56 (3)15/15
HE-ES Glasmachers 2.9 (1)7.8 (1)13 (2)17 (2)22 (3)32 (3)42 (3)15/15
SLSQP+lq-CMA-ES Hansen 0.68 (0)0.65 (0)0.65 (0)0.65 (0)0.65 (0)0.65 (0)0.65 (0)15/15
SLSQP-11-scipy Hansen 0.68 (0)0.65 (0)0.65 (0)0.65 (0)0.65 (0)0.65 (0)0.65 (0)15/15
lq-CMA-ES Hansen 1.5 (0.0)1.7 (0.3)2.1 (0.5)2.5 (0.4)3.0 (0.2)3.7 (0.3)4.5 (0.2)15/15

Δ fopt
f2, 10-D		 1e1
187		 1e0
190		 1e-1
191		 1e-2
191		 1e-3
193		 1e-5
194		 1e-7
195		 #succ
15/15
CMA-ES-2019 Hansen 12 (4)15 (2)16 (2)17 (1)17 (1)19 (1)20 (1)15/15
HE-ES Glasmachers 8.7 (2)10 (1)11 (2)12 (1)12 (2)13 (1)15 (2)15/15
SLSQP+lq-CMA-ES Hansen 1.5 (0.4)1.6 (0.3)1.7 (0.4)1.9 (0.3)1.9 (0.4)2.1 (0.5)2.4 (0.6)15/15
SLSQP-11-scipy Hansen 1.6 (0.4)1.6 (0.6)1.7 (0.6)1.9 (0.6)2.0 (0.4)2.3 (0.6)2.6 (0.8)15/15
lq-CMA-ES Hansen 1.7 (0.5)1.9 (0.6)2.1 (0.5)2.3 (0.6)2.5 (0.6)2.8 (0.5)3.2 (0.7)15/15

Δ fopt
f3, 10-D		 1e1
1739		 1e0
3600		 1e-1
3609		 1e-2
3636		 1e-3
3642		 1e-5
3646		 1e-7
3651		 #succ
15/15
CMA-ES-2019 Hansen 3.7 (1)1082 (2237)1567 (2643)1555 (3644)1553 (1434)1552 (591)1551 (1989)3/15
HE-ES Glasmachers 1.8 (1)7644 (2e4)∞∞∞∞∞1e70/15
SLSQP+lq-CMA-ES Hansen 3.8 (1)2623 (3986)∞∞∞∞∞1e60/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞2e50/15
lq-CMA-ES Hansen 1.3 (2)4500 (6842)∞∞∞∞∞1e60/15

Δ fopt
f4, 10-D		 1e1
2234		 1e0
3626		 1e-1
3660		 1e-2
3695		 1e-3
3707		 1e-5
3744		 1e-7
28767		 #succ
12/15
CMA-ES-2019 Hansen 6.8 (9)∞∞∞∞∞∞1e60/15
HE-ES Glasmachers 3.2 (5)∞∞∞∞∞∞1e70/15
SLSQP+lq-CMA-ES Hansen 4.7 (3)∞∞∞∞∞∞1e60/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞2e50/15
lq-CMA-ES Hansen 4.6 (3)∞∞∞∞∞∞1e60/15

Δ fopt
f5, 10-D		 1e1
20		 1e0
20		 1e-1
20		 1e-2
20		 1e-3
20		 1e-5
20		 1e-7
20		 #succ
15/15
CMA-ES-2019 Hansen 5.0 (2)6.3 (2)6.5 (2)6.7 (1)6.7 (1)6.7 (3)6.7 (3)15/15
HE-ES Glasmachers 4.2 (1)5.2 (1)5.4 (1)5.5 (1)5.5 (2)5.5 (0.9)5.5 (1)15/15
SLSQP+lq-CMA-ES Hansen 1.3 (0)2.5 (0)2.5 (0)2.5 (0)2.5 (0)2.5 (0)2.5 (0)15/15
SLSQP-11-scipy Hansen 1.3 (0)2.5 (0)2.5 (0)2.5 (0)2.5 (0)2.5 (0)2.5 (0)15/15
lq-CMA-ES Hansen 1.6 (0.5)2.1 (0.7)2.2 (0.8)2.2 (0.8)2.2 (0.7)2.2 (0.7)2.2 (0.8)15/15

Δ fopt
f6, 10-D		 1e1
412		 1e0
623		 1e-1
826		 1e-2
1039		 1e-3
1292		 1e-5
1841		 1e-7
2370		 #succ
15/15
CMA-ES-2019 Hansen 1.7 (0.6)1.6 (0.4)1.7 (0.3)1.7 (0.1)1.7 (0.2)1.6 (0.2)1.6 (0.2)15/15
HE-ES Glasmachers 1.9 (0.5)2.0 (0.4)2.0 (0.4)2.0 (0.4)2.0 (0.3)1.8 (0.2)1.9 (0.2)15/15
SLSQP+lq-CMA-ES Hansen 2.4 (1)2.2 (0.6)2.3 (1.0)2.4 (0.9)2.7 (2)2.9 (0.9)3.2 (0.1)15/15
SLSQP-11-scipy Hansen 2.3 (1)2.0 (0.5)2.1 (0.4)2.3 (0.3)2.3 (0.7)2.4 (0.5)8.4 (7)4/15
lq-CMA-ES Hansen 1.4 (0.3)1.5 (0.3)1.6 (0.3)1.7 (0.2)1.6 (0.2)1.6 (0.1)1.5 (0.1)15/15

Δ fopt
f7, 10-D		 1e1
172		 1e0
1611		 1e-1
4195		 1e-2
5099		 1e-3
5141		 1e-5
5141		 1e-7
5389		 #succ
15/15
CMA-ES-2019 Hansen 1.6 (0.6)0.62 (0.3)0.59 (0.4)0.64 (0.3)0.70 (0.3)0.70 (0.3)0.72 (0.4)15/15
HE-ES Glasmachers 1.3 (0.4)0.34 (0.1)0.66 (0.2)0.61 (0.8)0.61 (0.5)0.61 (0.1)0.60 (0.8)15/15
SLSQP+lq-CMA-ES Hansen 2.0 (0.8)1.1 (0.9)0.92 (0.8)0.86 (0.6)0.86 (0.6)0.86 (0.3)0.87 (0.6)15/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞2e50/15
lq-CMA-ES Hansen 1.5 (1)0.72 (0.4)0.45 (0.2)0.54 (0.2)0.54 (0.2)0.54 (0.2)0.54 (0.2)15/15

Δ fopt
f8, 10-D		 1e1
326		 1e0
921		 1e-1
1114		 1e-2
1217		 1e-3
1267		 1e-5
1315		 1e-7
1343		 #succ
15/15
CMA-ES-2019 Hansen 1.9 (0.5)3.4 (0.6)3.6 (0.4)3.6 (0.3)3.6 (0.5)3.7 (0.3)3.9 (0.3)15/15
HE-ES Glasmachers 1.4 (0.3)2.8 (0.3)3.0 (0.6)3.2 (0.5)3.2 (0.5)3.3 (0.2)3.4 (0.5)15/15
SLSQP+lq-CMA-ES Hansen 1.4 (0.9)1.4 (1)1.3 (1)1.3 (1)1.3 (2)1.3 (2)1.3 (1)15/15
SLSQP-11-scipy Hansen 1.4 (1.0)1.1 (0.5)0.97 (0.4)0.94 (0.5)0.93 (0.6)0.92 (0.4)0.91 (0.4)15/15
lq-CMA-ES Hansen 1.1 (0.6)1.8 (1)1.6 (3)1.6 (1)1.6 (1)1.5 (1)1.5 (1)15/15

Δ fopt
f9, 10-D		 1e1
200		 1e0
648		 1e-1
857		 1e-2
993		 1e-3
1065		 1e-5
1138		 1e-7
1185		 #succ
15/15
CMA-ES-2019 Hansen 2.8 (0.6)5.2 (1)4.9 (2)4.6 (0.6)4.6 (2)4.6 (2)4.6 (1)15/15
HE-ES Glasmachers 2.0 (0.3)4.0 (0.5)3.9 (0.3)3.9 (0.2)3.8 (0.2)3.9 (0.2)3.9 (0.3)15/15
SLSQP+lq-CMA-ES Hansen 0.82 (0)0.39 (0)0.39 (0)0.39 (0)0.39 (0)0.39 (0)0.39 (0)15/15
SLSQP-11-scipy Hansen 0.82 (0)0.39 (0)0.39 (0)0.39 (0)0.39 (0)0.39 (0)0.39 (0)15/15
lq-CMA-ES Hansen 1.6 (0.4)2.0 (0.9)1.7 (1)1.6 (1)1.5 (1)1.5 (1)1.4 (1.0)15/15

