Overview page

Table showing the aRT in number of function evaluations divided by the best aRT 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
PSAaLmC-CMA-ES-Nishida 6.2 (8)10 (11)21 (9)44 (21)59 (14)112 (21)187 (39)15/15
PSAaLmD-CMA-ES-Nishida 5.4 (6)4.1 (3)9.1 (5)16 (10)26 (18)38 (10)55 (11)15/15
PSAaSmC-CMA-ES-Nishida 3.8 (2)7.4 (10)21 (12)38 (20)62 (15)118 (27)197 (21)15/15
PSAaSmD-CMA-ES-Nishida 6.6 (6)7.0 (11)14 (5)21 (52)46 (6)58 (110)74 (8)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
PSAaLmC-CMA-ES-Nishida 22 (13)36 (16)39 (11)48 (4)52 (5)59 (4)71 (8)15/15
PSAaLmD-CMA-ES-Nishida 39 (9)62 (50)53 (71)86 (40)85 (154)82 (66)83 (31)15/15
PSAaSmC-CMA-ES-Nishida 18 (7)32 (15)37 (18)48 (3)53 (5)60 (4)73 (8)15/15
PSAaSmD-CMA-ES-Nishida 82 (5)74 (233)76 (5)114 (313)115 (301)110 (55)143 (49)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
PSAaLmC-CMA-ES-Nishida 5.3 (1)2.8 (2)9.0 (13)20 (37)26 (33)28 (37)28 (24)15/15
PSAaLmD-CMA-ES-Nishida 33 (113)8.0 (5)10 (7)14 (15)15 (19)15 (13)15 (9)15/15
PSAaSmC-CMA-ES-Nishida 6.4 (8)2.7 (4)6.1 (8)22 (19)24 (19)25 (20)25 (22)15/15
PSAaSmD-CMA-ES-Nishida 11 (27)3.9 (7)7.4 (7)9.3 (10)10 (8)10 (6)10 (13)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
PSAaLmC-CMA-ES-Nishida 6.2 (4)27 (40)146 (122)502 (905)940 (1189)911 (1358)876 (1311)5/15
PSAaLmD-CMA-ES-Nishida 4.7 (2)7.7 (11)39 (77)146 (94)141 (45)156 (213)150 (253)13/15
PSAaSmC-CMA-ES-Nishida 5.0 (4)26 (24)111 (128)256 (279)392 (284)450 (662)433 (439)8/15
PSAaSmD-CMA-ES-Nishida 5.4 (1)12 (13)41 (66)53 (42)50 (98)50 (84)48 (149)15/15

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
PSAaLmC-CMA-ES-Nishida 10 (16)48 (44)54 (36)54 (32)54 (33)54 (40)54 (44)15/15
PSAaLmD-CMA-ES-Nishida 4.1 (4)17 (27)19 (13)19 (27)19 (23)19 (17)19 (14)15/15
PSAaSmC-CMA-ES-Nishida 18 (12)43 (16)49 (19)49 (26)49 (29)49 (29)49 (15)15/15
PSAaSmD-CMA-ES-Nishida 6.5 (8)37 (69)47 (107)63 (24)80 (195)80 (11)80 (109)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
PSAaLmC-CMA-ES-Nishida 4.7 (7)6.7 (5)12 (7)16 (4)17 (2)18 (3)19 (1)15/15
PSAaLmD-CMA-ES-Nishida 4.0 (2)5.5 (6)4.5 (2)5.5 (5)6.0 (1)7.3 (1)7.1 (7)15/15
PSAaSmC-CMA-ES-Nishida 4.2 (6)6.2 (6)10 (6)16 (3)16 (4)17 (2)19 (2)15/15
PSAaSmD-CMA-ES-Nishida 5.3 (6)5.7 (10)5.0 (4)8.5 (7)8.4 (0.9)11 (11)18 (24)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
PSAaLmC-CMA-ES-Nishida 16 (10)7.1 (4)6.2 (6)2.7 (1)2.6 (1)2.6 (0.6)2.4 (0.6)15/15
PSAaLmD-CMA-ES-Nishida 5.1 (7)1.7 (2)2.0 (2)1.2 (0.7)1.1 (1.0)1.1 (2)1.1 (1)15/15
PSAaSmC-CMA-ES-Nishida 7.0 (15)5.3 (7)4.0 (2)2.1 (1)2.5 (0.8)2.5 (0.9)2.6 (0.5)15/15
PSAaSmD-CMA-ES-Nishida 5.3 (5)4.7 (2)4.0 (4)1.7 (2)1.6 (1)1.6 (2)1.5 (1)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
PSAaLmC-CMA-ES-Nishida 8.9 (10)11 (11)20 (9)38 (21)27 (16)28 (19)27 (9)15/15
PSAaLmD-CMA-ES-Nishida 5.8 (3)25 (4)45 (45)64 (31)60 (100)62 (98)54 (66)15/15
PSAaSmC-CMA-ES-Nishida 12 (5)39 (4)38 (108)48 (55)30 (35)30 (49)28 (8)15/15
PSAaSmD-CMA-ES-Nishida 5.3 (5)7.7 (10)17 (21)72 (154)45 (86)63 (108)54 (11)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
PSAaLmC-CMA-ES-Nishida 38 (46)4.7 (4)18 (12)33 (27)30 (19)29 (17)28 (12)15/15
PSAaLmD-CMA-ES-Nishida 34 (25)4.1 (2)23 (49)51 (4)63 (69)73 (60)71 (62)15/15
PSAaSmC-CMA-ES-Nishida 31 (42)6.9 (6)32 (35)50 (25)38 (21)35 (13)33 (11)15/15
PSAaSmD-CMA-ES-Nishida 23 (26)14 (40)46 (49)120 (126)109 (92)97 (87)86 (51)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
PSAaLmC-CMA-ES-Nishida 14 (14)15 (12)18 (7)19 (4)19 (2)20 (2)21 (3)15/15
PSAaLmD-CMA-ES-Nishida 8.6 (5)8.7 (5)18 (15)20 (12)23 (34)22 (15)20 (34)15/15
PSAaSmC-CMA-ES-Nishida 13 (10)14 (7)17 (5)19 (2)19 (3)20 (2)21 (2)15/15
PSAaSmD-CMA-ES-Nishida 8.8 (8)20 (54)34 (58)33 (54)32 (44)27 (45)24 (38)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
PSAaLmC-CMA-ES-Nishida 12 (13)18 (11)20 (6)20 (5)20 (2)21 (1)22 (2)15/15
PSAaLmD-CMA-ES-Nishida 8.6 (2)19 (2)19 (48)20 (44)19 (1)17 (29)15 (26)15/15
PSAaSmC-CMA-ES-Nishida 13 (7)17 (9)21 (4)20 (5)20 (4)21 (4)21 (2)15/15
PSAaSmD-CMA-ES-Nishida 8.3 (13)16 (18)19 (28)21 (31)24 (35)20 (22)18 (11)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
PSAaLmC-CMA-ES-Nishida 9.4 (5)75 (78)108 (176)108 (191)109 (164)94 (303)81 (144)15/15
PSAaLmD-CMA-ES-Nishida 16 (5)174 (601)113 (669)112 (324)102 (290)75 (52)60 (32)15/15
PSAaSmC-CMA-ES-Nishida 9.4 (7)14 (6)40 (6)46 (4)48 (59)57 (3)87 (279)15/15
PSAaSmD-CMA-ES-Nishida 206 (16)431 (577)266 (599)214 (541)192 (432)133 (294)106 (449)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
PSAaLmC-CMA-ES-Nishida 8.8 (6)15 (3)17 (5)18 (2)20 (3)21 (3)22 (1)15/15
PSAaLmD-CMA-ES-Nishida 10 (23)12 (16)12 (18)14 (21)13 (12)12 (18)11 (13)15/15
PSAaSmC-CMA-ES-Nishida 9.4 (8)13 (4)16 (4)17 (5)18 (4)22 (2)22 (2)15/15
PSAaSmD-CMA-ES-Nishida 13 (30)19 (23)32 (55)26 (27)23 (18)20 (15)18 (34)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
PSAaLmC-CMA-ES-Nishida 8.6 (17)11 (6)13 (7)16 (6)15 (2)18 (3)21 (4)15/15
PSAaLmD-CMA-ES-Nishida 4.9 (1)2.6 (3)3.5 (2)5.4 (3)5.3 (2)5.7 (1)7.8 (6)15/15
PSAaSmC-CMA-ES-Nishida 4.2 (9)7.3 (11)11 (8)14 (5)15 (4)18 (2)21 (2)15/15
PSAaSmD-CMA-ES-Nishida 5.2 (6)3.8 (7)4.5 (3)5.7 (2)5.3 (3)5.2 (1)13 (1)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
PSAaLmC-CMA-ES-Nishida 2.1 (1)3.4 (2)1.9 (3)3.5 (3)3.7 (3)4.0 (2)3.8 (2)15/15
PSAaLmD-CMA-ES-Nishida 1.1 (0.6)1.4 (2)1.5 (0.9)2.1 (2)2.0 (3)2.1 (3)1.9 (2)15/15
PSAaSmC-CMA-ES-Nishida 2.3 (2)2.3 (1)2.1 (0.8)4.1 (2)4.4 (3)4.6 (4)4.2 (3)15/15
PSAaSmD-CMA-ES-Nishida 1.4 (0.9)6.3 (7)2.9 (3)3.8 (4)3.8 (4)3.5 (3)3.1 (4)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
PSAaLmC-CMA-ES-Nishida 2.4 (4)4.9 (7)15 (55)31 (63)63 (71)100 (185)77 (234)14/15
PSAaLmD-CMA-ES-Nishida 2.8 (3)5.6 (9)6.5 (10)14 (68)35 (7)37 (160)39 (17)14/15
PSAaSmC-CMA-ES-Nishida 2.1 (3)5.1 (6)10 (14)37 (157)49 (49)48 (123)37 (94)15/15
PSAaSmD-CMA-ES-Nishida 2.5 (3)6.6 (3)3.5 (3)4.8 (5)7.8 (16)12 (20)9.4 (6)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
PSAaLmC-CMA-ES-Nishida 4.1 (15)3.3 (2)4.5 (1)3.6 (0.8)4.1 (0.9)2.9 (0.4)3.0 (0.5)15/15
PSAaLmD-CMA-ES-Nishida 13 (10)4.0 (15)2.7 (2)1.7 (3)1.7 (0.7)1.3 (0.7)1.3 (0.6)15/15
PSAaSmC-CMA-ES-Nishida 3.6 (2)4.3 (8)4.3 (5)4.1 (2)4.2 (0.6)2.7 (0.4)3.0 (0.6)15/15
PSAaSmD-CMA-ES-Nishida 4.6 (6)6.7 (8)7.2 (10)4.3 (5)3.8 (2)3.2 (3)2.8 (2)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
PSAaLmC-CMA-ES-Nishida 3.3 (3)5.7 (2)1.9 (0.7)1.5 (1.0)1.5 (0.1)1.6 (0.2)2.0 (0.7)15/15
PSAaLmD-CMA-ES-Nishida 2.2 (2)8.9 (6)2.1 (1)1.4 (1)1.5 (0.9)1.6 (0.8)1.6 (1.0)15/15
PSAaSmC-CMA-ES-Nishida 4.2 (4)5.2 (4)1.6 (1.0)1.4 (0.2)1.4 (0.5)1.5 (0.3)2.0 (0.7)15/15
PSAaSmD-CMA-ES-Nishida 2.0 (2)5.5 (11)2.1 (4)1.3 (0.8)1.3 (0.3)2.6 (3)2.9 (3)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
PSAaLmC-CMA-ES-Nishida 6.5 (6)58 (116)8.1 (6)13 (2)43 (6)69 (147)69 (134)15/15
PSAaLmD-CMA-ES-Nishida 4.3 (4)53 (94)11 (24)31 (29)41 (54)51 (49)51 (62)15/15
PSAaSmC-CMA-ES-Nishida 8.5 (8)57 (57)7.9 (5)47 (27)49 (225)76 (207)80 (102)15/15
PSAaSmD-CMA-ES-Nishida 5.0 (7)34 (19)16 (9)177 (412)170 (146)256 (371)282 (390)14/15

