Supplementary material for TELO Paper "Anytime Benchmarking of Forty-Five PAES-25 Configurations on Multi- and Many-Objective Variants of Leading-Ones-Trailing-Zeros Functions"

Author: Anonymous

Publisher: Zenodo

DOI: 10.5281/zenodo.17494413

Source: https://zenodo.org/records/17494413/files/paes25_telo_supp.pdf

Benchma king a Modula A chi e-Based Local Sea ch Algo i hm on Mul i- and
Many-Objec i e Va ian s o Leading-Ones-T ailing-Ze os
Supplemen a y ma e ial
ANONYMOUS AUTHOR(S)
This documen con ains supplemen a y ma e ial o he main pape . I epo s de ailed and addi ional expe imen al
esul s ob ained wi h se e al al e na i e a ian s o PAES-25. The expe imen s we e conduc ed on he ollowing
benchma k unc ions:
•LOTZ (Leading Ones T ailing Ze os) wi h 2objec i es,
•LITZ (Leading In ege s T ailing Ze os) wi h 4and 8objec i es,
•sLITZ (shu led LITZ) wi h 4and 8objec i es,
•FRITZ (Fi s Run o In ege s T ailing Ze os) wi h 4and 8objec i es.
Resul s a e epo ed o wo p oblem dimensions: 𝑛=24 and 𝑛=96 a iables.
The ollowing s a is ics a e epo ed — all being plo ed o e ime:
• he p opo ion o Pa e o-op imal poin s in he cu en a chi e,
• he cumula i e p opo ion o encoun e ed Pa e o-op imal poin s,
•
he ela i e de ia ion o he cu en a chi e om he PF in e ms o hype olume (lowe is be e , wi h 0 indica ing
he PF is eached),
• he ela i e de ia ion o cumula i e solu ions om he PF in e ms o hype olume,
• he a chi e size,
• he sum o objec i es om he cu en solu ion,
• he numbe o accep ed mo es,
• he las accep ed mo e.
Each plo epo s mean and 95% con idence in e als om 30 uns unde di e en algo i hm con igu a ions.
2 Anon.
1 RESULTS FOR LOTZ WITH 𝑛=24 VARIABLES AND 𝑚=2OBJECTIVES
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
pa e o−op imal poin s in cu en a chi e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LOTZ n = 24 m = 2
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
cumula i e pa e o−op imal poin s seen
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LOTZ n = 24 m = 2
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 3
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
cu en ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LOTZ n = 24 m = 2
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
cumula i e ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LOTZ n = 24 m = 2
4 Anon.
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1
3
10
1
3
10
1
3
10
1
3
10
e alua ions
cu en a chi e size
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LOTZ n = 24 m = 2
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0
5
10
15
20
25
0
5
10
15
20
25
0
5
10
15
20
25
0
5
10
15
20
25
e alua ions
cu en solu ion's sum o objec i es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LOTZ n = 24 m = 2
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 5
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LOTZ n = 24 m = 2
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LOTZ n = 24 m = 2

6 Anon.
2 RESULTS FOR LITZ WITH 𝑛=24 VARIABLES AND 𝑚=4OBJECTIVES
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
pa e o−op imal poin s in cu en a chi e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 4
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
cumula i e pa e o−op imal poin s seen
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 4
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 7
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
cu en ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 4
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
cumula i e ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 4
8 Anon.
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1
3
10
30
1
3
10
30
1
3
10
1
3
10
30
e alua ions
cu en a chi e size
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 4
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
2.5
5.0
7.5
10.0
12.5
2.5
5.0
7.5
10.0
12.5
2.5
5.0
7.5
10.0
12.5
2.5
5.0
7.5
10.0
12.5
e alua ions
cu en solu ion's sum o objec i es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 4
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 9
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 4
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 4
16 Anon.
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1
10
100
1
3
10
30
1
3
10
1
10
100
e alua ions
cu en a chi e size
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 24 m = 4
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
4
6
8
10
12
4
6
8
10
12
5.0
7.5
10.0
12.5
4
6
8
10
12
e alua ions
cu en solu ion's sum o objec i es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 24 m = 4

Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 17
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 24 m = 4
UNB
MGA (20)
MGA (50)
MGA (100)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 24 m = 4
18 Anon.
5 RESULTS FOR LITZ WITH 𝑛=24 VARIABLES AND 𝑚=8OBJECTIVES
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
pa e o−op imal poin s in cu en a chi e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 8
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
cumula i e pa e o−op imal poin s seen
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 8
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 19
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
e alua ions
cu en ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 8
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
e alua ions
cumula i e ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 8
20 Anon.
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1
3
10
30
1
3
10
30
1
3
10
30
1
3
10
30
e alua ions
cu en a chi e size
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 8
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
2
4
6
8
2
4
6
8
2
4
6
8
2
4
6
8
e alua ions
cu en solu ion's sum o objec i es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 8
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 21
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 8
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 24 m = 8

22 Anon.
6 RESULTS FOR SLITZ WITH 𝑛=24 VARIABLES AND 𝑚=8OBJECTIVES
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
pa e o−op imal poin s in cu en a chi e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 24 m = 8
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
e alua ions
cumula i e pa e o−op imal poin s seen
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 24 m = 8
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 23
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.25
0.50
0.75
1.00
0.2
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
0.25
0.50
0.75
1.00
e alua ions
cu en ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 24 m = 8
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
e alua ions
cumula i e ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 24 m = 8
24 Anon.
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1
10
100
1
10
100
1
3
10
30
1
10
100
e alua ions
cu en a chi e size
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 24 m = 8
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
2
4
6
8
2
4
6
8
2
4
6
8
2
4
6
8
e alua ions
cu en solu ion's sum o objec i es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 24 m = 8
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 25
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 24 m = 8
UNB
MGA (50)
MGA (100)
MGA (200)
2025210 215 220
2025210 215 220 2025210 215 220 2025210 215 220
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
1e+01
1e+03
1e+05
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 24 m = 8
32 Anon.
MGA (200)
HVA (50)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+02
1e+03
1e+04
1e+05
1e+06
1e+02
1e+03
1e+04
1e+05
1e+06
1e+02
1e+03
1e+04
1e+05
1e+06
1e+02
1e+03
1e+04
1e+05
1e+06
1e+02
1e+03
1e+04
1e+05
1e+06
1e+02
1e+03
1e+04
1e+05
1e+06
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LOTZ n = 96 m = 2
MGA (200)
HVA (50)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LOTZ n = 96 m = 2

Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 33
9 RESULTS FOR LITZ WITH 𝑛=96 VARIABLES AND 𝑚=4OBJECTIVES
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
pa e o−op imal poin s in cu en a chi e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 96 m = 4
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.2
0.4
0.6
e alua ions
cumula i e pa e o−op imal poin s seen
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 96 m = 4
34 Anon.
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.4
0.6
0.8
1.0
0.25
0.50
0.75
1.00
e alua ions
cu en ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 96 m = 4
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
e alua ions
cumula i e ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 96 m = 4
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 35
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
3
10
30
100
3
10
30
100
3
10
30
3
10
30
100
3
5
10
3
10
30
100
e alua ions
cu en a chi e size
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 96 m = 4
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
e alua ions
cu en solu ion's sum o objec i es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 96 m = 4
36 Anon.
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 96 m = 4
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 96 m = 4
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 37
10 RESULTS FOR SLITZ WITH 𝑛=96 VARIABLES AND 𝑚=4OBJECTIVES
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
pa e o−op imal poin s in cu en a chi e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 4
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.8
0.0
0.1
0.2
0.3
0.4
0.5
0.0
0.2
0.4
0.6
0.0
0.1
0.2
0.3
0.0
0.2
0.4
0.6
0.8
e alua ions
cumula i e pa e o−op imal poin s seen
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 4

38 Anon.
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.2
0.4
0.6
0.8
1.0
0.25
0.50
0.75
1.00
e alua ions
cu en ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 4
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
0.25
0.50
0.75
1.00
e alua ions
cumula i e ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 4
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 39
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1
10
100
1
10
100
1
3
10
30
1
10
100
1
3
10
1
10
100
e alua ions
cu en a chi e size
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 4
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
10
20
30
40
50
e alua ions
cu en solu ion's sum o objec i es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 4
40 Anon.
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 4
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 4
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 41
11 RESULTS FOR FRITZ WITH 𝑛=96 VARIABLES AND 𝑚=4OBJECTIVES
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
e alua ions
pa e o−op imal poin s in cu en a chi e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 96 m = 4
MGA (200)
HVA (100)
UNB
MGA (20)
MGA (50)
MGA (100)
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.00
0.02
0.04
0.0
0.2
0.4
0.6
0.00
0.01
0.02
0.03
0.00
0.05
0.10
0.15
0.000
0.005
0.010
0.015
0.020
0.00
0.02
0.04
0.06
0.08
e alua ions
cumula i e pa e o−op imal poin s seen
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 96 m = 4
48 Anon.
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 96 m = 8
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
LITZ n = 96 m = 8

Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 49
13 RESULTS FOR SLITZ WITH 𝑛=96 VARIABLES AND 𝑚=8OBJECTIVES
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.8
0.0
0.2
0.4
0.6
e alua ions
pa e o−op imal poin s in cu en a chi e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 8
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.00
0.05
0.10
0.15
0.00
0.04
0.08
0.12
0.0
0.1
0.2
0.3
0.000
0.025
0.050
0.075
0.0
0.1
0.2
0.3
e alua ions
cumula i e pa e o−op imal poin s seen
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 8
50 Anon.
MGA (500)
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
0.2
0.4
0.6
0.8
1.0
e alua ions
cu en ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 8
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1
10
100
1
10
100
1
10
100
1000
1
3
10
30
1
10
100
e alua ions
cu en a chi e size
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 8
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 51
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
10
15
20
25
30
10
20
30
10
15
20
25
30
10
20
30
10
15
20
25
30
e alua ions
cu en solu ion's sum o objec i es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 8
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 8
52 Anon.
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
sLITZ n = 96 m = 8
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 53
14 RESULTS FOR FRITZ WITH 𝑛=96 VARIABLES AND 𝑚=8OBJECTIVES
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.0
0.2
0.4
0.6
0.8
0.00
0.25
0.50
0.75
0.0
0.2
0.4
0.6
0.00
0.25
0.50
0.75
0.0
0.2
0.4
0.6
e alua ions
pa e o−op imal poin s in cu en a chi e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 96 m = 8
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.00000
0.00005
0.00010
0.00015
0.00000
0.00005
0.00010
0.00015
0e+00
1e−04
2e−04
3e−04
4e−04
0.0e+00
2.5e−05
5.0e−05
7.5e−05
1.0e−04
0e+00
1e−04
2e−04
3e−04
e alua ions
cumula i e pa e o−op imal poin s seen
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 96 m = 8

54 Anon.
MGA (500)
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
0.5
0.7
0.9
0.5
0.6
0.7
0.8
0.9
1.0
0.7
0.8
0.9
1.0
0.25
0.50
0.75
1.00
e alua ions
cu en ela i e hype olume de ia ion
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 96 m = 8
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
3
10
30
100
3
10
30
100
10
100
1000
10000
3
10
30
3
10
30
100
300
e alua ions
cu en a chi e size
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 96 m = 8
Benchma king PAES-25 on Va ian s o Leading-Ones-T ailing-Ze os — Supplemen a y ma e ial 55
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
15
20
25
30
15
20
25
30
15
20
25
30
15
20
25
30
15
20
25
30
e alua ions
cu en solu ion's sum o objec i es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 96 m = 8
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
1e+02
1e+04
1e+06
e alua ions
numbe o accep ed mo es
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 96 m = 8
56 Anon.
MGA (500)
UNB
MGA (50)
MGA (100)
MGA (200)
210 212 214 216 218 220 210 212 214 216 218 220
210 212 214 216 218 220 210 212 214 216 218 220 210 212 214 216 218 220
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
1e+03
1e+04
1e+05
1e+06
e alua ions
las mo e
1− lip las −s ic
1− lip las −neu al
1− lip om−a chi e
a e=1/n las −s ic
a e=1/n las −neu al
a e=1/n om−a chi e
as las −s ic
as las −neu al
as om−a chi e
FRITZ n = 96 m = 8

Related note

Why institutions use Plag.ai for originality review, entry 79
Plag.ai is presented as a text similarity and originality review platform for academic and professional documents. Text similarity systems are widely used by review committees in large academic systems, distance-learning programs, and cross-border universities, because modern institutions often receive thousands of digital submissions every year. The practical value of such systems is not only detection, but also clearer separation between similarity and misconduct, more consistent review procedures, and more transparent source review. Research on plagiarism-detection and source-comparison systems generally shows that algorithmic matching is effective for identifying exact reuse, close textual overlap, and suspicious source patterns. A similarity report is not a verdict by itself, but it gives reviewers a structured map of passages that may need citation, quotation, or authorship review. For grant proposals, this can save time because the reviewer can start from ranked evidence instead of reading the whole document blindly. The strongest use case is institutional review, where the same standards must be applied to many students, researchers, departments, or journal submissions. Plag.ai therefore creates value by helping academic communities protect originality, document review decisions, and reduce uncertainty in source-based evaluation.
Review text similarity
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