Δ fopt
f10, 10-D		 1e1
1835		 1e0
2172		 1e-1
2455		 1e-2
2728		 1e-3
2802		 1e-5
4543		 1e-7
4739		 #succ
15/15
CMA-ES-2019 Hansen 1.2 (0.2)1.2 (0.2)1.2 (0.1)1.2 (0.1)1.2 (0.1)0.80 (0.0)0.83 (0.1)15/15
HE-ES Glasmachers 1.0 (0.1)1.00 (0.1)0.94 (0.1)0.89 (0.1)0.91 (0.1)0.61 (0.0)0.63 (0.0)15/15
SLSQP+lq-CMA-ES Hansen 0.16 (0.1)0.15 (0.1)0.14 (0.0)0.14 (0.0)0.14 (0.0)0.11 (0.0)0.97 (0.5)15/15
SLSQP-11-scipy Hansen 0.16 (0.1)0.15 (0.0)0.14 (0.1)0.14 (0.1)0.15 (0.1)0.10 (0.0)5.3 (11)9/15
lq-CMA-ES Hansen 0.21 (0.0)0.21 (0.0)0.21 (0.1)0.20 (0.1)0.21 (0.0)0.14 (0.0)0.18 (0.0)★15/15

Δ fopt
f11, 10-D		 1e1
266		 1e0
1041		 1e-1
2602		 1e-2
2954		 1e-3
3338		 1e-5
4092		 1e-7
4843		 #succ
15/15
CMA-ES-2019 Hansen 5.7 (0.9)1.7 (0.3)0.75 (0.1)0.73 (0.1)0.70 (0.1)0.64 (0.0)0.61 (0.0)15/15
HE-ES Glasmachers 4.6 (0.5)1.4 (0.2)0.64 (0.1)0.61 (0.1)0.57 (0.1)0.52 (0.1)0.49 (0.0)15/15
SLSQP+lq-CMA-ES Hansen 0.25 (0.1)0.09 (0.0)0.04 (0.0)0.05 (9e-3)0.05 (0.0)0.40 (0.7)1.0 (0.6)15/15
SLSQP-11-scipy Hansen 0.25 (0.1)0.09 (0.0)0.04 (8e-3)0.04 (0.0)0.05 (0.0)0.62 (2)85 (104)0/15
lq-CMA-ES Hansen 1.6 (0.2)0.46 (0.1)0.20 (0.0)0.19 (0.0)0.18 (0.0)0.16 (0.0)0.17 (0.0)★215/15

Δ fopt
f12, 10-D		 1e1
515		 1e0
896		 1e-1
1240		 1e-2
1390		 1e-3
1569		 1e-5
3660		 1e-7
5154		 #succ
15/15
CMA-ES-2019 Hansen 2.9 (1)3.7 (3)4.1 (3)4.3 (3)4.3 (3)2.4 (1)1.9 (1.0)15/15
HE-ES Glasmachers 3.3 (2)4.3 (3)4.5 (3)4.9 (3)4.9 (4)2.7 (2)2.2 (1)15/15
SLSQP+lq-CMA-ES Hansen 1.9 (1)1.5 (0.9)1.4 (0.8)1.3 (0.7)1.3 (0.7)1.3 (1)1.8 (2)15/15
SLSQP-11-scipy Hansen 1.9 (2)1.6 (1)1.4 (0.9)1.3 (0.8)1.3 (0.7)1.2 (1)4.2 (7)10/15
lq-CMA-ES Hansen 0.79 (0.4)1.1 (0.8)1.1 (0.9)1.1 (0.8)1.2 (0.8)0.82 (0.5)0.82 (0.5)15/15

Δ fopt
f13, 10-D		 1e1
387		 1e0
596		 1e-1
797		 1e-2
1014		 1e-3
4587		 1e-5
6208		 1e-7
7779		 #succ
15/15
CMA-ES-2019 Hansen 2.2 (1)2.7 (1)3.5 (1)3.4 (0.9)0.83 (0.2)0.94 (0.2)0.95 (0.3)15/15
HE-ES Glasmachers 1.3 (0.1)2.5 (2)3.2 (2)3.8 (2)1.0 (0.4)1.2 (0.7)43 (86)15/15
SLSQP+lq-CMA-ES Hansen 0.65 (0.1)0.64 (0.0)0.62 (0.0)0.61 (0.0)1.3 (1)1.7 (0.4)1.6 (0.5)15/15
SLSQP-11-scipy Hansen 0.65 (0.1)0.64 (0.0)0.62 (0.0)0.61 (0.0)52 (57)266 (362)∞3e50/15
lq-CMA-ES Hansen 0.82 (0.2)0.89 (0.2)1.0 (0.3)0.93 (0.2)0.27 (0.1)0.42 (0.2)★20.53 (0.1)★315/15

Δ fopt
f14, 10-D		 1e1
37		 1e0
98		 1e-1
133		 1e-2
205		 1e-3
392		 1e-5
687		 1e-7
4305		 #succ
15/15
CMA-ES-2019 Hansen 1.1 (1.0)2.7 (0.8)3.6 (0.9)3.7 (0.6)2.9 (0.5)3.1 (0.3)0.75 (0.1)15/15
HE-ES Glasmachers 1.4 (1)2.3 (0.7)2.8 (0.6)2.8 (0.5)2.4 (0.5)2.7 (0.3)0.64 (0.0)15/15
SLSQP+lq-CMA-ES Hansen 0.66 (0.3)0.58 (0.1)0.70 (0.1)0.74 (0.1)0.56 (0.1)0.54 (0.1)1.4 (0.6)15/15
SLSQP-11-scipy Hansen 0.66 (0.3)0.58 (0.2)0.70 (0.2)0.74 (0.1)0.56 (0.1)0.53 (0.1)727 (697)0/15
lq-CMA-ES Hansen 2.1 (1)1.7 (0.6)1.9 (0.5)1.9 (0.3)1.3 (0.2)1.1 (0.1)0.36 (0.1)★415/15

Δ fopt
f15, 10-D		 1e1
4774		 1e0
39246		 1e-1
73643		 1e-2
74669		 1e-3
75790		 1e-5
77814		 1e-7
79834		 #succ
12/15
CMA-ES-2019 Hansen 1.3 (0.9)0.99 (0.5)0.81 (0.3)0.82 (0.3)0.82 (0.3)0.83 (0.3)0.84 (0.4)15/15
HE-ES Glasmachers 0.61 (0.4)0.89 (0.6)0.87 (0.6)0.88 (0.7)0.88 (0.6)0.88 (0.6)0.89 (0.6)15/15
SLSQP+lq-CMA-ES Hansen 1.2 (0.3)1.00 (0.7)0.95 (0.3)0.95 (0.7)0.96 (0.7)0.97 (0.7)0.98 (0.2)15/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞2e50/15
lq-CMA-ES Hansen 0.78 (0.6)0.79 (0.4)0.57 (0.2)0.57 (0.3)0.56 (0.3)0.55 (0.3)0.54 (0.3)15/15

Δ fopt
f16, 10-D		 1e1
425		 1e0
7029		 1e-1
15779		 1e-2
45669		 1e-3
51151		 1e-5
65798		 1e-7
71570		 #succ
15/15
CMA-ES-2019 Hansen 3.0 (0.6)0.78 (0.5)0.99 (1)0.72 (1)0.78 (0.5)0.79 (1.0)0.75 (0.5)15/15
HE-ES Glasmachers 4.0 (2)0.63 (0.4)0.91 (1)0.78 (1)0.75 (0.8)0.63 (0.7)0.61 (0.4)15/15
SLSQP+lq-CMA-ES Hansen 4.5 (1)0.92 (0.7)1.0 (1)0.45 (0.4)0.41 (0.4)0.34 (0.3)0.33 (0.3)15/15
SLSQP-11-scipy Hansen 6940 (6625)∞∞∞∞∞∞2e50/15
lq-CMA-ES Hansen 1.6 (0.4)1.0 (1.0)0.99 (0.9)0.47 (0.3)0.77 (0.8)0.62 (0.4)0.59 (0.4)15/15

Δ fopt
f17, 10-D		 1e1
26		 1e0
429		 1e-1
2203		 1e-2
6329		 1e-3
9851		 1e-5
20190		 1e-7
26503		 #succ
15/15
CMA-ES-2019 Hansen 0.90 (1.0)1.0 (0.5)0.82 (1)0.65 (0.5)1.1 (0.9)1.1 (0.3)1.2 (0.4)15/15
HE-ES Glasmachers 1.2 (2)0.77 (0.2)0.35 (0.1)0.35 (0.4)0.40 (0.3)★0.36 (0.1)★30.41 (0.1)★415/15
SLSQP+lq-CMA-ES Hansen 7.9 (15)2.2 (0.7)1.3 (1)0.93 (0.5)0.85 (0.6)0.89 (0.3)1.1 (0.4)15/15
SLSQP-11-scipy Hansen 32 (17)∞∞∞∞∞∞2e50/15
lq-CMA-ES Hansen 1.4 (2)3.0 (8)2.5 (4)1.3 (0.9)1.2 (0.8)1.1 (0.6)1.1 (0.5)15/15