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
PSAaLmC-CMA-ES-Nishida 7.3 (7)8.3 (7)11 (18)19 (35)21 (12)22 (54)22 (13)15/15
PSAaLmD-CMA-ES-Nishida 3.7 (5)9.1 (7)14 (14)18 (12)18 (12)19 (25)20 (20)15/15
PSAaSmC-CMA-ES-Nishida 4.3 (5)7.5 (8)15 (25)24 (40)25 (21)26 (30)27 (29)15/15
PSAaSmD-CMA-ES-Nishida 1.7 (2)16 (17)14 (11)17 (22)17 (30)18 (12)19 (24)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
PSAaLmC-CMA-ES-Nishida 0.93 (0.8)3.1 (6)12 (11)8.0 (7)11 (15)11 (16)12 (23)15/15
PSAaLmD-CMA-ES-Nishida 1.4 (0.9)14 (17)6.6 (4)4.4 (4)4.3 (3)4.2 (4)4.2 (3)15/15
PSAaSmC-CMA-ES-Nishida 1.7 (0.9)16 (36)16 (26)11 (16)12 (23)14 (30)17 (20)15/15
PSAaSmD-CMA-ES-Nishida 0.73 (0.4)17 (37)7.9 (12)6.3 (9)6.7 (9)6.3 (8)6.3 (7)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
PSAaLmC-CMA-ES-Nishida 2.3 (5)17 (1)10 (16)22 (9)22 (9)21 (85)24 (54)15/15
PSAaLmD-CMA-ES-Nishida 3.1 (6)29 (16)10 (15)8.5 (6)8.5 (9)8.4 (9)8.1 (6)15/15
PSAaSmC-CMA-ES-Nishida 2.6 (2)15 (44)9.4 (23)33 (64)32 (37)38 (85)38 (20)15/15
PSAaSmD-CMA-ES-Nishida 12 (40)9.1 (42)4.8 (9)5.6 (9)5.1 (8)4.7 (7)5.9 (6)15/15

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
PSAaLmC-CMA-ES-Nishida 2.2 (2)14 (12)5741 (7324)2e50/15
PSAaLmD-CMA-ES-Nishida 1.8 (2)47 (19)1074 (1076)2e50/15
PSAaSmC-CMA-ES-Nishida 2.4 (2)20 (15)1171 (1807)2e50/15
PSAaSmD-CMA-ES-Nishida 2.6 (2)7.9 (11)1082 (879)1.1e4 (1e4)9721 (8327)8352 (6733)2e50/15

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
PSAaLmC-CMA-ES-Nishida 1.7 (2)183 (324)25 (41)10 (11)36 (51)116 (136)116 (138)1/15
PSAaLmD-CMA-ES-Nishida 1.6 (1)212 (295)23 (25)11 (13)38 (38)57 (66)118 (109)1/15
PSAaSmC-CMA-ES-Nishida 1.7 (1)355 (472)44 (48)17 (23)26 (21)26 (30)26 (20)4/15
PSAaSmD-CMA-ES-Nishida 1.6 (2)148 (182)20 (20)21 (16)37 (63)123 (144)123 (138)1/15

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
PSAaLmC-CMA-ES-Nishida 15 (19)17 (5)37 (15)59 (10)82 (21)143 (29)215 (22)15/15
PSAaLmD-CMA-ES-Nishida 8.0 (8)10 (7)18 (6)29 (6)38 (4)65 (3)88 (8)15/15
PSAaSmC-CMA-ES-Nishida 13 (14)18 (12)38 (20)58 (18)80 (6)142 (40)220 (18)15/15
PSAaSmD-CMA-ES-Nishida 6.0 (4)10 (5)18 (3)27 (6)39 (4)57 (10)79 (12)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
PSAaLmC-CMA-ES-Nishida 28 (17)35 (16)39 (14)43 (13)46 (9)54 (10)64 (11)15/15
PSAaLmD-CMA-ES-Nishida 79 (91)120 (158)221 (186)218 (6)215 (192)210 (617)210 (70)15/15
PSAaSmC-CMA-ES-Nishida 29 (25)35 (15)39 (10)42 (15)45 (7)53 (6)63 (6)15/15
PSAaSmD-CMA-ES-Nishida 40 (125)76 (117)111 (144)121 (153)147 (137)144 (154)144 (139)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
PSAaLmC-CMA-ES-Nishida 8.8 (6)7.9 (6)24 (21)50 (36)50 (42)50 (68)51 (89)15/15
PSAaLmD-CMA-ES-Nishida 7.0 (6)18 (9)48 (31)83 (31)92 (190)92 (127)91 (127)14/15
PSAaSmC-CMA-ES-Nishida 7.2 (4)17 (21)64 (75)68 (73)69 (26)69 (84)69 (86)15/15
PSAaSmD-CMA-ES-Nishida 10 (21)7.5 (8)23 (18)25 (23)25 (25)25 (24)25 (21)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
PSAaLmC-CMA-ES-Nishida 19 (59)411 (607)3e50/15
PSAaLmD-CMA-ES-Nishida 13 (2)116 (110)1587 (1107)2240 (3590)2167 (846)2033 (1947)1976 (3576)2/15
PSAaSmC-CMA-ES-Nishida 11 (5)543 (290)3e50/15
PSAaSmD-CMA-ES-Nishida 12 (13)40 (59)755 (624)710 (885)698 (1425)655 (581)637 (289)5/15

