Lennard-Jones 38

SystemLennard-Jones

Atoms38

Runs200

Cap10000 force calls

The main metric is Force calls. Scoring rules.

Charts

Success rate on Lennard-Jones 38, in rank order. The rate is the share of runs that finished. 6 ranked rows did not record a success rate and are not drawn. PDF.

Dolan-Moré profile for Minimum mode on Lennard-Jones 38. The curve is the fraction of starts whose cost is at most tau times the best finite cost in this family. Tau is 1, 2, 4, 8, and 16. An unsolved start stays in the denominator and does not cross a finite tau. Dolan, E. D. and Moré, J. J., Math. Program. 91:201-213, 2002. Colored lines are the six largest areas. The other curves are gray. PDF.

Dolan-Moré profile for Single-ended saddle on Lennard-Jones 38. The curve is the fraction of starts whose cost is at most tau times the best finite cost in this family. Tau is 1, 2, 4, 8, and 16. An unsolved start stays in the denominator and does not cross a finite tau. Dolan, E. D. and Moré, J. J., Math. Program. 91:201-213, 2002. PDF.

Force calls on each recorded start for Lennard-Jones 38. The box is the quartiles of those counts. A blue point is a success and a vermillion cross is a recorded failure (1367). The horizontal position is the recorded count. The vertical offset only keeps marks from covering one another. PDF.

Sella on Lennard-Jones 38. Each point is one recorded version of one method. Versions run left to right in numeric order. PAR-2 is omitted where that row has none. No line is drawn across a missing value. PDF.

eOn on Lennard-Jones 38. Each point is one recorded version of one method. Versions run left to right in numeric order. PAR-2 is omitted where that row has none. No line is drawn across a missing value. PDF.

Performance profile. Higher means more starts solved within that cost ratio. Colored lines are the six largest areas. Thin lines are the other 12.

• Sella (2.6.0) · Sella
• Eon svn (r2549) · Lanczos improved L-BFGS
• eOn (3.5.0) · Lanczos improved L-BFGS
• Eon svn (r2549) · Lanczos L-BFGS
• eOn (3.5.0) · Lanczos L-BFGS
• Eon svn (r2549) · Dimer L-BFGS

Cost distribution of 24 ranked rows. Logarithmic bins, from 68.74 to 20000.

Performance profile SVG Cost and success SVG

Performance profile. Select the plot for the full SVG.

Cost and success. Select the plot for the full SVG.

A shorter bar is a lower cost on a log scale shared by the codes of this problem.

Leaderboard

A shorter bar is a lower cost on the log scale for that problem. Select a column heading to sort.

Rank	Code	Best	Median	Success	PAR-2
1	Sella	68.74	69.145	100.0%	68.74
2	OPTIM	145	145	100.0%	145
3	pele	192	192	100.0%	192
4	Eon svn	237	306.89	100.0%	237
5	eOn	280.33	2102.72	100.0%	280.33
6	OptKing	7030.36	7363.89	66.5%	7030.36
7	rgsaddle	7803.19	19418.8	63.0%	7803.19
8	pARTn	20000	20000	0.0%	20000
9	TSASE	20000	20000	0.0%	20000

The tables below list every ranked row, by method family and overall.

eOn rows are not yet on the harness counter.

A run short of the full set, or a run that is not the stock method, stays off the ranked table.

Files with no per-start harness record stay off the ranked table.

Minimum mode

Minimum mode. One row is one code, one version, and one method. A lower cost is better. PAR-2 counts a finished run as the calls it used and a failed run as twice the cap. An archived row shows the average it published, and its PAR-2 applies that rule to the failures the entry records. Hessians is the mean analytic Hessian count. FD calls is that count times one force call per coordinate.