Δ fopt
f18, 10-D		 1e1
238		 1e0
836		 1e-1
7012		 1e-2
15928		 1e-3
27536		 1e-5
37234		 1e-7
42708		 #succ
15/15
CMA-ES-2019 Hansen 0.85 (0.3)0.95 (0.6)0.47 (0.5)0.73 (0.5)0.56 (0.2)0.72 (0.3)0.77 (0.3)15/15
HE-ES Glasmachers 0.68 (0.4)0.70 (0.2)0.37 (0.8)98 (162)92 (272)69 (70)60 (176)12/15
SLSQP+lq-CMA-ES Hansen 3.1 (1)1.6 (0.5)0.98 (0.9)0.86 (0.4)0.64 (0.4)0.72 (0.4)0.78 (0.3)15/15
SLSQP-11-scipy Hansen 2547 (2629)∞∞∞∞∞∞2e50/15
lq-CMA-ES Hansen 0.86 (0.4)3.0 (4)1.3 (0.6)1.0 (0.6)0.93 (0.4)0.83 (0.3)0.91 (0.2)15/15

Δ fopt
f19, 10-D		 1e1
1		 1e0
1		 1e-1
10609		 1e-2
9.8e5		 1e-3
1.4e6		 1e-5
1.4e6		 1e-7
1.4e6		 #succ
15/15
CMA-ES-2019 Hansen 1 (0)1 (0)11 (8)0.45 (0.3)0.44 (0.3)0.44 (0.3)0.44 (0.3)15/15
HE-ES Glasmachers 1 (0)1 (0)23 (32)0.54 (0.4)0.42 (0.3)0.42 (0.4)0.42 (0.4)15/15
SLSQP+lq-CMA-ES Hansen 1 (0)1 (0)6.8e-3 (5e-5)0.52 (0.1)0.42 (0.1)0.42 (0.1)0.43 (0.1)15/15
SLSQP-11-scipy Hansen 1 (0)1 (0)6.8e-3 (5e-5)∞∞∞∞3e50/15
lq-CMA-ES Hansen 1 (0)1 (0)9.0 (7)0.53 (0.1)0.51 (0.2)0.51 (0.2)0.52 (0.2)15/15

Δ fopt
f20, 10-D		 1e1
32		 1e0
15426		 1e-1
5.5e5		 1e-2
5.7e5		 1e-3
5.7e5		 1e-5
5.8e5		 1e-7
5.9e5		 #succ
15/15
CMA-ES-2019 Hansen 3.5 (2)2.5 (2)0.75 (0.3)0.76 (0.4)0.77 (0.5)0.77 (0.5)0.78 (0.4)15/15
HE-ES Glasmachers 2.4 (0.7)143 (329)∞∞∞∞∞1e70/15
SLSQP+lq-CMA-ES Hansen 1 (0)2.0 (1)0.79 (0.4)0.80 (0.4)0.80 (0.4)0.81 (0.4)0.82 (0.4)15/15
SLSQP-11-scipy Hansen 1 (0)4.0 (5)∞∞∞∞∞2e50/15
lq-CMA-ES Hansen 1.7 (0.8)1.2 (0.9)0.62 (0.4)0.64 (0.3)0.63 (0.4)0.63 (0.4)0.62 (0.3)15/15

Δ fopt
f21, 10-D		 1e1
130		 1e0
2236		 1e-1
4392		 1e-2
4487		 1e-3
4618		 1e-5
5074		 1e-7
11329		 #succ
15/15
CMA-ES-2019 Hansen 4.1 (6)1.2 (2)6.0 (13)6.3 (8)6.2 (19)5.9 (2)2.7 (3)15/15
HE-ES Glasmachers 2.8 (0.8)690 (2240)571 (571)559 (2232)543 (1628)494 (1480)221 (221)12/15
SLSQP+lq-CMA-ES Hansen 4.4 (8)30 (27)17 (51)17 (47)17 (47)15 (35)7.0 (3)14/15
SLSQP-11-scipy Hansen 1.8 (2)1.4 (1)1.2 (2)1.1 (1)1.1 (1)1.0 (2)0.70 (1)15/15
lq-CMA-ES Hansen 7.8 (11)11 (6)7.4 (16)7.3 (7)7.1 (6)6.5 (6)2.9 (7)14/15

Δ fopt
f22, 10-D		 1e1
98		 1e0
2839		 1e-1
6353		 1e-2
6620		 1e-3
6798		 1e-5
8296		 1e-7
10351		 #succ
15/15
CMA-ES-2019 Hansen 30 (64)186 (212)258 (251)247 (224)241 (374)198 (158)158 (210)4/15
HE-ES Glasmachers 7.6 (7)3518 (6172)∞∞∞∞∞1e70/15
SLSQP+lq-CMA-ES Hansen 38 (114)147 (275)∞∞∞∞∞6e50/15
SLSQP-11-scipy Hansen 1.2 (2)0.60 (1)0.82 (0.9)★0.79 (0.9)★0.78 (2)★0.67 (1)★2.9 (5)9/15
lq-CMA-ES Hansen 6.4 (6)46 (45)93 (84)89 (132)87 (93)71 (142)57 (151)4/15

Δ fopt
f23, 10-D		 1e1
3.0		 1e0
915		 1e-1
16425		 1e-2
1.8e5		 1e-3
2.0e5		 1e-5
2.1e5		 1e-7
2.1e5		 #succ
15/15
CMA-ES-2019 Hansen 2.2 (2)33 (19)21 (49)32 (55)29 (31)28 (24)27 (39)5/15
HE-ES Glasmachers 2.2 (2)39 (59)56 (112)41 (31)58 (103)57 (135)55 (55)8/15
SLSQP+lq-CMA-ES Hansen 10 (12)15 (16)11 (13)19 (27)17 (22)16 (44)16 (20)7/15
SLSQP-11-scipy Hansen 9.3 (9)15 (21)87 (93)∞∞∞∞2e50/15
lq-CMA-ES Hansen 3.3 (2)20 (39)16 (19)25 (58)23 (28)22 (24)22 (14)6/15

Δ fopt
f24, 10-D		 1e1
98761		 1e0
1.0e6		 1e-1
7.5e7		 1e-2
7.5e7		 1e-3
7.5e7		 1e-5
7.5e7		 1e-7
7.5e7		 #succ
1/15
CMA-ES-2019 Hansen 56 (100)10 (13)∞∞∞∞∞4e60/15
HE-ES Glasmachers 203 (279)∞∞∞∞∞∞1e70/15
SLSQP+lq-CMA-ES Hansen 57 (89)10 (13)0.69 (1.0)0.69 (0.9)0.69 (1.0)0.69 (0.5)0.69 (0.7)1/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞2e50/15
lq-CMA-ES Hansen 41 (59)22 (26)∞∞∞∞∞3e60/15

Previous dimension | Dimension = 20 | Next dimension

Δ fopt
f1, 20-D		 1e1
43		 1e0
43		 1e-1
43		 1e-2
43		 1e-3
43		 1e-5
43		 1e-7
43		 #succ
15/15
CMA-ES-2019 Hansen 6.2 (0.8)13 (1)19 (2)25 (3)32 (3)44 (3)58 (4)15/15
HE-ES Glasmachers 4.4 (2)9.4 (1)15 (1)19 (1)24 (2)34 (1)45 (2)15/15
SLSQP+lq-CMA-ES Hansen 0.58 (0)0.58 (0)0.58 (0)0.58 (0)0.58 (0)0.58 (0)0.58 (0)15/15
SLSQP-11-scipy Hansen 0.58 (0)0.58 (0)0.58 (0)0.58 (0)0.58 (0)0.58 (0)0.58 (0)15/15
lq-CMA-ES Hansen 1.5 (6e-3)1.7 (0.3)2.2 (0.2)2.4 (0.3)2.7 (0.1)3.2 (0.1)3.7 (0.1)15/15

Δ fopt
f2, 20-D		 1e1
385		 1e0
386		 1e-1
387		 1e-2
388		 1e-3
390		 1e-5
391		 1e-7
393		 #succ
15/15
CMA-ES-2019 Hansen 22 (3)26 (4)28 (4)30 (2)31 (2)33 (2)34 (2)15/15
HE-ES Glasmachers 14 (3)17 (1)19 (3)19 (2)20 (2)21 (3)22 (2)15/15
SLSQP+lq-CMA-ES Hansen 2.4 (0.6)2.6 (0.8)2.8 (0.8)2.9 (0.7)3.1 (0.9)3.4 (0.7)3.7 (1)15/15
SLSQP-11-scipy Hansen 2.5 (0.5)2.6 (0.7)2.8 (0.6)3.0 (1.0)3.2 (0.7)3.5 (1)3.8 (0.9)15/15
lq-CMA-ES Hansen 2.9 (0.9)3.6 (1)4.0 (2)4.3 (1)4.6 (1)5.1 (2)6.0 (2)15/15