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
PSAaLmC-CMA-ES-Nishida 17 (15)37 (25)39 (26)39 (35)39 (31)39 (35)39 (23)15/15
PSAaLmD-CMA-ES-Nishida 10 (6)20 (11)21 (5)21 (6)21 (9)21 (11)21 (6)15/15
PSAaSmC-CMA-ES-Nishida 15 (18)39 (36)42 (27)42 (33)42 (30)43 (34)43 (36)15/15
PSAaSmD-CMA-ES-Nishida 12 (19)23 (30)24 (22)24 (30)24 (30)24 (40)24 (25)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
PSAaLmC-CMA-ES-Nishida 4.3 (4)10 (4)11 (2)12 (1)12 (0.9)12 (1)13 (0.6)15/15
PSAaLmD-CMA-ES-Nishida 3.9 (5)5.0 (3)5.2 (2)6.2 (4)9.1 (0.7)9.0 (7)8.6 (8)15/15
PSAaSmC-CMA-ES-Nishida 5.3 (2)11 (1)11 (2)12 (0.9)12 (1)12 (0.9)13 (0.6)15/15
PSAaSmD-CMA-ES-Nishida 5.8 (3)6.7 (3)18 (52)16 (40)15 (14)14 (14)14 (16)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
PSAaLmC-CMA-ES-Nishida 7.3 (8)4.8 (4)1.9 (1)1.9 (1)2.0 (1)2.0 (0.9)2.0 (1)15/15
PSAaLmD-CMA-ES-Nishida 4.2 (6)4.6 (3)1.2 (3)1.2 (0.1)1.2 (1)1.2 (1)1.1 (0.3)15/15
PSAaSmC-CMA-ES-Nishida 5.5 (3)4.2 (2)1.5 (0.4)1.7 (2)2.0 (0.4)2.0 (0.2)1.8 (0.9)15/15
PSAaSmD-CMA-ES-Nishida 3.7 (5)3.2 (2)2.2 (1)1.9 (2)2.1 (1)2.1 (2)1.9 (2)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
PSAaLmC-CMA-ES-Nishida 7.5 (7)17 (10)16 (5)20 (9)22 (8)23 (7)24 (9)15/15
PSAaLmD-CMA-ES-Nishida 4.6 (2)30 (2)32 (46)171 (232)166 (156)199 (277)191 (314)15/15
PSAaSmC-CMA-ES-Nishida 6.9 (5)15 (9)17 (5)24 (7)34 (22)57 (77)56 (89)15/15
PSAaSmD-CMA-ES-Nishida 4.4 (3)53 (46)71 (120)183 (403)242 (299)240 (229)229 (143)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
PSAaLmC-CMA-ES-Nishida 8.3 (7)17 (6)45 (4)48 (5)52 (21)67 (112)71 (63)15/15
PSAaLmD-CMA-ES-Nishida 5.9 (2)5.6 (3)80 (166)156 (180)295 (295)431 (655)410 (362)14/15
PSAaSmC-CMA-ES-Nishida 7.2 (4)14 (3)23 (6)34 (11)43 (9)44 (8)44 (10)15/15
PSAaSmD-CMA-ES-Nishida 4.9 (3)54 (61)108 (94)176 (251)414 (684)411 (664)397 (780)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
PSAaLmC-CMA-ES-Nishida 9.3 (5)10 (2)10 (3)10 (2)10 (2)11 (2)13 (2)15/15
PSAaLmD-CMA-ES-Nishida 10 (2)20 (53)29 (28)31 (27)32 (26)29 (23)27 (34)15/15
PSAaSmC-CMA-ES-Nishida 8.9 (4)9.2 (3)9.3 (1)10 (2)10 (1)11 (0.9)12 (0.4)15/15
PSAaSmD-CMA-ES-Nishida 5.3 (2)24 (46)36 (75)36 (20)35 (65)33 (47)30 (38)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
PSAaLmC-CMA-ES-Nishida 12 (6)12 (3)6.6 (1)6.3 (0.9)6.6 (0.5)7.6 (1.0)8.8 (0.7)15/15
PSAaLmD-CMA-ES-Nishida 27 (7)45 (91)28 (24)44 (56)49 (58)48 (87)45 (74)15/15
PSAaSmC-CMA-ES-Nishida 11 (7)12 (4)6.7 (2)6.4 (1)6.9 (0.7)7.5 (1)8.9 (0.9)15/15
PSAaSmD-CMA-ES-Nishida 35 (56)37 (46)52 (94)59 (89)65 (77)60 (74)64 (65)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
PSAaLmC-CMA-ES-Nishida 68 (6)72 (150)114 (531)126 (387)116 (233)137 (308)180 (389)11/15
PSAaLmD-CMA-ES-Nishida 31 (2)96 (512)216 (240)301 (489)392 (605)450 (874)397 (288)8/15
PSAaSmC-CMA-ES-Nishida 16 (11)162 (76)94 (42)160 (639)207 (346)136 (18)126 (300)11/15
PSAaSmD-CMA-ES-Nishida 30 (60)304 (498)282 (677)329 (305)340 (283)508 (656)448 (671)7/15

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
PSAaLmC-CMA-ES-Nishida 10 (5)12 (2)13 (3)13 (2)11 (1)12 (0.5)12 (0.6)15/15
PSAaLmD-CMA-ES-Nishida 4.6 (1)4.9 (0.9)11 (23)10 (0.5)7.2 (12)6.8 (18)6.2 (7)15/15
PSAaSmC-CMA-ES-Nishida 10 (2)9.5 (3)12 (2)13 (2)11 (1)12 (0.5)12 (0.4)15/15
PSAaSmD-CMA-ES-Nishida 17 (47)16 (5)20 (18)17 (25)14 (18)12 (16)11 (15)15/15

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
PSAaLmC-CMA-ES-Nishida 5.8 (10)7.7 (13)11 (3)12 (4)12 (4)15 (1)13 (0.9)15/15
PSAaLmD-CMA-ES-Nishida 3.2 (5)3.1 (5)5.1 (3)5.9 (2)6.1 (1)11 (2)10 (11)15/15
PSAaSmC-CMA-ES-Nishida 10 (22)7.3 (5)11 (6)13 (5)13 (4)16 (3)13 (0.8)15/15
PSAaSmD-CMA-ES-Nishida 7.6 (8)4.9 (4)16 (2)17 (3)13 (3)18 (2)13 (16)15/15

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
PSAaLmC-CMA-ES-Nishida 2.1 (1)2.5 (2)1.9 (0.9)1.8 (2)1.8 (1)1.8 (2)1.8 (0.3)15/15
PSAaLmD-CMA-ES-Nishida 1.7 (1.0)3.5 (3)2.3 (2)1.8 (1)1.8 (1)1.7 (2)1.7 (2)15/15
PSAaSmC-CMA-ES-Nishida 2.2 (0.5)2.9 (3)1.2 (1)1.1 (0.8)1.2 (0.8)1.2 (0.7)1.2 (0.8)15/15
PSAaSmD-CMA-ES-Nishida 1.2 (0.8)1.6 (2)1.9 (2)1.9 (1)1.9 (2)1.8 (1)1.8 (2)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
PSAaLmC-CMA-ES-Nishida 1.8 (0.7)9.2 (14)76 (86)96 (193)41 (106)24 (79)23 (59)13/15
PSAaLmD-CMA-ES-Nishida 2.0 (2)4.6 (6)29 (26)29 (19)12 (35)7.2 (13)6.9 (6)15/15
PSAaSmC-CMA-ES-Nishida 2.0 (1)4.2 (2)33 (27)65 (101)27 (102)16 (15)16 (23)14/15
PSAaSmD-CMA-ES-Nishida 2.1 (2)6.1 (7)10 (16)8.4 (12)3.6 (5)2.1 (3)2.1 (3)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
PSAaLmC-CMA-ES-Nishida 9.4 (9)4.0 (2)2.7 (0.8)3.1 (0.3)2.0 (0.2)1.8 (0.7)1.7 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 4.5 (3)2.0 (2)5.5 (16)3.9 (0.3)2.1 (0.7)1.4 (2)1.3 (0.7)15/15
PSAaSmC-CMA-ES-Nishida 3.5 (3)3.6 (2)2.6 (0.9)2.9 (0.7)1.9 (0.4)1.6 (0.2)1.7 (0.6)15/15
PSAaSmD-CMA-ES-Nishida 2.9 (7)2.3 (0.9)2.5 (0.3)2.0 (0.2)1.1 (0.1)1.5 (2)1.2 (0.7)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
PSAaLmC-CMA-ES-Nishida 3.8 (3)4.0 (2)1.0 (0.5)0.94 (0.1)1.1 (0.8)1.2 (0.4)1.4 (1.0)15/15
PSAaLmD-CMA-ES-Nishida 2.8 (4)2.6 (2)1.5 (0.2)0.94 (0.9)0.94 (0.1)1.8 (3)1.7 (0.9)15/15
PSAaSmC-CMA-ES-Nishida 3.8 (2)4.4 (2)5.2 (16)2.5 (7)2.4 (3)2.2 (2)2.2 (2)15/15
PSAaSmD-CMA-ES-Nishida 3.0 (3)7.1 (3)2.1 (7)1.3 (1)1.2 (0.4)1.7 (1)1.9 (2)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
PSAaLmC-CMA-ES-Nishida 15 (16)186 (102)212 (419)6.1 (8)6.3 (12)6.7 (11)6.7 (1.0)15/15
PSAaLmD-CMA-ES-Nishida 6.2 (3)161 (72)25 (28)2.9 (3)4.4 (8)4.7 (4)4.7 (2)15/15
PSAaSmC-CMA-ES-Nishida 6.1 (3)123 (64)25 (34)3.2 (2)4.0 (11)4.1 (11)4.2 (11)15/15
PSAaSmD-CMA-ES-Nishida 12 (11)173 (212)386 (1306)16 (19)27 (23)41 (22)41 (42)9/15

