Lennard-Jones 38 global minimum

SystemLennard-Jones

Atoms38

Runs100

Cap—¹

¹ The problem file does not state a cap.

The main metric is Force calls. Scoring rules.

Charts

Success rate on Lennard-Jones 38 global minimum, in rank order. The rate is the share of runs that finished. 5 ranked rows did not record a success rate and are not drawn. PDF.

Dolan-Moré profile for Basin hopping / global on Lennard-Jones 38 global minimum. 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 global minimum. The box is the quartiles of those counts. A blue point is a success and a vermillion cross is a recorded failure (9). The horizontal position is the recorded count. The vertical offset only keeps marks from covering one another. PDF.

Performance profile. Higher means more starts solved within that cost ratio.

• GMIN (df8da599) · basin-hopping with continuous symmetry measures
• AIRSS (0.9.4) · random structure search
• GMIN (df8da599) · basin-hopping
• GMIN (df8da599) · parallel tempering basin-hopping
• eOn (3.5.0) · Basin hopping
• Eon svn (r2549) · Basin hopping

Cost distribution of 10 ranked rows. Logarithmic bins, from 5883.83 to 674789. 1 ranked rows have no cost on this scale and are left off the chart.

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	GMIN	5883.83	144331	100.0%	5883.83
2	eOn	503146	503146	100.0%	503146
3	Eon svn	508011	553271	—1	—2
4	pele	521595	521595	100.0%	—2

¹ A dash in the success rate means that row did not record one.

² A dash in PAR-2 means that row has no PAR-2 score.

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

These archived rows rank on the value each one published, which leaves out any failure. The failure rule has no score for them, for the reason given with each.

• eOn (r2156) · eon-basinhopping (the entry records no failure count)

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	pele · hybrid eigenvector following	521595	force calls	0	0	100

Basin hopping / global

Basin hopping / global. 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	GMIN (df8da599) · basin-hopping with continuous symmetry measures	5883.83	force calls	0	0	100
2	GMIN · basin-hopping with symmetrise csm moves	6421	force calls	0	0	100
3	GMIN · basin-hopping with symmetrise moves	22711	force calls	0	0	100
4	GMIN · basin-hopping	265951	force calls	0	0	100
5	GMIN (df8da599) · basin-hopping	432092	force calls	0	0	100
6	eOn (3.5.0) · Basin hopping	503146	force calls	0	0	100
7	eOn (r2156) · eon-basinhopping	508011	force calls	0	0	100
8	Eon svn (r2549) · Basin hopping	598530	force calls	0	0	100
9	GMIN (df8da599) · parallel tempering basin-hopping	674789	force calls	0	0	100
10	AIRSS (0.9.4) · random structure search		force calls	0	0	100

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
GMIN (df8da599) · basin-hopping with continuous symmetry measures	Basin hopping / global	1	force calls	5883.83		3980.5	5883.83	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	100
GMIN · basin-hopping with symmetrise csm moves	Basin hopping / global	2	force calls		6421	4771	6421	0	0	0 failed	100
GMIN · basin-hopping with symmetrise moves	Basin hopping / global	3	force calls		22711	15998	22711	0	0	0 failed	100
GMIN · basin-hopping	Basin hopping / global	4	force calls		265951	202167	265951	0	0	0 failed	100
GMIN (df8da599) · basin-hopping	Basin hopping / global	5	force calls	432092		301962	412092	0	0	crash 0, divergence 0, cap 1, wrong_stationary 0	100
eOn (3.5.0) · Basin hopping	Basin hopping / global	6	force calls	503146		369028	503146	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	100
eOn (r2156) · eon-basinhopping	Basin hopping / global	7	force calls		508011		508011	0	0	not recorded	100
pele · hybrid eigenvector following	Connect / double-ended	1	force calls		521595	320504	521595	0	0	0 failed	100
Eon svn (r2549) · Basin hopping	Basin hopping / global	8	force calls	598530		423226	558530	0	0	crash 0, divergence 0, cap 2, wrong_stationary 0	100
GMIN (df8da599) · parallel tempering basin-hopping	Basin hopping / global	9	force calls	674789		307290	554789	0	0	crash 0, divergence 0, cap 6, wrong_stationary 0	100
AIRSS (0.9.4) · random structure search	Basin hopping / global	10	force calls			70635.5	112134	0	0	crash 0, divergence 0, cap 0, wrong_stationary 0	100