Δ fopt
f3, 20-D		 1e1
5066		 1e0
7626		 1e-1
7635		 1e-2
7637		 1e-3
7643		 1e-5
7646		 1e-7
7651		 #succ
15/15
CMA-ES-2019 Hansen 15 (11)∞∞∞∞∞∞3e60/15
HE-ES Glasmachers 7.1 (6)∞∞∞∞∞∞2e70/15
SLSQP+lq-CMA-ES Hansen 11 (8)∞∞∞∞∞∞3e60/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞4e50/15
lq-CMA-ES Hansen 11 (18)∞∞∞∞∞∞2e60/15

Δ fopt
f4, 20-D		 1e1
4722		 1e0
7628		 1e-1
7666		 1e-2
7686		 1e-3
7700		 1e-5
7758		 1e-7
1.4e5		 #succ
9/15
CMA-ES-2019 Hansen ∞∞∞∞∞∞∞2e60/15
HE-ES Glasmachers ∞∞∞∞∞∞∞2e70/15
SLSQP+lq-CMA-ES Hansen ∞∞∞∞∞∞∞2e60/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞4e50/15
lq-CMA-ES Hansen ∞∞∞∞∞∞∞2e60/15

Δ fopt
f5, 20-D		 1e1
41		 1e0
41		 1e-1
41		 1e-2
41		 1e-3
41		 1e-5
41		 1e-7
41		 #succ
15/15
CMA-ES-2019 Hansen 5.1 (0.8)6.1 (1)6.4 (1)6.4 (1)6.4 (1)6.4 (1)6.4 (1)15/15
HE-ES Glasmachers 4.8 (1)5.7 (1)6.0 (2)6.0 (1)6.0 (2)6.0 (1)6.0 (1)15/15
SLSQP+lq-CMA-ES Hansen 1.7 (0)2.2 (0)2.2 (0)2.2 (0)2.2 (0)2.2 (0)2.2 (0)15/15
SLSQP-11-scipy Hansen 1.7 (0)2.2 (0)2.2 (0)2.2 (0)2.2 (0)2.2 (0)2.2 (0)15/15
lq-CMA-ES Hansen 2.0 (0.8)2.4 (0.7)2.4 (0.7)2.4 (0.8)2.4 (0.6)2.4 (0.8)2.4 (0.7)15/15

Δ fopt
f6, 20-D		 1e1
1296		 1e0
2343		 1e-1
3413		 1e-2
4255		 1e-3
5220		 1e-5
6728		 1e-7
8409		 #succ
15/15
CMA-ES-2019 Hansen 1.5 (0.3)1.2 (0.2)1.1 (0.1)1.1 (0.1)1.0 (0.1)1.1 (0.1)1.1 (0.1)15/15
HE-ES Glasmachers 2.0 (0.5)2.0 (0.8)2.2 (1)2.8 (2)3.2 (2)5.1 (2)7.1 (3)15/15
SLSQP+lq-CMA-ES Hansen 3.2 (2)2.6 (1)2.7 (0.9)2.7 (0.4)2.4 (0.2)2.1 (0.1)1.9 (0.1)15/15
SLSQP-11-scipy Hansen 2.5 (1)2.0 (0.8)2.1 (0.7)2.3 (1)2.4 (1)2.6 (1)8.7 (7)0/15
lq-CMA-ES Hansen 1.4 (0.3)1.2 (0.2)1.1 (0.1)1.1 (0.1)1.1 (0.1)1.2 (0.2)1.2 (0.1)15/15

Δ fopt
f7, 20-D		 1e1
1351		 1e0
4274		 1e-1
9503		 1e-2
16523		 1e-3
16524		 1e-5
16524		 1e-7
16969		 #succ
15/15
CMA-ES-2019 Hansen 1.4 (1)2.3 (1.0)1.5 (0.3)0.92 (0.4)0.92 (0.2)0.92 (0.1)0.90 (0.2)15/15
HE-ES Glasmachers 0.53 (0.1)136 (503)195 (1)129 (89)129 (130)129 (350)126 (127)15/15
SLSQP+lq-CMA-ES Hansen 0.92 (0.7)2.4 (0.8)1.5 (0.6)1.0 (0.3)1.0 (0.3)1.0 (0.4)1.00 (0.4)15/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞4e50/15
lq-CMA-ES Hansen 1.0 (0.9)1.6 (0.6)0.99 (0.5)0.70 (0.3)0.70 (0.3)0.70 (0.3)0.69 (0.3)15/15

Δ fopt
f8, 20-D		 1e1
2039		 1e0
3871		 1e-1
4040		 1e-2
4148		 1e-3
4219		 1e-5
4371		 1e-7
4484		 #succ
15/15
CMA-ES-2019 Hansen 3.3 (0.8)3.9 (3)4.2 (1)4.2 (3)4.3 (3)4.3 (0.4)4.3 (2)15/15
HE-ES Glasmachers 3.5 (0.5)3.7 (2)4.1 (0.3)4.3 (0.2)4.4 (1)4.5 (1)4.5 (1)15/15
SLSQP+lq-CMA-ES Hansen 0.79 (0.2)0.93 (0.8)1.0 (2)1.0 (0.9)1.0 (0.9)1.0 (2)1.0 (2)15/15
SLSQP-11-scipy Hansen 0.78 (0.3)0.76 (0.9)0.78 (0.2)0.78 (0.7)0.78 (0.8)0.77 (0.3)0.76 (0.7)15/15
lq-CMA-ES Hansen 1.4 (0.2)1.4 (0.6)1.5 (0.6)1.5 (1)1.5 (0.6)1.5 (1)1.5 (1.0)15/15

Δ fopt
f9, 20-D		 1e1
1716		 1e0
3102		 1e-1
3277		 1e-2
3379		 1e-3
3455		 1e-5
3594		 1e-7
3727		 #succ
15/15
CMA-ES-2019 Hansen 3.6 (0.4)3.9 (0.3)4.2 (0.3)4.3 (0.3)4.3 (0.3)4.4 (0.3)4.4 (0.3)15/15
HE-ES Glasmachers 3.9 (0.9)4.4 (0.5)4.9 (0.5)5.2 (2)5.3 (0.3)5.3 (2)5.3 (2)15/15
SLSQP+lq-CMA-ES Hansen 0.35 (0)0.28 (0)0.32 (0)0.35 (0)0.36 (3e-3)0.36 (3e-3)0.36 (3e-3)15/15
SLSQP-11-scipy Hansen 0.35 (0)0.28 (0)0.32 (0)0.35 (0)0.36 (3e-3)0.36 (3e-3)0.36 (3e-3)15/15
lq-CMA-ES Hansen 1.5 (0.2)1.5 (0.7)1.6 (0.6)1.6 (0.6)1.6 (0.1)1.6 (0.6)1.6 (0.6)15/15

Δ fopt
f10, 20-D		 1e1
7413		 1e0
8661		 1e-1
10735		 1e-2
13641		 1e-3
14920		 1e-5
17073		 1e-7
17476		 #succ
15/15
CMA-ES-2019 Hansen 1.1 (0.2)1.1 (0.1)1.0 (0.1)0.84 (0.1)0.80 (0.0)0.74 (0.0)0.75 (0.0)15/15
HE-ES Glasmachers 0.80 (0.1)0.78 (0.1)0.68 (0.1)0.56 (0.1)0.53 (0.0)0.50 (0.1)0.51 (0.0)15/15
SLSQP+lq-CMA-ES Hansen 0.13 (0.0)0.12 (0.0)0.10 (0.0)0.09 (0.0)0.08 (0.0)0.13 (0.0)0.84 (0.0)15/15
SLSQP-11-scipy Hansen 0.13 (0.0)0.12 (0.0)0.10 (0.0)0.09 (0.0)0.08 (0.0)0.09 (0.0)8.0 (11)1/15
lq-CMA-ES Hansen 0.21 (0.1)0.21 (0.0)0.19 (0.0)0.16 (0.0)0.15 (0.0)0.15 (0.0)0.17 (0.0)★215/15