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
PSAaLmC-CMA-ES-Nishida 4.7 (6)5.1 (6)16 (18)16 (14)15 (16)15 (11)14 (10)15/15
PSAaLmD-CMA-ES-Nishida 3.1 (5)5.6 (6)13 (10)12 (11)13 (11)13 (8)12 (10)15/15
PSAaSmC-CMA-ES-Nishida 5.5 (5)6.6 (8)9.4 (5)13 (21)13 (35)12 (8)12 (20)15/15
PSAaSmD-CMA-ES-Nishida 4.2 (4)6.0 (8)13 (14)12 (24)12 (4)11 (8)11 (8)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
PSAaLmC-CMA-ES-Nishida 1.3 (2)19 (44)21 (32)28 (23)27 (30)28 (23)28 (26)15/15
PSAaLmD-CMA-ES-Nishida 1.9 (2)14 (6)12 (7)16 (34)15 (30)15 (11)15 (30)15/15
PSAaSmC-CMA-ES-Nishida 2.2 (2)19 (36)32 (41)31 (35)30 (20)30 (30)30 (38)15/15
PSAaSmD-CMA-ES-Nishida 2.2 (2)15 (35)10 (12)10 (16)10 (14)10 (10)10 (13)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
PSAaLmC-CMA-ES-Nishida 2.1 (3)13 (12)39 (59)69 (171)73 (145)70 (153)68 (206)15/15
PSAaLmD-CMA-ES-Nishida 1.6 (3)9.3 (14)17 (22)17 (19)25 (43)24 (17)24 (68)15/15
PSAaSmC-CMA-ES-Nishida 16 (50)24 (55)33 (76)39 (73)40 (38)38 (29)37 (44)15/15
PSAaSmD-CMA-ES-Nishida 1.8 (1)10 (16)15 (20)15 (21)15 (20)15 (11)19 (35)15/15

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
PSAaLmC-CMA-ES-Nishida 5.3 (8)18 (19)3e50/15
PSAaLmD-CMA-ES-Nishida 2.7 (2)16 (14)5014 (3893)3e50/15
PSAaSmC-CMA-ES-Nishida 3.3 (2)18 (10)3e50/15
PSAaSmD-CMA-ES-Nishida 3.0 (3)13 (12)3e50/15

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
PSAaLmC-CMA-ES-Nishida 3.1 (3)40 (29)13 (10)12 (6)3e50/15
PSAaLmD-CMA-ES-Nishida 4.3 (2)117 (124)43 (37)3e50/15
PSAaSmC-CMA-ES-Nishida 2.7 (2)51 (33)13 (18)3e50/15
PSAaSmD-CMA-ES-Nishida 1.8 (1)39 (44)21 (9)3e50/15

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
PSAaLmC-CMA-ES-Nishida 7.3 (3)25 (8)48 (8)68 (12)104 (18)181 (10)247 (35)15/15
PSAaLmD-CMA-ES-Nishida 6.4 (7)16 (6)26 (6)47 (10)69 (8)120 (14)170 (14)15/15
PSAaSmC-CMA-ES-Nishida 6.3 (4)23 (8)45 (12)72 (15)102 (24)169 (11)236 (12)15/15
PSAaSmD-CMA-ES-Nishida 9.5 (18)19 (7)35 (19)51 (14)70 (11)114 (9)151 (13)★215/15

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
PSAaLmC-CMA-ES-Nishida 22 (2)26 (9)30 (9)33 (9)36 (7)44 (3)52 (4)15/15
PSAaLmD-CMA-ES-Nishida 13 (3)18 (5)30 (59)41 (67)43 (9)49 (3)62 (65)15/15
PSAaSmC-CMA-ES-Nishida 21 (5)25 (4)29 (4)31 (4)34 (4)42 (2)50 (2)15/15
PSAaSmD-CMA-ES-Nishida 296 (1871)840 (2762)870 (2697)978 (2661)1276 (2534)1273 (1727)1252 (2211)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
PSAaLmC-CMA-ES-Nishida 2.6 (2)103 (112)2194 (3556)4555 (3200)4544 (3649)4534 (6445)4523 (6657)1/15
PSAaLmD-CMA-ES-Nishida 4.8 (2)70 (86)1427 (1758)1423 (814)1420 (1089)1417 (1238)1414 (1033)3/15
PSAaSmC-CMA-ES-Nishida 2.2 (2)56 (79)337 (157)336 (293)336 (383)335 (230)335 (483)9/15
PSAaSmD-CMA-ES-Nishida 2.2 (2)31 (31)146 (119)146 (121)146 (184)146 (164)146 (221)14/15

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
PSAaLmC-CMA-ES-Nishida 3.9 (2)5e50/15
PSAaLmD-CMA-ES-Nishida 3.4 (1)5e50/15
PSAaSmC-CMA-ES-Nishida 3.8 (3)5e50/15
PSAaSmD-CMA-ES-Nishida 3.1 (2)5e50/15

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
PSAaLmC-CMA-ES-Nishida 26 (9)47 (11)51 (38)51 (37)51 (18)51 (30)51 (16)15/15
PSAaLmD-CMA-ES-Nishida 16 (13)26 (9)27 (8)27 (19)27 (10)27 (10)27 (15)15/15
PSAaSmC-CMA-ES-Nishida 24 (12)38 (17)41 (29)41 (12)41 (15)41 (31)41 (22)15/15
PSAaSmD-CMA-ES-Nishida 15 (9)28 (6)30 (27)30 (11)30 (33)30 (27)30 (23)15/15

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
PSAaLmC-CMA-ES-Nishida 5.3 (4)6.5 (0.7)7.4 (0.6)6.9 (0.8)6.0 (0.7)4.8 (0.3)4.8 (0.4)15/15
PSAaLmD-CMA-ES-Nishida 4.3 (2)4.4 (0.5)4.8 (0.8)4.5 (0.3)3.9 (0.3)3.1 (0.2)3.1 (0.2)15/15
PSAaSmC-CMA-ES-Nishida 5.7 (2)6.0 (1)7.1 (0.7)6.4 (0.8)5.6 (0.7)4.4 (0.2)4.5 (0.3)15/15
PSAaSmD-CMA-ES-Nishida 4.4 (1)14 (35)17 (3)19 (27)16 (13)11 (16)8.8 (14)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
PSAaLmC-CMA-ES-Nishida 7.4 (4)1.7 (0.6)0.92 (0.3)1.1 (0.1)1.1 (0.2)1.1 (0.1)1.1 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 8.3 (3)1.5 (0.3)0.80 (0.6)0.87 (0.8)0.86 (0.6)0.86 (0.6)0.92 (0.1)15/15
PSAaSmC-CMA-ES-Nishida 9.3 (8)1.8 (0.4)0.81 (0.2)1.00 (0.1)1.0 (0.1)1.0 (0.1)1.1 (0.1)15/15
PSAaSmD-CMA-ES-Nishida 7.3 (5)1.7 (1)0.87 (0.7)0.92 (0.4)0.91 (0.3)0.91 (0.6)0.95 (0.4)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
PSAaLmC-CMA-ES-Nishida 11 (3)82 (74)229 (210)1540 (1972)3063 (2074)3016 (3110)3783 (5077)4/15
PSAaLmD-CMA-ES-Nishida 7.2 (1)84 (114)1181 (1265)2643 (3160)4237 (4558)5424 (4565)5272 (4310)2/15
PSAaSmC-CMA-ES-Nishida 11 (4)28 (7)457 (541)1624 (2925)2885 (3401)3743 (3585)3638 (1757)4/15
PSAaSmD-CMA-ES-Nishida 6.3 (2)135 (332)1435 (1644)3871 (3432)3801 (6305)3626 (7191)3523 (3395)4/15

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
PSAaLmC-CMA-ES-Nishida 19 (7)127 (172)900 (1907)8600 (1e4)1.2e4 (1e4)5e50/15
PSAaLmD-CMA-ES-Nishida 14 (4)142 (211)1616 (1927)1.4e4 (3e4)1.2e4 (2e4)2.2e4 (3e4)2.0e4 (2e4)1/15
PSAaSmC-CMA-ES-Nishida 18 (7)78 (168)465 (539)1416 (1332)3151 (3351)2871 (2582)4391 (3011)4/15
PSAaSmD-CMA-ES-Nishida 12 (8)142 (229)4204 (6955)5e50/15

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
PSAaLmC-CMA-ES-Nishida 5.3 (0.9)4.4 (0.6)4.4 (0.5)4.8 (0.5)5.1 (0.4)4.8 (0.2)5.6 (0.2)15/15
PSAaLmD-CMA-ES-Nishida 36 (0.3)81 (0.3)71 (474)68 (225)70 (16)53 (6)51 (0.2)14/15
PSAaSmC-CMA-ES-Nishida 5.1 (1.0)4.5 (2)5.0 (0.8)11 (0.4)11 (23)9.2 (17)10 (33)15/15
PSAaSmD-CMA-ES-Nishida 108 (224)222 (3)256 (531)291 (632)284 (446)279 (526)263 (382)12/15