Rank	Row	Cost	Unit	Hessians	FD calls	Runs
1	eOn (r2156) · eon-lanczos-improved	237	force calls	0	0	200
2	Eon svn (r2549) · Lanczos improved L-BFGS	270.85	force calls	0	0	200
3	eOn (3.5.0) · Lanczos improved L-BFGS	280.33	force calls	0	0	200
4	Eon svn (r2549) · Lanczos L-BFGS	292.78	force calls	0	0	200
5	eOn (3.5.0) · Lanczos L-BFGS	311.19	force calls	0	0	200
6	eOn (r2156) · eon-lanczos	321	force calls	0	0	200
7	eOn (r2156) · eon-dimer	528	force calls	0	0	200
8	Eon svn (r2549) · Dimer L-BFGS	619.89	force calls	0	0	200
9	eOn (3.5.0) · Dimer L-BFGS	2102.72	force calls	0	0	200
10	eOn (3.6.0) · Lanczos	3144.55	force calls	0	0	200
11	rgsaddle (0.2.2) · Dimer rotation-skip L-BFGS	7803.19	force calls	0	0	200
12	rgsaddle (0.2.2) · Lanczos L-BFGS	19418.8	force calls	0	0	200
13	rgsaddle (0.2.2) · Dimer FIRE	19455	force calls	0	0	200
14	TSASE (1.0) · SSDimer	20000	force calls	0	0	200
15	rgsaddle (0.2.2) · Dimer L-BFGS	20000	force calls	0	0	200

Single-ended saddle

Single-ended saddle. One row is one code, one version, and one method. A lower cost is better. PAR-2 counts a finished run as the calls it used and a failed run as twice the cap. An archived row shows the average it published, and its PAR-2 applies that rule to the failures the entry records. Hessians is the mean analytic Hessian count. FD calls is that count times one force call per coordinate.

Rank	Row	Cost	Unit	Hessians	FD calls	Runs
1	Sella (2.6.0) · Sella	68.74	force calls	0	0	200
2	Sella (0.1.1) · sella	69.55	force calls	0	0	200
3	eOn (3.6.0) · LBFGS	2159.53	force calls	0	0	200
4	OptKing (0.5.1.dev2+g767e2c0c1) · P_RFO	7030.36	force calls	1	114	200
5	OptKing (0.5.1.dev2+g767e2c0c1) · RS_I_RFO	7697.42	force calls	1	114	200
6	rgsaddle (0.2.2) · P-RFO	15147	force calls	0	0	200
7	pARTn (1.1.0) · ARTn	20000	force calls	0	0	200

Connect / double-ended

Connect / double-ended. One row is one code, one version, and one method. A lower cost is better. PAR-2 counts a finished run as the calls it used and a failed run as twice the cap. An archived row shows the average it published, and its PAR-2 applies that rule to the failures the entry records. Hessians is the mean analytic Hessian count. FD calls is that count times one force call per coordinate.

Rank	Row	Cost	Unit	Hessians	FD calls	Runs
1	OPTIM · hybrid eigenvector following	145	force calls	0	0	200
2	pele · hybrid eigenvector following	192	force calls	0	0	200

Overall

One row is one code, one version, and one method. A lower cost is better. PAR-2 counts a finished run as the calls it used and a failed run as twice the cap. An archived row shows the average it published, and its PAR-2 applies that rule to the failures the entry records. Hessians is the mean analytic Hessian count. FD calls is that count times one force call per coordinate.