Δ fopt
f11, 20-D		 1e1
1002		 1e0
2228		 1e-1
6278		 1e-2
8586		 1e-3
9762		 1e-5
12285		 1e-7
14831		 #succ
15/15
CMA-ES-2019 Hansen 4.3 (0.4)2.2 (0.1)0.85 (0.0)0.67 (0.0)0.62 (0.0)0.55 (0.0)0.49 (0.0)15/15
HE-ES Glasmachers 2.9 (0.5)1.6 (0.3)0.65 (0.1)0.52 (0.0)0.49 (0.0)0.43 (0.0)0.38 (0.0)15/15
SLSQP+lq-CMA-ES Hansen 0.15 (0.0)0.09 (0.1)0.04 (1e-2)0.03 (0.0)0.03 (7e-3)0.20 (0.5)0.60 (0.2)15/15
SLSQP-11-scipy Hansen 0.15 (0.1)0.09 (0.1)0.04 (0.0)0.03 (0.0)0.03 (6e-3)0.64 (2)36 (23)0/15
lq-CMA-ES Hansen 1.4 (0.1)0.70 (0.1)0.27 (0.0)0.21 (0.0)0.20 (0.0)0.18 (0.0)0.17 (0.0)★215/15

Δ fopt
f12, 20-D		 1e1
1042		 1e0
1938		 1e-1
2740		 1e-2
3156		 1e-3
4140		 1e-5
12407		 1e-7
13827		 #succ
15/15
CMA-ES-2019 Hansen 2.9 (2)3.8 (3)3.9 (2)4.0 (2)3.5 (2)1.5 (0.7)1.5 (0.5)15/15
HE-ES Glasmachers 3.8 (7)5.9 (7)7.3 (3)7.5 (4)6.5 (3)2.8 (1)2.9 (0.4)15/15
SLSQP+lq-CMA-ES Hansen 2.8 (1)2.1 (1)1.9 (2)2.4 (3)2.0 (2)1.3 (0.9)2.0 (0.5)15/15
SLSQP-11-scipy Hansen 2.8 (2)2.1 (0.9)1.7 (0.8)1.6 (0.7)1.3 (0.4)1.8 (1)3.3 (5)9/15
lq-CMA-ES Hansen 1.1 (0.1)★21.4 (1)1.5 (0.6)1.6 (0.7)1.4 (0.5)0.74 (0.2)0.85 (0.2)★215/15

Δ fopt
f13, 20-D		 1e1
652		 1e0
2021		 1e-1
2751		 1e-2
3507		 1e-3
18749		 1e-5
24455		 1e-7
30201		 #succ
15/15
CMA-ES-2019 Hansen 2.9 (2)2.8 (3)4.4 (3)4.6 (3)1.0 (0.4)1.2 (0.7)1.1 (0.5)15/15
HE-ES Glasmachers 1.6 (0.2)3.4 (2)6.4 (8)16 (16)11 (10)17 (0.8)45 (15)15/15
SLSQP+lq-CMA-ES Hansen 1.2 (0.1)0.55 (0.0)0.51 (0.0)0.50 (0.0)1.0 (0.9)1.4 (0.7)1.6 (0.8)15/15
SLSQP-11-scipy Hansen 1.2 (0.1)0.55 (0.0)0.51 (0.0)0.50 (0.0)31 (51)131 (78)∞5e50/15
lq-CMA-ES Hansen 2.0 (2)2.3 (2)2.7 (0.9)2.4 (0.9)0.48 (0.2)0.69 (0.3)★0.83 (0.5)15/15

Δ fopt
f14, 20-D		 1e1
75		 1e0
239		 1e-1
304		 1e-2
451		 1e-3
932		 1e-5
1648		 1e-7
15661		 #succ
15/15
CMA-ES-2019 Hansen 2.9 (2)2.5 (0.6)3.4 (0.7)3.9 (0.5)3.2 (0.3)3.9 (0.3)0.66 (0.0)15/15
HE-ES Glasmachers 3.0 (2)2.2 (0.5)2.7 (0.4)2.9 (0.3)2.5 (0.4)3.2 (0.3)0.50 (0.0)15/15
SLSQP+lq-CMA-ES Hansen 0.75 (0.2)0.52 (0.1)0.69 (0.0)0.76 (0.1)0.53 (0.0)0.51 (0.0)0.97 (0.3)15/15
SLSQP-11-scipy Hansen 0.75 (0.1)0.52 (0.1)0.69 (0.1)0.76 (0.1)0.53 (0.1)0.51 (0.0)∞4e50/15
lq-CMA-ES Hansen 3.2 (1)2.2 (0.5)2.7 (0.4)2.8 (0.3)1.9 (0.1)1.6 (0.1)0.36 (0.0)★415/15

Δ fopt
f15, 20-D		 1e1
30378		 1e0
1.5e5		 1e-1
3.1e5		 1e-2
3.2e5		 1e-3
3.2e5		 1e-5
4.5e5		 1e-7
4.6e5		 #succ
15/15
CMA-ES-2019 Hansen 1.0 (0.6)1.1 (0.3)0.65 (0.3)0.66 (0.3)0.66 (0.3)0.49 (0.2)0.50 (0.2)15/15
HE-ES Glasmachers 0.54 (0.2)0.69 (0.4)0.55 (0.4)0.55 (0.3)0.55 (0.3)0.40 (0.3)0.41 (0.2)15/15
SLSQP+lq-CMA-ES Hansen 0.98 (0.6)1.0 (0.4)0.68 (0.2)0.69 (0.3)0.69 (0.2)0.51 (0.2)0.52 (0.2)15/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞4e50/15
lq-CMA-ES Hansen 0.67 (0.5)0.81 (0.4)0.46 (0.1)0.46 (0.2)0.45 (0.2)0.32 (0.1)0.32 (0.1)15/15

Δ fopt
f16, 20-D		 1e1
1384		 1e0
27265		 1e-1
77015		 1e-2
1.4e5		 1e-3
1.9e5		 1e-5
2.0e5		 1e-7
2.2e5		 #succ
15/15
CMA-ES-2019 Hansen 2.1 (0.9)0.94 (0.4)0.95 (0.7)0.69 (0.3)0.72 (0.4)0.84 (0.3)0.78 (0.7)15/15
HE-ES Glasmachers 1.8 (0.5)0.80 (0.3)0.82 (0.6)0.81 (0.6)0.92 (1)1.0 (0.5)0.93 (0.8)15/15
SLSQP+lq-CMA-ES Hansen 3.3 (0.4)0.85 (0.5)0.79 (0.3)0.85 (0.6)1.4 (1)1.8 (1)1.6 (1)15/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞4e50/15
lq-CMA-ES Hansen 1.0 (0.2)★30.93 (0.9)0.95 (0.7)0.67 (0.4)0.93 (1.0)0.94 (0.6)0.87 (0.8)15/15

Δ fopt
f17, 20-D		 1e1
63		 1e0
1030		 1e-1
4005		 1e-2
12242		 1e-3
30677		 1e-5
56288		 1e-7
80472		 #succ
15/15
CMA-ES-2019 Hansen 1.1 (1)0.81 (0.2)0.94 (0.9)1.2 (1)0.77 (0.4)0.79 (0.4)0.87 (0.3)15/15
HE-ES Glasmachers 1.8 (1)0.75 (0.2)0.44 (0.1)0.49 (0.4)★0.42 (0.3)★0.53 (0.3)0.46 (0.1)★15/15
SLSQP+lq-CMA-ES Hansen 12 (9)3.1 (0.9)2.0 (2)1.1 (0.6)0.93 (0.7)0.98 (0.5)0.99 (0.3)15/15
SLSQP-11-scipy Hansen 111 (390)∞∞∞∞∞∞4e50/15
lq-CMA-ES Hansen 2.4 (1)1.7 (0.3)1.7 (1)1.9 (1)1.1 (0.8)1.2 (0.2)1.0 (0.3)15/15

Δ fopt
f18, 20-D		 1e1
621		 1e0
3972		 1e-1
19561		 1e-2
28555		 1e-3
67569		 1e-5
1.3e5		 1e-7
1.5e5		 #succ
15/15
CMA-ES-2019 Hansen 0.94 (0.4)0.75 (0.9)1.1 (0.7)1.2 (1)0.93 (0.9)1.0 (0.4)1.00 (0.4)15/15
HE-ES Glasmachers 0.80 (0.2)0.38 (0.1)158 (511)110 (350)76 (148)43 (84)39 (70)12/15
SLSQP+lq-CMA-ES Hansen 4.3 (1)2.1 (2)0.96 (0.9)1.1 (0.5)0.88 (0.2)0.77 (0.4)0.82 (0.3)15/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞4e50/15
lq-CMA-ES Hansen 0.90 (0.4)2.9 (6)1.6 (0.9)1.7 (0.8)1.1 (0.6)0.79 (0.3)0.78 (0.3)15/15