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
PSAaLmC-CMA-ES-Nishida 11 (6)11 (3)3.3 (0.6)2.8 (0.4)2.6 (0.8)2.6 (0.3)2.7 (0.3)15/15
PSAaLmD-CMA-ES-Nishida 7.4 (3)25 (5)22 (101)19 (53)17 (9)15 (18)13 (6)15/15
PSAaSmC-CMA-ES-Nishida 10 (4)10 (2)3.1 (0.7)2.7 (0.9)2.5 (0.2)2.4 (0.4)2.6 (0.1)15/15
PSAaSmD-CMA-ES-Nishida 250 (7)341 (613)162 (236)159 (246)132 (222)106 (250)94 (250)13/15

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
PSAaLmC-CMA-ES-Nishida 22 (6)99 (152)175 (359)253 (589)416 (818)396 (324)438 (428)7/15
PSAaLmD-CMA-ES-Nishida 14 (4)192 (167)409 (1249)832 (1579)1224 (1377)1558 (1745)1359 (678)3/15
PSAaSmC-CMA-ES-Nishida 19 (4)11 (5)35 (6)122 (364)383 (551)376 (444)444 (740)6/15
PSAaSmD-CMA-ES-Nishida 169 (1)229 (583)566 (1359)690 (968)969 (2215)908 (1375)1000 (822)4/15

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
PSAaLmC-CMA-ES-Nishida 7.4 (2)9.0 (1.0)10 (0.6)10 (1)3.1 (0.1)3.2 (0.2)3.2 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 5.2 (2)6.4 (1.0)7.0 (0.4)7.2 (0.5)2.2 (0.1)2.2 (0.1)2.3 (0.0)15/15
PSAaSmC-CMA-ES-Nishida 7.2 (2)8.6 (2)10 (2)10 (0.6)3.1 (0.1)3.2 (0.2)3.1 (0.1)15/15
PSAaSmD-CMA-ES-Nishida 5.2 (3)5.9 (2)6.5 (1)6.5 (0.7)13 (0.2)10 (0.1)8.5 (0.1)15/15

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
PSAaLmC-CMA-ES-Nishida 3.8 (1)8.6 (3)11 (2)12 (3)12 (1)11 (2)8.7 (0.5)15/15
PSAaLmD-CMA-ES-Nishida 3.4 (4)4.5 (3)7.1 (1)7.3 (2)8.1 (1)7.8 (1)6.0 (0.5)15/15
PSAaSmC-CMA-ES-Nishida 2.8 (4)6.9 (4)10 (2)11 (2)11 (2)11 (0.9)8.1 (0.6)15/15
PSAaSmD-CMA-ES-Nishida 4.0 (7)5.2 (2)7.2 (2)8.0 (1)7.6 (1.0)7.0 (0.8)5.1 (0.5)★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
PSAaLmC-CMA-ES-Nishida 3.9 (3)2.2 (0.7)1.5 (0.6)1.4 (0.4)1.4 (1.0)1.4 (0.9)1.4 (0.4)15/15
PSAaLmD-CMA-ES-Nishida 2.3 (0.7)2.5 (1)1.6 (0.4)1.6 (0.7)1.6 (0.6)1.5 (0.7)1.5 (0.5)15/15
PSAaSmC-CMA-ES-Nishida 3.7 (2)1.0 (0.7)0.71 (1.0)0.72 (0.3)0.73 (0.6)0.75 (0.6)0.76 (0.3)15/15
PSAaSmD-CMA-ES-Nishida 3.0 (4)0.88 (0.4)1.1 (1)1.1 (0.9)1.1 (1)1.1 (2)1.1 (0.9)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
PSAaLmC-CMA-ES-Nishida 1.9 (2)144 (192)104 (81)27 (44)27 (33)25 (48)24 (26)13/15
PSAaLmD-CMA-ES-Nishida 3.0 (3)155 (89)105 (257)28 (31)27 (41)24 (58)24 (43)11/15
PSAaSmC-CMA-ES-Nishida 3.1 (2)69 (40)36 (81)11 (15)12 (9)11 (9)11 (9)14/15
PSAaSmD-CMA-ES-Nishida 4.2 (3)49 (8)14 (4)5.5 (9)5.5 (3)5.5 (9)5.4 (6)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
PSAaLmC-CMA-ES-Nishida 10 (20)2.9 (1)1.6 (0.3)1.0 (0.3)1.2 (0.1)1.2 (0.1)1.3 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 11 (13)2.1 (0.5)1.2 (0.6)0.76 (0.2)0.85 (0.1)0.85 (0.0)0.94 (0.1)15/15
PSAaSmC-CMA-ES-Nishida 10 (8)2.3 (0.7)1.5 (0.3)0.90 (0.1)1.0 (0.1)1.0 (0.1)1.2 (0.6)15/15
PSAaSmD-CMA-ES-Nishida 6.3 (13)1.7 (0.5)1.1 (1)0.62 (0.1)0.70 (0.1)★20.68 (0.1)★21.1 (0.1)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
PSAaLmC-CMA-ES-Nishida 2.3 (2)2.7 (1)0.89 (1)0.59 (0.1)0.70 (0.9)0.87 (0.4)0.98 (0.0)15/15
PSAaLmD-CMA-ES-Nishida 1.6 (1)1.9 (0.5)1.1 (0.1)0.66 (0.1)0.71 (0.0)0.81 (0.9)0.88 (0.0)15/15
PSAaSmC-CMA-ES-Nishida 3.1 (2)2.8 (1)2.3 (3)1.3 (3)1.3 (1)1.3 (1)1.4 (1)15/15
PSAaSmD-CMA-ES-Nishida 2.2 (2)2.2 (0.6)1.7 (4)0.88 (1.0)0.89 (2)1.0 (1)1.0 (0.7)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
PSAaLmC-CMA-ES-Nishida 39 (68)1343 (982)220 (70)0.62 (0.2)0.69 (0.7)0.69 (0.1)0.69 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 25 (27)1277 (725)263 (330)0.78 (0.8)0.84 (0.6)0.84 (0.6)0.97 (0.8)15/15
PSAaSmC-CMA-ES-Nishida 24 (22)1736 (2181)100 (17)0.75 (0.8)1.5 (3)1.5 (3)1.5 (2)12/15
PSAaSmD-CMA-ES-Nishida 18 (8)1242 (833)284 (539)1.1 (1)1.9 (2)1.9 (2)2.0 (5)13/15

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
PSAaLmC-CMA-ES-Nishida 6.8 (6)14 (7)2.6 (3)2.1 (3)2.0 (2)2.0 (2)2.0 (2)15/15
PSAaLmD-CMA-ES-Nishida 5.3 (6)13 (6)3.4 (4)2.6 (3)2.5 (3)2.5 (1)2.4 (3)15/15
PSAaSmC-CMA-ES-Nishida 7.6 (5)10 (12)12 (21)9.1 (10)8.6 (12)8.6 (5)8.5 (7)10/15
PSAaSmD-CMA-ES-Nishida 6.0 (5)6.7 (9)13 (25)10 (18)9.0 (11)9.0 (9)8.9 (12)10/15

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
PSAaLmC-CMA-ES-Nishida 4.2 (6)18 (13)23 (36)24 (37)23 (16)23 (18)23 (18)15/15
PSAaLmD-CMA-ES-Nishida 2.2 (2)14 (17)15 (16)15 (22)15 (16)15 (19)15 (20)15/15
PSAaSmC-CMA-ES-Nishida 3.3 (3)18 (30)18 (35)18 (17)18 (26)18 (11)18 (16)15/15
PSAaSmD-CMA-ES-Nishida 2.2 (2)13 (8)16 (6)16 (7)16 (41)16 (31)16 (39)15/15

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
PSAaLmC-CMA-ES-Nishida 13 (22)36 (105)125 (113)138 (124)134 (196)130 (190)127 (48)14/15
PSAaLmD-CMA-ES-Nishida 6.9 (17)49 (39)115 (101)113 (113)110 (302)107 (106)105 (295)14/15
PSAaSmC-CMA-ES-Nishida 3.2 (4)43 (55)124 (53)119 (218)115 (313)112 (72)110 (133)14/15
PSAaSmD-CMA-ES-Nishida 9.4 (2)62 (102)63 (48)72 (254)70 (42)68 (138)70 (64)14/15

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
PSAaLmC-CMA-ES-Nishida 2.3 (2)43 (42)5e50/15
PSAaLmD-CMA-ES-Nishida 3.0 (3)74 (48)5e50/15
PSAaSmC-CMA-ES-Nishida 1.7 (2)54 (34)5e50/15
PSAaSmD-CMA-ES-Nishida 1.9 (2)36 (45)5e50/15

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
PSAaLmC-CMA-ES-Nishida 5.8 (6)33 (19)5e50/15
PSAaLmD-CMA-ES-Nishida 3.7 (6)11 (16)5e50/15
PSAaSmC-CMA-ES-Nishida 4.1 (2)10 (6)5e50/15
PSAaSmD-CMA-ES-Nishida 4.7 (4)33 (45)5e50/15