Row	Family	Family rank	Unit	PAR-2	Published	Median calls	Mean calls	Hessians	FD calls	Failures	Runs
Sella (2.6.0) · Sella	Single-ended saddle	1	force calls	68.74		59.5	68.74	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	200
Sella (0.1.1) · sella	Single-ended saddle	2	force calls	69.55	69.55	64	69.55	0	0	0 failed	200
OPTIM · hybrid eigenvector following	Connect / double-ended	1	force calls	145	145	119	145	0	0	0 failed	200
pele · hybrid eigenvector following	Connect / double-ended	2	force calls	192	192	150	192	0	0	0 failed	200
eOn (r2156) · eon-lanczos-improved	Minimum mode	1	force calls	237	237	181	237	0	0	0 failed	200
Eon svn (r2549) · Lanczos improved L-BFGS	Minimum mode	2	force calls	270.85		180	270.85	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	200
eOn (3.5.0) · Lanczos improved L-BFGS	Minimum mode	3	force calls	280.33		214	280.33	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	200
Eon svn (r2549) · Lanczos L-BFGS	Minimum mode	4	force calls	292.78		219	292.78	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	200
eOn (3.5.0) · Lanczos L-BFGS	Minimum mode	5	force calls	311.19		255.5	311.19	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	200
eOn (r2156) · eon-lanczos	Minimum mode	6	force calls	321	321	220.5	321	0	0	0 failed	200
eOn (r2156) · eon-dimer	Minimum mode	7	force calls	528	528	388.5	528	0	0	0 failed	200
Eon svn (r2549) · Dimer L-BFGS	Minimum mode	8	force calls	619.89		360.5	536.585	0	0	crash 0, divergence 1, cap 0, wrong_stationary 0	200
eOn (3.5.0) · Dimer L-BFGS	Minimum mode	9	force calls	2102.72		411	810.06	0	0	crash 0, divergence 15, cap 0, wrong_stationary 0	200
eOn (3.6.0) · LBFGS	Single-ended saddle	3	force calls	2159.53		411	790.055	0	0	crash 0, divergence 16, cap 0, wrong_stationary 0	200
eOn (3.6.0) · Lanczos	Minimum mode	10	force calls	3144.55		454.5	874.33	0	0	crash 0, divergence 27, cap 0, wrong_stationary 0	200
OptKing (0.5.1.dev2+g767e2c0c1) · P_RFO	Single-ended saddle	4	force calls	7030.36		555	1494.34	1	114	crash 0, divergence 0, cap 3, wrong_stationary 64	200
OptKing (0.5.1.dev2+g767e2c0c1) · RS_I_RFO	Single-ended saddle	5	force calls	7697.42		332.5	353.535	1	114	crash 0, divergence 0, cap 0, wrong_stationary 75	200
rgsaddle (0.2.2) · Dimer rotation-skip L-BFGS	Minimum mode	11	force calls	7803.19		856.5	2926.82	0	0	crash 0, divergence 0, cap 27, wrong_stationary 47	200
rgsaddle (0.2.2) · P-RFO	Single-ended saddle	6	force calls	15147		460.5	723.265	0	0	crash 0, divergence 0, cap 3, wrong_stationary 147	200
rgsaddle (0.2.2) · Lanczos L-BFGS	Minimum mode	12	force calls	19418.8		10011	9779.39	0	0	crash 0, divergence 0, cap 193, wrong_stationary 0	200
rgsaddle (0.2.2) · Dimer FIRE	Minimum mode	13	force calls	19455		3666	4792.34	0	0	crash 0, divergence 164, cap 28, wrong_stationary 0	200
TSASE (1.0) · SSDimer	Minimum mode	14	force calls	20000		10000	10000	0	0	crash 0, divergence 0, cap 200, wrong_stationary 0	200
pARTn (1.1.0) · ARTn	Single-ended saddle	7	force calls	20000		45	49.045	0	0	crash 200, divergence 0, cap 0, wrong_stationary 0	200
rgsaddle (0.2.2) · Dimer L-BFGS	Minimum mode	15	force calls	20000		10011	9991.44	0	0	crash 0, divergence 0, cap 199, wrong_stationary 1	200

Off the ranked table

• eOn (3.6.0) · LBFGS n=200, not yet on the harness counter.
• eOn (3.6.0) · LBFGS n=200, not yet on the harness counter.

Not scored

• Sella: no per-start record

Success on this problem: harness force calls under the cap, Euclidean force norm at the stop, and Hessian index 1.