Δ fopt
f19, 20-D		 1e1
1		 1e0
1		 1e-1
3.4e5		 1e-2
4.7e6		 1e-3
6.2e6		 1e-5
6.7e6		 1e-7
6.7e6		 #succ
15/15
CMA-ES-2019 Hansen 1 (0)1 (0)1.3 (0.4)0.49 (0.2)0.56 (0.2)0.61 (0.3)0.62 (0.6)13/15
HE-ES Glasmachers 1 (0)1 (0)5.0 (4)0.55 (0.7)0.52 (0.6)0.50 (0.3)0.51 (0.2)15/15
SLSQP+lq-CMA-ES Hansen 1 (0)1 (0)5.6e-4 (0)0.54 (0.3)0.46 (0.2)0.49 (0.2)0.49 (0.2)15/15
SLSQP-11-scipy Hansen 1 (0)1 (0)5.6e-4 (7e-7)∞∞∞∞5e50/15
lq-CMA-ES Hansen 1 (0)1 (0)0.56 (0.5)0.47 (0.3)0.45 (0.2)0.46 (0.2)0.47 (0.2)15/15

Δ fopt
f20, 20-D		 1e1
82		 1e0
46150		 1e-1
3.1e6		 1e-2
5.5e6		 1e-3
5.5e6		 1e-5
5.6e6		 1e-7
5.6e6		 #succ
14/15
CMA-ES-2019 Hansen 3.7 (0.7)3.9 (1)0.69 (0.4)0.62 (0.2)0.62 (0.2)0.63 (0.2)0.63 (0.2)15/15
HE-ES Glasmachers 2.6 (0.6)∞∞∞∞∞∞2e70/15
SLSQP+lq-CMA-ES Hansen 0.65 (0)3.5 (1)0.74 (0.4)0.68 (0.3)0.68 (0.2)0.68 (0.4)0.68 (0.3)14/15
SLSQP-11-scipy Hansen 0.65 (0)14 (10)∞∞∞∞∞4e50/15
lq-CMA-ES Hansen 1.6 (0.6)3.0 (1)0.70 (0.3)0.56 (0.1)0.56 (0.2)0.55 (0.2)0.55 (0.2)15/15

Δ fopt
f21, 20-D		 1e1
561		 1e0
6541		 1e-1
14103		 1e-2
14318		 1e-3
14643		 1e-5
15567		 1e-7
17589		 #succ
15/15
CMA-ES-2019 Hansen 4.7 (11)121 (215)62 (93)62 (56)61 (111)57 (106)51 (87)9/15
HE-ES Glasmachers 1.2 (3)6118 (7649)2838 (3547)2795 (4542)2733 (3075)2571 (3535)2275 (1706)5/15
SLSQP+lq-CMA-ES Hansen 4.5 (5)116 (345)55 (100)54 (99)53 (77)50 (112)44 (64)9/15
SLSQP-11-scipy Hansen 0.66 (0.6)0.56 (0.8)2.8 (6)2.8 (3)2.7 (8)2.6 (5)3.3 (8)7/15
lq-CMA-ES Hansen 6.1 (18)47 (56)35 (48)34 (48)34 (39)32 (79)28 (38)7/15

Δ fopt
f22, 20-D		 1e1
467		 1e0
5580		 1e-1
23491		 1e-2
24163		 1e-3
24948		 1e-5
26847		 1e-7
1.3e5		 #succ
12/15
CMA-ES-2019 Hansen 6.6 (13)156 (228)∞∞∞∞∞1e60/15
HE-ES Glasmachers 3063 (1e4)4100 (8966)∞∞∞∞∞2e70/15
SLSQP+lq-CMA-ES Hansen 2.1 (3)144 (262)∞∞∞∞∞1e60/15
SLSQP-11-scipy Hansen 1.0 (2)3.2 (8)4.1 (4)★34.0 (11)★33.8 (8)★33.6 (4)★34.3 (4)★31/15
lq-CMA-ES Hansen 4.5 (8)103 (89)∞∞∞∞∞4e50/15

Δ fopt
f23, 20-D		 1e1
3.0		 1e0
1614		 1e-1
67457		 1e-2
3.7e5		 1e-3
4.9e5		 1e-5
8.1e5		 1e-7
8.4e5		 #succ
15/15
CMA-ES-2019 Hansen 1.9 (1)1064 (4078)154 (223)∞∞∞∞7e60/15
HE-ES Glasmachers 3.9 (7)45 (62)90 (111)105 (136)280 (123)169 (345)164 (119)2/15
SLSQP+lq-CMA-ES Hansen 13 (8)1346 (3016)200 (371)74 (138)192 (327)116 (183)112 (69)1/15
SLSQP-11-scipy Hansen 13 (10)18 (28)∞∞∞∞∞4e50/15
lq-CMA-ES Hansen 6.8 (7)2.4 (0.7)152 (156)∞∞∞∞7e60/15

Δ fopt
f24, 20-D		 1e1
1.3e6		 1e0
7.5e6		 1e-1
5.2e7		 1e-2
5.2e7		 1e-3
5.2e7		 1e-5
5.2e7		 1e-7
5.2e7		 #succ
3/15
CMA-ES-2019 Hansen 16 (33)10 (7)∞∞∞∞∞5e60/15
HE-ES Glasmachers 30 (15)∞∞∞∞∞∞2e70/15
SLSQP+lq-CMA-ES Hansen ∞∞∞∞∞∞∞5e60/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞4e50/15
lq-CMA-ES Hansen 14 (18)8.5 (14)∞∞∞∞∞5e60/15

Previous dimension | Dimension = 40 | First dimension

Δ fopt
f1, 40-D		 1e1
83		 1e0
83		 1e-1
83		 1e-2
83		 1e-3
83		 1e-5
83		 1e-7
83		 #succ
15/15
CMA-ES-2019 Hansen 8.4 (0.9)14 (1)20 (1)26 (2)32 (2)45 (2)57 (2)15/15
SLSQP+lq-CMA-ES Hansen 0.54 (0)0.54 (0)0.54 (0)0.54 (0)0.54 (0)0.54 (0)0.54 (0)15/15
SLSQP-11-scipy Hansen 0.54 (0)0.54 (0)0.54 (0)0.54 (0)0.54 (0)0.54 (0)0.54 (0)15/15
lq-CMA-ES Hansen 1.5 (0.1)1.7 (0.2)1.9 (0.3)2.2 (0.0)2.4 (0.0)2.7 (0.1)3.1 (0.0)15/15

Δ fopt
f2, 40-D		 1e1
796		 1e0
797		 1e-1
799		 1e-2
799		 1e-3
800		 1e-5
802		 1e-7
804		 #succ
15/15
CMA-ES-2019 Hansen 38 (3)46 (3)52 (4)55 (4)58 (4)62 (3)63 (1)15/15
SLSQP+lq-CMA-ES Hansen 3.7 (0.9)4.0 (0.9)4.2 (0.6)4.5 (1)4.7 (1.0)5.1 (1.0)5.5 (0.6)15/15
SLSQP-11-scipy Hansen 3.7 (0.5)4.0 (0.5)4.2 (1)4.5 (0.5)4.7 (0.5)5.1 (1.0)5.5 (1)15/15
lq-CMA-ES Hansen 5.1 (0.9)6.1 (2)7.1 (1)7.8 (3)8.4 (3)9.5 (3)11 (2)15/15

Δ fopt
f3, 40-D		 1e1
15526		 1e0
15602		 1e-1
15612		 1e-2
15641		 1e-3
15646		 1e-5
15651		 1e-7
15656		 #succ
15/15
CMA-ES-2019 Hansen 4981 (8393)∞∞∞∞∞∞5e60/15
SLSQP+lq-CMA-ES Hansen 5009 (3463)∞∞∞∞∞∞6e60/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞8e50/15
lq-CMA-ES Hansen ∞∞∞∞∞∞∞9e40/15

Δ fopt
f4, 40-D		 1e1
15536		 1e0
15601		 1e-1
15659		 1e-2
15678		 1e-3
15703		 1e-5
15733		 1e-7
2.8e5		 #succ
6/15
CMA-ES-2019 Hansen ∞∞∞∞∞∞∞5e60/15
SLSQP+lq-CMA-ES Hansen ∞∞∞∞∞∞∞5e60/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞8e50/15
lq-CMA-ES Hansen ∞∞∞∞∞∞∞1e50/15

Δ fopt
f5, 40-D		 1e1
98		 1e0
116		 1e-1
120		 1e-2
121		 1e-3
121		 1e-5
121		 1e-7
121		 #succ
15/15
CMA-ES-2019 Hansen 4.7 (0.5)4.7 (0.7)4.6 (0.6)4.6 (0.4)4.6 (0.6)4.6 (0.6)4.6 (0.5)15/15
SLSQP+lq-CMA-ES Hansen 1.3 (0)1.5 (0)1.4 (0)1.4 (0)1.4 (0)1.4 (0)1.4 (0)15/15
SLSQP-11-scipy Hansen 1.3 (0)1.5 (0)1.4 (0)1.4 (0)1.4 (0)1.4 (0)1.4 (0)15/15
lq-CMA-ES Hansen 1.6 (0.5)1.6 (0.4)1.6 (0.4)1.6 (0.4)1.6 (0.4)1.6 (0.3)1.6 (0.3)15/15