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
PSAaLmC-CMA-ES-Nishida 12 (4)30 (8)60 (9)114 (15)180 (13)320 (16)462 (21)15/15
PSAaLmD-CMA-ES-Nishida 15 (6)31 (6)61 (13)116 (8)190 (18)322 (22)468 (34)15/15
PSAaSmC-CMA-ES-Nishida 16 (9)33 (11)63 (12)100 (11)158 (22)266 (16)368 (25)15/15
PSAaSmD-CMA-ES-Nishida 15 (3)29 (3)57 (7)105 (19)156 (12)259 (23)371 (18)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
PSAaLmC-CMA-ES-Nishida 30 (5)35 (3)39 (3)45 (2)52 (2)68 (5)84 (3)15/15
PSAaLmD-CMA-ES-Nishida 30 (2)35 (3)38 (3)43 (3)50 (3)66 (2)83 (4)15/15
PSAaSmC-CMA-ES-Nishida 27 (7)55 (172)86 (197)124 (186)128 (3)139 (96)159 (189)15/15
PSAaSmD-CMA-ES-Nishida 26 (5)30 (4)33 (5)36 (3)41 (4)51 (3)64 (3)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
PSAaLmC-CMA-ES-Nishida 73 (15)1e60/15
PSAaLmD-CMA-ES-Nishida 75 (7)1e60/15
PSAaSmC-CMA-ES-Nishida 27 (5)1e60/15
PSAaSmD-CMA-ES-Nishida 27 (9)1294 (1595)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
PSAaLmC-CMA-ES-Nishida 22 (10)1e60/15
PSAaLmD-CMA-ES-Nishida 23 (13)1e60/15
PSAaSmC-CMA-ES-Nishida 10 (3)1e60/15
PSAaSmD-CMA-ES-Nishida 12 (9)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
PSAaLmC-CMA-ES-Nishida 29 (10)39 (8)41 (22)41 (6)41 (9)41 (20)41 (24)15/15
PSAaLmD-CMA-ES-Nishida 29 (9)42 (11)45 (17)45 (15)45 (11)45 (14)45 (12)15/15
PSAaSmC-CMA-ES-Nishida 28 (12)38 (14)40 (14)40 (11)40 (10)40 (16)40 (7)15/15
PSAaSmD-CMA-ES-Nishida 36 (22)50 (9)53 (24)53 (23)53 (25)53 (20)53 (29)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
PSAaLmC-CMA-ES-Nishida 6.8 (0.5)7.5 (0.6)8.3 (0.5)8.6 (0.5)8.6 (0.5)8.3 (0.3)8.3 (0.3)15/15
PSAaLmD-CMA-ES-Nishida 6.6 (0.5)7.6 (1)8.4 (0.4)8.8 (0.5)8.7 (0.4)8.4 (0.3)8.3 (0.4)15/15
PSAaSmC-CMA-ES-Nishida 5.7 (1.0)6.3 (0.6)6.7 (0.7)10 (13)9.5 (2)9.4 (7)8.7 (4)15/15
PSAaSmD-CMA-ES-Nishida 5.5 (0.5)6.2 (0.4)6.7 (0.8)6.8 (0.7)6.6 (0.4)8.1 (0.3)7.5 (0.2)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
PSAaLmC-CMA-ES-Nishida 5.5 (2)1.4 (0.4)0.84 (0.1)1.1 (0.2)1.1 (0.2)1.1 (0.1)1.1 (0.2)15/15
PSAaLmD-CMA-ES-Nishida 6.1 (2)1.5 (0.5)0.87 (0.2)1.1 (0.2)1.1 (0.2)1.1 (0.1)1.1 (0.1)15/15
PSAaSmC-CMA-ES-Nishida 4.9 (1)1.3 (0.3)0.73 (0.1)0.84 (0.1)0.86 (0.1)0.86 (0.1)0.87 (0.2)15/15
PSAaSmD-CMA-ES-Nishida 4.9 (2)1.2 (0.5)0.73 (0.3)0.83 (0.1)0.85 (0.1)0.85 (0.1)0.89 (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
PSAaLmC-CMA-ES-Nishida 12 (0.8)1e60/15
PSAaLmD-CMA-ES-Nishida 12 (0.8)1e60/15
PSAaSmC-CMA-ES-Nishida 10 (2)1e60/15
PSAaSmD-CMA-ES-Nishida 10 (1)7556 (7840)6249 (9081)1.2e4 (1e4)1.2e4 (1e4)1.1e4 (7357)1e60/15

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
PSAaLmC-CMA-ES-Nishida 20 (2)1e60/15
PSAaLmD-CMA-ES-Nishida 20 (2)1e60/15
PSAaSmC-CMA-ES-Nishida 16 (1)1e60/15
PSAaSmD-CMA-ES-Nishida 16 (2)1e60/15

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
PSAaLmC-CMA-ES-Nishida 3.0 (0.5)3.0 (0.2)3.0 (0.2)3.0 (0.1)3.5 (0.1)2.9 (0.1)3.4 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 2.9 (0.4)3.0 (0.2)3.0 (0.1)3.0 (0.2)3.5 (0.2)2.8 (0.1)3.4 (0.1)15/15
PSAaSmC-CMA-ES-Nishida 2.6 (0.4)2.6 (0.3)2.7 (0.4)2.6 (0.3)2.8 (0.3)2.3 (0.1)2.7 (0.2)15/15
PSAaSmD-CMA-ES-Nishida 2.7 (0.4)2.8 (0.2)20 (0.3)18 (0.5)18 (56)12 (69)12 (0.1)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
PSAaLmC-CMA-ES-Nishida 17 (3)5.0 (0.3)2.3 (0.4)2.3 (0.4)3.3 (4)3.5 (6)3.6 (5)15/15
PSAaLmD-CMA-ES-Nishida 16 (5)4.9 (1.0)2.2 (0.3)2.2 (0.1)2.3 (0.2)2.6 (0.2)2.9 (0.1)15/15
PSAaSmC-CMA-ES-Nishida 13 (2)4.1 (0.6)2.0 (0.4)2.0 (0.5)1.9 (0.2)2.8 (3)2.9 (0.1)15/15
PSAaSmD-CMA-ES-Nishida 13 (3)4.7 (0.7)15 (100)14 (44)14 (1)17 (63)15 (29)15/15

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
PSAaLmC-CMA-ES-Nishida 15 (3)22 (1)30 (31)134 (470)357 (328)1148 (891)842 (719)3/15
PSAaLmD-CMA-ES-Nishida 16 (1)83 (230)344 (412)763 (799)2185 (4152)1952 (1681)2779 (2846)1/15
PSAaSmC-CMA-ES-Nishida 13 (5)102 (334)123 (344)166 (168)406 (563)3885 (4649)2759 (3849)1/15
PSAaSmD-CMA-ES-Nishida 12 (0.8)59 (189)94 (183)269 (225)952 (1206)3941 (5003)2799 (2222)1/15

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
PSAaLmC-CMA-ES-Nishida 7.9 (1.0)10 (1.0)11 (0.7)12 (0.3)3.4 (0.1)3.5 (0.1)3.6 (0.0)15/15
PSAaLmD-CMA-ES-Nishida 8.6 (2)10 (1)12 (0.6)12 (0.6)3.4 (0.1)3.5 (0.1)3.6 (0.1)15/15
PSAaSmC-CMA-ES-Nishida 6.9 (2)8.4 (0.6)9.2 (0.4)10 (0.4)2.6 (0.1)2.7 (0.1)2.8 (0.1)15/15
PSAaSmD-CMA-ES-Nishida 7.2 (0.6)8.4 (0.5)9.3 (0.3)10 (0.3)2.6 (0.1)2.7 (0.1)2.8 (0.1)15/15

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
PSAaLmC-CMA-ES-Nishida 7.0 (4)11 (3)13 (3)15 (2)13 (1)13 (0.8)3.1 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 7.3 (4)11 (2)14 (2)16 (2)13 (2)14 (0.5)3.1 (0.2)15/15
PSAaSmC-CMA-ES-Nishida 5.9 (3)9.2 (2)11 (2)12 (0.7)11 (0.9)11 (0.7)2.5 (0.1)15/15
PSAaSmD-CMA-ES-Nishida 8.4 (5)10 (3)13 (1)13 (2)11 (1.0)11 (0.8)2.5 (0.1)15/15

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
PSAaLmC-CMA-ES-Nishida 19 (10)4.9 (1)2.6 (0.4)2.6 (0.5)2.6 (0.6)2.6 (0.6)2.5 (0.5)15/15
PSAaLmD-CMA-ES-Nishida 20 (12)5.6 (0.2)3.0 (0.2)3.0 (0.2)3.0 (0.2)2.9 (0.3)2.9 (0.2)15/15
PSAaSmC-CMA-ES-Nishida 9.3 (4)1.4 (0.4)0.77 (0.2)0.77 (0.3)0.78 (0.2)0.79 (0.2)0.80 (0.2)15/15
PSAaSmD-CMA-ES-Nishida 10 (6)1.6 (1.0)1.1 (0.7)1.1 (0.7)1.1 (0.7)1.1 (0.8)1.1 (0.7)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
PSAaLmC-CMA-ES-Nishida 74 (59)247 (206)111 (163)38 (64)34 (19)27 (25)25 (41)7/15
PSAaLmD-CMA-ES-Nishida 39 (57)233 (266)104 (193)36 (28)32 (38)25 (22)23 (6)7/15
PSAaSmC-CMA-ES-Nishida 46 (85)38 (94)17 (30)5.9 (14)5.3 (5)4.2 (9)3.9 (0.5)14/15
PSAaSmD-CMA-ES-Nishida 49 (67)37 (15)17 (13)5.8 (11)5.3 (6)4.2 (3)3.9 (4)14/15

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
PSAaLmC-CMA-ES-Nishida 6.5 (4)3.6 (0.8)1.9 (0.3)1.8 (0.2)1.7 (0.2)1.5 (0.1)1.6 (0.0)15/15
PSAaLmD-CMA-ES-Nishida 6.5 (4)3.8 (0.8)2.2 (0.4)1.8 (0.2)1.7 (0.1)1.5 (0.1)1.6 (0.1)15/15
PSAaSmC-CMA-ES-Nishida 5.6 (2)3.3 (0.9)1.7 (0.4)1.3 (0.1)1.2 (0.1)1.1 (0.1)1.1 (0.0)15/15
PSAaSmD-CMA-ES-Nishida 4.2 (6)3.3 (0.6)1.8 (0.5)1.3 (0.1)1.2 (0.1)1.1 (0.0)1.1 (0.0)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
PSAaLmC-CMA-ES-Nishida 3.1 (0.7)3.3 (0.4)1.3 (0.2)0.97 (0.1)0.78 (0.0)0.90 (0.1)1.1 (0.0)15/15
PSAaLmD-CMA-ES-Nishida 3.8 (1)3.7 (0.8)1.2 (0.2)0.99 (0.1)1.1 (0.0)1.1 (0.0)1.3 (0.0)15/15
PSAaSmC-CMA-ES-Nishida 3.4 (2)3.1 (0.3)0.97 (0.1)0.71 (0.0)0.55 (0.0)0.66 (0.0)0.78 (0.0)15/15
PSAaSmD-CMA-ES-Nishida 3.4 (3)3.0 (0.8)0.94 (0.1)0.69 (0.0)0.53 (0.0)0.64 (0.0)0.75 (0.0)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
PSAaLmC-CMA-ES-Nishida 145 (94)1.5e5 (5e4)38 (5)0.42 (0.0)0.30 (0.0)0.30 (0.0)0.30 (0.0)15/15
PSAaLmD-CMA-ES-Nishida 173 (94)1.8e5 (1e5)37 (3)0.41 (0.0)0.29 (0.0)0.29 (0.0)0.29 (0.0)15/15
PSAaSmC-CMA-ES-Nishida 91 (67)7.5e4 (5e4)13 (3)0.15 (0.0)0.22 (0.3)0.22 (0.4)0.22 (0.2)14/15
PSAaSmD-CMA-ES-Nishida 105 (104)7.6e4 (4e4)12 (3)0.18 (0.0)0.21 (0.4)0.22 (0.2)0.23 (0.1)14/15

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
PSAaLmC-CMA-ES-Nishida 15 (5)8.8 (4)3.8 (2)3.7 (5)3.6 (4)3.6 (3)3.5 (2)6/15
PSAaLmD-CMA-ES-Nishida 11 (4)10 (3)5.8 (6)5.7 (7)5.6 (5)5.5 (4)5.5 (5)4/15
PSAaSmC-CMA-ES-Nishida 12 (6)2.3 (1)1e60/15
PSAaSmD-CMA-ES-Nishida 10 (3)2.8 (0.6)27 (36)26 (26)26 (55)25 (29)25 (40)1/15

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
PSAaLmC-CMA-ES-Nishida 25 (72)37 (55)32 (7)31 (25)31 (39)28 (26)13 (4)15/15
PSAaLmD-CMA-ES-Nishida 20 (2)79 (129)45 (21)44 (22)43 (18)39 (73)18 (53)14/15
PSAaSmC-CMA-ES-Nishida 13 (30)31 (25)31 (38)31 (29)30 (27)28 (31)12 (15)15/15
PSAaSmD-CMA-ES-Nishida 41 (33)47 (29)47 (79)46 (15)45 (27)41 (68)18 (50)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
PSAaLmC-CMA-ES-Nishida 210 (460)118 (165)271 (394)260 (146)253 (405)208 (251)167 (104)7/15
PSAaLmD-CMA-ES-Nishida 190 (1027)180 (357)245 (285)235 (216)229 (379)188 (108)151 (203)7/15
PSAaSmC-CMA-ES-Nishida 130 (77)137 (138)364 (467)349 (358)340 (481)279 (339)224 (317)5/15
PSAaSmD-CMA-ES-Nishida 122 (88)124 (357)683 (1115)655 (479)638 (377)523 (315)419 (459)3/15

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
PSAaLmC-CMA-ES-Nishida 2.0 (2)700 (744)1e60/15
PSAaLmD-CMA-ES-Nishida 2.3 (2)321 (162)1e60/15
PSAaSmC-CMA-ES-Nishida 3.0 (2)491 (371)1e60/15
PSAaSmD-CMA-ES-Nishida 1.8 (1)382 (209)1e60/15

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
PSAaLmC-CMA-ES-Nishida 1e60/15
PSAaLmD-CMA-ES-Nishida 1e60/15
PSAaSmC-CMA-ES-Nishida 70 (30)1e60/15
PSAaSmD-CMA-ES-Nishida 143 (185)1e60/15

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
PSAaLmC-CMA-ES-Nishida 20 (3)51 (7)118 (24)306 (38)519 (31)951 (40)1375 (47)15/15
PSAaLmD-CMA-ES-Nishida 29 (9)64 (14)142 (29)323 (49)563 (29)1018 (28)1471 (26)15/15
PSAaSmC-CMA-ES-Nishida 19 (10)47 (16)105 (18)218 (38)★2376 (48)★3675 (15)★4981 (34)★415/15
PSAaSmD-CMA-ES-Nishida 25 (7)60 (9)138 (27)276 (37)455 (44)782 (29)1108 (18)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
PSAaLmC-CMA-ES-Nishida 66 (3)76 (8)89 (5)108 (6)132 (7)181 (8)226 (5)15/15
PSAaLmD-CMA-ES-Nishida 74 (7)86 (5)98 (6)118 (4)144 (7)195 (7)243 (5)15/15
PSAaSmC-CMA-ES-Nishida 45 (4)★452 (5)★359 (8)★369 (8)★482 (11)★3114 (22)★3146 (9)★415/15
PSAaSmD-CMA-ES-Nishida 58 (5)66 (7)74 (5)85 (4)101 (9)138 (3)174 (5)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
PSAaLmC-CMA-ES-Nishida 847 (1382)2e60/15
PSAaLmD-CMA-ES-Nishida 635 (549)2e60/15
PSAaSmC-CMA-ES-Nishida 95 (54)2e60/15
PSAaSmD-CMA-ES-Nishida 102 (53)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
PSAaLmC-CMA-ES-Nishida 2e60/15
PSAaLmD-CMA-ES-Nishida 2e60/15
PSAaSmC-CMA-ES-Nishida 2e60/15
PSAaSmD-CMA-ES-Nishida 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
PSAaLmC-CMA-ES-Nishida 32 (6)40 (12)41 (11)41 (6)41 (11)41 (6)41 (8)15/15
PSAaLmD-CMA-ES-Nishida 50 (11)62 (13)64 (18)65 (9)65 (9)65 (10)65 (25)15/15
PSAaSmC-CMA-ES-Nishida 30 (7)39 (10)40 (9)40 (13)40 (15)40 (10)40 (15)15/15
PSAaSmD-CMA-ES-Nishida 49 (11)61 (15)63 (16)63 (21)63 (15)63 (18)63 (19)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
PSAaLmC-CMA-ES-Nishida 11 (1)10 (0.6)10 (0.5)10 (0.5)10 (0.5)11 (0.2)11 (0.4)15/15
PSAaLmD-CMA-ES-Nishida 14 (1)12 (0.6)12 (0.9)12 (0.5)12 (0.7)13 (0.1)13 (0.5)15/15
PSAaSmC-CMA-ES-Nishida 7.0 (0.6)★46.1 (0.7)★45.7 (0.5)★45.7 (0.7)★45.7 (0.2)★46.1 (0.4)★46.2 (0.5)★415/15
PSAaSmD-CMA-ES-Nishida 10 (0.9)8.6 (0.6)8.0 (0.6)8.1 (0.6)8.1 (0.5)8.4 (0.4)8.5 (0.3)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
PSAaLmC-CMA-ES-Nishida 3.0 (0.7)2.3 (0.3)1.6 (0.3)1.7 (0.1)1.7 (0.2)1.7 (0.1)1.7 (0.2)15/15
PSAaLmD-CMA-ES-Nishida 3.7 (0.9)2.6 (0.5)1.7 (0.2)1.8 (0.3)1.9 (0.3)1.9 (0.2)1.9 (0.3)15/15
PSAaSmC-CMA-ES-Nishida 2.6 (0.8)1.7 (0.3)1.2 (0.1)★21.1 (0.2)★21.1 (0.1)★21.1 (0.2)★21.2 (0.2)15/15
PSAaSmD-CMA-ES-Nishida 3.6 (0.4)2.6 (0.6)1.6 (0.3)1.3 (0.1)1.3 (0.1)1.3 (0.1)1.4 (0.1)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
PSAaLmC-CMA-ES-Nishida 2e60/15
PSAaLmD-CMA-ES-Nishida 2e60/15
PSAaSmC-CMA-ES-Nishida 2e60/15
PSAaSmD-CMA-ES-Nishida 2e60/15