Δ fopt
f6, 40-D		 1e1
3507		 1e0
5523		 1e-1
7168		 1e-2
9470		 1e-3
11538		 1e-5
15007		 1e-7
19222		 #succ
15/15
CMA-ES-2019 Hansen 1.5 (0.2)1.4 (0.2)1.4 (0.1)1.3 (0.1)1.3 (0.1)1.3 (0.1)1.2 (0.1)15/15
SLSQP+lq-CMA-ES Hansen 3.8 (2)3.4 (1)3.2 (0.2)2.7 (0.1)2.4 (0.1)2.2 (0.1)1.9 (0.1)15/15
SLSQP-11-scipy Hansen 3.5 (2)3.5 (1)3.7 (0.9)3.6 (0.9)3.7 (0.9)4.1 (1)16 (11)0/15
lq-CMA-ES Hansen 1.4 (0.2)1.4 (0.2)1.4 (0.2)1.3 (0.2)1.3 (0.2)1.4 (0.1)1.4 (0.1)15/15

Δ fopt
f7, 40-D		 1e1
10698		 1e0
17839		 1e-1
41037		 1e-2
66294		 1e-3
66294		 1e-5
66294		 1e-7
68145		 #succ
15/15
CMA-ES-2019 Hansen 1.1 (0.7)3.8 (1)1.9 (0.5)1.2 (0.3)1.2 (0.3)1.2 (0.3)1.2 (0.3)15/15
SLSQP+lq-CMA-ES Hansen 1.5 (0.6)3.6 (1)1.8 (0.6)1.1 (0.4)1.1 (0.4)1.1 (0.4)1.1 (0.4)15/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞8e50/15
lq-CMA-ES Hansen 1.3 (0.5)2.1 (0.6)★21.2 (0.4)0.77 (0.2)0.77 (0.3)0.77 (0.3)0.76 (0.3)15/15

Δ fopt
f8, 40-D		 1e1
7080		 1e0
10655		 1e-1
11012		 1e-2
11265		 1e-3
11430		 1e-5
11701		 1e-7
11969		 #succ
15/15
CMA-ES-2019 Hansen 5.6 (0.7)5.7 (1.0)5.8 (5)5.9 (4)5.9 (4)5.9 (2)5.8 (0.8)15/15
SLSQP+lq-CMA-ES Hansen 0.94 (0.5)1.4 (2)1.4 (2)1.4 (3)1.4 (1)1.4 (2)1.4 (2)15/15
SLSQP-11-scipy Hansen 0.94 (0.5)0.94 (1.0)0.94 (0.3)0.94 (0.3)0.94 (0.3)0.93 (0.9)0.91 (0.9)15/15
lq-CMA-ES Hansen 2.2 (0.3)2.0 (0.3)2.1 (0.9)2.1 (0.3)2.1 (0.9)2.1 (0.3)2.1 (0.8)15/15

Δ fopt
f9, 40-D		 1e1
6122		 1e0
12982		 1e-1
13300		 1e-2
13496		 1e-3
13651		 1e-5
13909		 1e-7
14142		 #succ
15/15
CMA-ES-2019 Hansen 6.5 (0.3)4.1 (0.2)4.3 (0.2)4.3 (0.2)4.3 (0.1)4.4 (0.1)4.4 (0.2)15/15
SLSQP+lq-CMA-ES Hansen 0.34 (0)0.20 (0)0.22 (0)0.23 (0)0.24 (0)0.24 (8e-4)0.24 (1e-3)15/15
SLSQP-11-scipy Hansen 0.34 (0)0.20 (0)0.22 (0)0.23 (0)0.24 (0)0.24 (8e-4)0.24 (1e-3)15/15
lq-CMA-ES Hansen 2.7 (0.2)1.7 (0.6)1.8 (0.1)1.8 (0.6)1.8 (0.6)1.9 (0.1)1.9 (0.6)15/15

Δ fopt
f10, 40-D		 1e1
25536		 1e0
29762		 1e-1
35676		 1e-2
51579		 1e-3
56007		 1e-5
65128		 1e-7
70824		 #succ
15/15
CMA-ES-2019 Hansen 1.3 (0.1)1.3 (0.1)1.2 (0.1)0.87 (0.1)0.84 (0.1)0.76 (0.0)0.72 (0.0)15/15
SLSQP+lq-CMA-ES Hansen 0.12 (0.0)0.11 (0.0)0.10 (0.0)0.07 (0.0)0.07 (9e-3)0.12 (0.2)0.80 (0.0)15/15
SLSQP-11-scipy Hansen 0.12 (0.0)0.11 (0.0)0.10 (0.0)0.07 (9e-3)0.07 (0.0)0.07 (0.0)53 (40)0/15
lq-CMA-ES Hansen 0.25 (0.0)0.25 (0.0)0.23 (0.0)0.18 (0.0)0.17 (0.0)0.16 (0.0)0.17 (0.0)★415/15

Δ fopt
f11, 40-D		 1e1
2368		 1e0
4855		 1e-1
11681		 1e-2
25315		 1e-3
29749		 1e-5
38949		 1e-7
48211		 #succ
15/15
CMA-ES-2019 Hansen 5.8 (0.3)3.1 (0.1)1.4 (0.0)0.66 (0.0)0.59 (0.0)0.48 (1e-2)0.42 (5e-3)15/15
SLSQP+lq-CMA-ES Hansen 0.09 (0.0)0.06 (0.0)0.03 (8e-3)0.02 (4e-3)0.02 (4e-3)0.13 (0.3)0.46 (0.0)15/15
SLSQP-11-scipy Hansen 0.09 (0.0)0.06 (0.0)0.03 (7e-3)0.02 (4e-3)0.02 (4e-3)0.04 (0.0)9.0 (9)0/15
lq-CMA-ES Hansen 2.2 (0.1)1.2 (0.1)0.55 (0.0)0.27 (0.0)0.24 (0.0)0.21 (0.0)0.19 (0.0)★215/15

Δ fopt
f12, 40-D		 1e1
4169		 1e0
7452		 1e-1
9174		 1e-2
10751		 1e-3
13146		 1e-5
22758		 1e-7
25192		 #succ
15/15
CMA-ES-2019 Hansen 2.0 (2)2.1 (2)2.3 (1)2.3 (1)2.2 (1)1.5 (0.5)1.6 (0.5)15/15
SLSQP+lq-CMA-ES Hansen 2.8 (2)2.4 (2)2.3 (2)2.4 (2)2.3 (2)1.7 (1)2.0 (0.6)15/15
SLSQP-11-scipy Hansen 2.4 (2)1.6 (0.8)1.4 (1)1.3 (0.8)1.1 (0.6)4.0 (10)8.1 (11)11/15
lq-CMA-ES Hansen 1.0 (0.5)1.2 (0.6)1.4 (0.6)1.4 (0.4)1.4 (0.4)1.1 (0.2)1.2 (0.2)15/15

Δ fopt
f13, 40-D		 1e1
2029		 1e0
6916		 1e-1
8734		 1e-2
11861		 1e-3
71936		 1e-5
98467		 1e-7
1.2e5		 #succ
15/15
CMA-ES-2019 Hansen 2.4 (2)3.7 (4)6.3 (6)6.9 (5)1.3 (0.6)2.0 (0.9)2.2 (1.0)15/15
SLSQP+lq-CMA-ES Hansen 1.2 (0.0)0.48 (0.0)0.52 (0.0)0.45 (0.0)1.2 (1)1.7 (0.9)2.2 (0.7)15/15
SLSQP-11-scipy Hansen 1.2 (0.0)0.48 (0.0)0.52 (0.0)0.45 (0.0)25 (23)∞∞9e50/15
lq-CMA-ES Hansen 1.9 (0.2)3.4 (3)5.2 (3)5.8 (1)1.0 (0.2)1.2 (0.4)1.4 (1)9/15

Δ fopt
f14, 40-D		 1e1
304		 1e0
616		 1e-1
777		 1e-2
1105		 1e-3
2207		 1e-5
4825		 1e-7
57711		 #succ
15/15
CMA-ES-2019 Hansen 2.1 (0.4)2.2 (0.4)2.8 (0.3)3.5 (0.2)3.6 (0.2)4.3 (0.2)0.65 (0.0)15/15
SLSQP+lq-CMA-ES Hansen 0.50 (0.1)0.49 (0.1)0.60 (0.1)0.75 (0.1)0.56 (0.1)0.47 (0.0)0.76 (0.1)15/15
SLSQP-11-scipy Hansen 0.50 (0.1)0.49 (0.1)0.60 (0.1)0.75 (0.1)0.56 (0.1)0.47 (0.0)∞8e50/15
lq-CMA-ES Hansen 2.1 (0.6)2.1 (0.4)2.6 (0.3)3.3 (0.3)2.4 (0.2)1.9 (0.2)0.36 (0.0)★415/15