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
PSAaLmC-CMA-ES-Nishida 2e60/15
PSAaLmD-CMA-ES-Nishida 2e60/15
PSAaSmC-CMA-ES-Nishida 2e60/15
PSAaSmD-CMA-ES-Nishida 2e60/15

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
PSAaLmC-CMA-ES-Nishida 3.3 (0.2)3.3 (0.2)3.1 (0.2)3.1 (0.1)3.4 (0.2)4.0 (0.2)5.1 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 3.9 (0.4)3.8 (0.1)3.6 (0.2)3.4 (0.1)3.8 (0.2)4.5 (0.1)5.5 (0.2)15/15
PSAaSmC-CMA-ES-Nishida 2.3 (0.2)★42.3 (0.2)★42.1 (0.2)★42.0 (0.2)★42.2 (0.2)★32.7 (0.2)★43.4 (0.2)★415/15
PSAaSmD-CMA-ES-Nishida 3.1 (0.3)3.0 (0.1)2.7 (0.1)2.5 (0.1)2.7 (0.2)3.2 (0.1)4.0 (0.1)15/15

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
PSAaLmC-CMA-ES-Nishida 16 (0.9)8.4 (0.7)3.4 (0.2)3.2 (0.2)3.8 (0.1)4.5 (0.2)5.0 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 19 (0.9)9.4 (0.7)3.8 (0.2)3.6 (0.2)4.1 (0.2)4.9 (0.2)5.3 (0.2)15/15
PSAaSmC-CMA-ES-Nishida 10 (0.9)★45.4 (0.5)★42.2 (0.2)★42.0 (0.2)★42.3 (0.3)★32.8 (0.1)★43.2 (0.2)★415/15
PSAaSmD-CMA-ES-Nishida 13 (0.5)6.8 (0.3)2.8 (0.1)2.4 (0.1)2.7 (0.2)3.3 (0.2)3.8 (0.1)15/15

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
PSAaLmC-CMA-ES-Nishida 38 (2)26 (1)27 (3)47 (124)210 (169)1184 (3034)2e60/15
PSAaLmD-CMA-ES-Nishida 43 (4)29 (3)55 (100)139 (339)456 (1452)2e60/15
PSAaSmC-CMA-ES-Nishida 27 (2)★418 (1)★418 (2)53 (50)753 (607)2e60/15
PSAaSmD-CMA-ES-Nishida 33 (1)21 (1)22 (4)149 (237)656 (829)2e60/15

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
PSAaLmC-CMA-ES-Nishida 24 (3)17 (1)19 (0.7)20 (0.4)4.7 (0.1)5.1 (0.1)5.3 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 28 (1)19 (0.6)21 (0.6)22 (0.3)5.1 (0.1)5.5 (0.1)5.7 (0.1)15/15
PSAaSmC-CMA-ES-Nishida 18 (3)★312 (0.7)★313 (0.4)★414 (0.3)★43.3 (0.1)★43.6 (0.1)★43.7 (0.1)★415/15
PSAaSmD-CMA-ES-Nishida 23 (2)14 (0.3)15 (0.5)16 (0.3)3.8 (0.0)4.0 (0.1)4.2 (0.0)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
PSAaLmC-CMA-ES-Nishida 14 (8)15 (3)22 (4)32 (5)28 (3)30 (2)4.8 (0.2)15/15
PSAaLmD-CMA-ES-Nishida 17 (4)21 (2)26 (3)37 (7)31 (2)33 (1)5.1 (0.3)15/15
PSAaSmC-CMA-ES-Nishida 12 (7)12 (3)17 (3)★324 (3)★320 (1)★221 (0.9)★43.2 (0.1)★415/15
PSAaSmD-CMA-ES-Nishida 17 (5)17 (4)23 (2)31 (6)23 (1)24 (1.0)3.7 (0.2)15/15

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
PSAaLmC-CMA-ES-Nishida 7.5 (4)2e60/15
PSAaLmD-CMA-ES-Nishida 8.6 (6)2e60/15
PSAaSmC-CMA-ES-Nishida 10 (3)3.6 (0.8)1.7 (0.4)1.7 (0.4)1.7 (0.3)1.3 (0.2)1.3 (0.2)15/15
PSAaSmD-CMA-ES-Nishida 11 (4)3.4 (0.5)1.6 (0.2)1.6 (0.2)1.6 (0.2)1.2 (0.1)1.2 (0.2)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
PSAaLmC-CMA-ES-Nishida 2e60/15
PSAaLmD-CMA-ES-Nishida 2e60/15
PSAaSmC-CMA-ES-Nishida 1.0e4 (6513)521 (404)185 (160)102 (50)76 (60)72 (49)65 (84)2/15
PSAaSmD-CMA-ES-Nishida 2.1e4 (4e4)2e60/15

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
PSAaLmC-CMA-ES-Nishida 7.1 (3)4.9 (0.9)4.9 (1)5.2 (0.2)3.1 (0.1)3.2 (0.1)3.3 (0.1)15/15
PSAaLmD-CMA-ES-Nishida 12 (8)6.1 (0.6)5.5 (1)5.6 (0.3)3.3 (0.1)3.4 (0.1)3.5 (0.1)15/15
PSAaSmC-CMA-ES-Nishida 8.2 (4)4.0 (0.7)3.9 (0.8)3.4 (0.2)★32.0 (0.1)★32.0 (0.1)★42.1 (0.0)★415/15
PSAaSmD-CMA-ES-Nishida 12 (6)5.3 (0.8)4.3 (0.9)3.8 (0.2)2.2 (0.1)2.3 (0.1)2.3 (0.0)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
PSAaLmC-CMA-ES-Nishida 4.4 (2)2.7 (0.5)2.6 (0.2)3.0 (0.1)1.8 (0.0)1.5 (0.0)2.0 (0.0)15/15
PSAaLmD-CMA-ES-Nishida 5.4 (1)3.2 (0.3)2.8 (0.2)3.3 (0.2)1.9 (0.0)1.6 (0.0)2.1 (0.0)15/15
PSAaSmC-CMA-ES-Nishida 3.3 (0.7)1.9 (0.3)★31.7 (0.1)2.0 (0.1)★21.2 (0.0)★30.99 (0.0)★41.2 (0.0)★415/15
PSAaSmD-CMA-ES-Nishida 4.8 (0.9)2.6 (0.4)1.9 (0.2)2.2 (0.1)1.3 (0.1)1.1 (0.0)1.3 (0.0)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
PSAaLmC-CMA-ES-Nishida 408 (95)2e60/15
PSAaLmD-CMA-ES-Nishida 518 (205)2e60/15
PSAaSmC-CMA-ES-Nishida 351 (135)3.9e6 (3e6)13 (4)0.99 (1)0.74 (1.0)0.86 (0.5)1.1 (1)4/15
PSAaSmD-CMA-ES-Nishida 455 (107)1.6e6 (5e5)5.2 (6)0.51 (0.3)0.46 (0.5)0.48 (0.3)0.55 (0.7)7/15

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
PSAaLmC-CMA-ES-Nishida 15 (5)2e60/15
PSAaLmD-CMA-ES-Nishida 22 (11)2e60/15
PSAaSmC-CMA-ES-Nishida 14 (8)8.9 (3)2e60/15
PSAaSmD-CMA-ES-Nishida 20 (13)9.2 (2)2e60/15

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
PSAaLmC-CMA-ES-Nishida 3.7 (4)188 (227)100 (115)99 (89)97 (56)92 (137)82 (178)11/15
PSAaLmD-CMA-ES-Nishida 129 (59)104 (90)53 (96)52 (27)51 (86)48 (74)43 (48)14/15
PSAaSmC-CMA-ES-Nishida 49 (103)120 (188)61 (85)60 (98)59 (50)55 (42)49 (102)14/15
PSAaSmD-CMA-ES-Nishida 61 (3)126 (248)73 (81)72 (77)71 (93)67 (95)60 (17)13/15

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
PSAaLmC-CMA-ES-Nishida 183 (301)171 (300)2e60/15
PSAaLmD-CMA-ES-Nishida 24 (2)285 (338)2e60/15
PSAaSmC-CMA-ES-Nishida 131 (253)145 (118)2e60/15
PSAaSmD-CMA-ES-Nishida 196 (207)177 (184)2e60/15

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
PSAaLmC-CMA-ES-Nishida 4.3 (5)2e60/15
PSAaLmD-CMA-ES-Nishida 3.1 (3)2e60/15
PSAaSmC-CMA-ES-Nishida 2.2 (1)2e60/15
PSAaSmD-CMA-ES-Nishida 3.5 (2)2e60/15

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
PSAaLmC-CMA-ES-Nishida 2e60/15
PSAaLmD-CMA-ES-Nishida 2e60/15
PSAaSmC-CMA-ES-Nishida 2e60/15
PSAaSmD-CMA-ES-Nishida 2e60/15

Previous dimension | Dimension = 40 | First dimension

Average runtime (aRT in number of function evaluations) divided by the respective best aRT measured during BBOB-2009 in different dimensions. The aRT 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 aRT  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.
Data produced with COCO v2.0.760