Δ fopt
f15, 40-D		 1e1
1.9e5		 1e0
7.9e5		 1e-1
1.0e6		 1e-2
1.1e6		 1e-3
1.1e6		 1e-5
1.1e6		 1e-7
1.1e6		 #succ
15/15
CMA-ES-2019 Hansen 0.80 (0.3)0.64 (0.3)0.73 (0.4)0.74 (0.4)0.75 (0.2)0.76 (0.1)0.77 (0.4)15/15
SLSQP+lq-CMA-ES Hansen 0.76 (0.3)0.60 (0.3)0.55 (0.2)0.55 (0.2)0.56 (0.2)0.57 (0.2)0.58 (0.2)15/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞8e50/15
lq-CMA-ES Hansen 0.76 (0.7)2.0 (2)1.5 (1)1.5 (1)1.5 (1)1.4 (0.6)1.4 (1)1/15

Δ fopt
f16, 40-D		 1e1
5244		 1e0
72122		 1e-1
3.2e5		 1e-2
7.1e5		 1e-3
1.4e6		 1e-5
2.0e6		 1e-7
2.0e6		 #succ
15/15
CMA-ES-2019 Hansen 0.93 (0.3)0.92 (0.3)0.70 (0.3)0.47 (0.4)0.36 (0.3)0.43 (0.2)0.44 (0.2)15/15
SLSQP+lq-CMA-ES Hansen 2.8 (2)1.1 (0.7)0.60 (0.3)0.55 (0.4)0.57 (0.2)0.52 (0.6)0.53 (0.9)15/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞8e50/15
lq-CMA-ES Hansen 0.58 (0.1)★30.83 (0.3)1.4 (2)∞∞∞∞1e50/15

Δ fopt
f17, 40-D		 1e1
399		 1e0
4220		 1e-1
14158		 1e-2
34948		 1e-3
51958		 1e-5
1.3e5		 1e-7
2.7e5		 #succ
14/15
CMA-ES-2019 Hansen 0.49 (0.3)0.45 (0.1)0.73 (1.0)1.0 (0.3)1.2 (0.6)0.92 (0.2)0.70 (0.3)15/15
SLSQP+lq-CMA-ES Hansen 3.4 (5)2.3 (0.8)1.9 (1)1.3 (0.6)1.2 (0.3)1.1 (0.3)0.68 (0.3)15/15
SLSQP-11-scipy Hansen 12 (20)∞∞∞∞∞∞8e50/15
lq-CMA-ES Hansen 0.87 (0.4)0.47 (0.2)0.73 (0.8)1.1 (0.5)1.4 (1)5.0 (3)∞9e40/15

Δ fopt
f18, 40-D		 1e1
1442		 1e0
16998		 1e-1
47068		 1e-2
1.3e5		 1e-3
1.9e5		 1e-5
6.7e5		 1e-7
9.5e5		 #succ
15/15
CMA-ES-2019 Hansen 0.82 (0.2)0.59 (0.9)1.1 (0.4)0.66 (0.4)0.80 (0.4)0.59 (0.3)0.56 (0.4)15/15
SLSQP+lq-CMA-ES Hansen 6.0 (1)1.4 (0.8)1.2 (0.4)0.73 (0.4)0.80 (0.3)0.56 (0.2)0.49 (0.2)15/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞8e50/15
lq-CMA-ES Hansen 0.74 (0.2)0.63 (1)1.5 (0.4)1.4 (3)∞∞∞1e50/15

Δ fopt
f19, 40-D		 1e1
1		 1e0
1		 1e-1
1.4e6		 1e-2
1.7e7		 1e-3
2.6e7		 1e-5
4.5e7		 1e-7
4.5e7		 #succ
8/15
CMA-ES-2019 Hansen 1 (0)1 (0)1.2 (0.8)0.58 (0.3)0.69 (0.9)0.64 (0.3)0.64 (1)5/15
SLSQP+lq-CMA-ES Hansen 1 (0)1 (0)4.7e-4 (0)0.99 (0.6)1.5 (1)1.7 (2)1.7 (2)2/15
SLSQP-11-scipy Hansen 1 (0)1 (0)4.7e-4 (0)∞∞∞∞9e50/15
lq-CMA-ES Hansen 1 (0)1 (0)∞∞∞∞∞2e50/15

Δ fopt
f20, 40-D		 1e1
222		 1e0
1.3e5		 1e-1
1.6e8		 1e-2
∞		 1e-3
∞		 1e-5
∞		 1e-7
∞		 #succ
0/15
CMA-ES-2019 Hansen 3.1 (0.5)12 (5)0.99 (0.6)    0/15
SLSQP+lq-CMA-ES Hansen 0.42 (0)10 (4)0.99 (0.7)    0/15
SLSQP-11-scipy Hansen 0.42 (0)∞∞    0/15
lq-CMA-ES Hansen 1.6 (0.3)∞∞    0/15

Δ fopt
f21, 40-D		 1e1
1044		 1e0
21144		 1e-1
1.0e5		 1e-2
1.0e5		 1e-3
1.0e5		 1e-5
1.0e5		 1e-7
1.0e5		 #succ
26/30
CMA-ES-2019 Hansen 1.8 (4)134 (205)98 (104)98 (104)98 (147)97 (85)97 (72)3/15
SLSQP+lq-CMA-ES Hansen 4.6 (3)59 (59)28 (31)28 (25)28 (37)28 (49)28 (60)7/15
SLSQP-11-scipy Hansen 0.55 (1)0.84 (2)0.29 (0.5)0.29 (0.3)0.29 (0.5)0.30 (0.4)1.6 (4)5/15
lq-CMA-ES Hansen 1.9 (4)9.0 (11)2.5 (3)2.5 (4)2.5 (5)2.5 (3)2.5 (2)5/15

Δ fopt
f22, 40-D		 1e1
3090		 1e0
35442		 1e-1
6.5e5		 1e-2
6.5e5		 1e-3
6.5e5		 1e-5
6.5e5		 1e-7
6.5e5		 #succ
8/30
CMA-ES-2019 Hansen 64 (11)105 (123)∞∞∞∞∞2e60/15
SLSQP+lq-CMA-ES Hansen 135 (206)69 (118)∞∞∞∞∞2e60/15
SLSQP-11-scipy Hansen 0.83 (0.8)5.2 (11)2.4 (4)2.4 (3)2.4 (2)2.4 (2)8.6 (12)0/15
lq-CMA-ES Hansen 8.1 (11)3.7 (5)∞∞∞∞∞1e50/15

Δ fopt
f23, 40-D		 1e1
7.0		 1e0
11925		 1e-1
75453		 1e-2
6.6e5		 1e-3
1.3e6		 1e-5
3.2e6		 1e-7
3.4e6		 #succ
15/15
CMA-ES-2019 Hansen 1.3 (2)800 (1187)440 (602)176 (187)∞∞∞8e60/15
SLSQP+lq-CMA-ES Hansen 12 (11)813 (742)451 (584)180 (202)∞∞∞9e60/15
SLSQP-11-scipy Hansen 12 (13)6.8 (7)∞∞∞∞∞8e50/15
lq-CMA-ES Hansen 8.5 (22)0.66 (0.1)0.69 (1)★3∞∞∞∞1e50/15

Δ fopt
f24, 40-D		 1e1
5.8e6		 1e0
9.8e7		 1e-1
3.0e8		 1e-2
3.0e8		 1e-3
3.0e8		 1e-5
3.0e8		 1e-7
3.0e8		 #succ
1/15
CMA-ES-2019 Hansen 22 (10)1.3 (1)0.44 (0.3)0.44 (0.7)0.44 (0.6)0.44 (0.6)0.44 (0.4)1/15
SLSQP+lq-CMA-ES Hansen 4.2 (5)∞∞∞∞∞∞9e60/15
SLSQP-11-scipy Hansen ∞∞∞∞∞∞∞8e50/15
lq-CMA-ES Hansen 0.30 (0.2)∞∞∞∞∞∞1e50/15

Expected runtime (ERT in number of function evaluations) divided by the respective best ERT measured during BBOB-2009 in different dimensions. This ERT ratio and, in braces as dispersion measure, the half difference between 10 and 90%-tile of bootstrapped run lengths appear for each algorithm and target, the corresponding reference ERT  in the first row. The different target ∆f-values are shown in the top row. #succ is the number of trials that reached the (final) target fopt+ 10−8. The median number of conducted function evaluations is additionally given in italics, if the target in the last column was never reached. Entries, succeeded by a star, are statistically significantly better (according to the rank-sum test) when compared to all other algorithms of the table, with p = 0.05 or p = 10−k when the number k following the star is larger than 1, with Bonferroni correction by the number of functions (24). A ↓ indicates the same tested against the best algorithm from BBOB 2009. Best results are printed in bold.