SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Table 2: Gap closed and running times after the root node for the multi-dimensional knapsack instances; each line represents the average over 10 instances.
m	n	α	KL	LP	FW
gap closed	time	sepa time	#calls	#cuts	gap closed	time	sepa time	#calls	#cuts
100	5	25	17.96	18.88	1.60	1.60	26.1	113.0	12.54	0.77	0.76	21.3	78.4
100	5	50	21.65	22.36	2.13	2.12	29.3	124.5	15.55	0.88	0.87	20.8	77.7
100	5	75	22.88	23.19	2.18	2.17	28.8	122.9	16.91	0.96	0.95	21.3	85.8
100	10	25	5.55	5.75	2.69	2.68	14.5	105.7	2.73	0.80	0.79	8.0	43.0
100	10	50	7.33	7.63	3.62	3.62	16.5	120.1	4.30	1.50	1.49	11.4	59.2
100	10	75	7.23	7.44	2.71	2.71	14.0	100.6	4.37	1.29	1.29	10.7	51.5
100	30	25	0.16	0.14	2.89	2.87	2.4	12.0	0.00	1.05	1.05	0.2	0.1
100	30	50	0.49	0.47	4.45	4.44	4.9	38.2	0.02	0.84	0.83	0.6	0.7
100	30	75	0.52	0.53	4.30	4.29	4.8	35.9	0.07	1.02	1.01	0.8	0.7
250	5	25	14.56	15.44	4.03	4.00	36.3	161.0	8.03	1.08	1.06	20.4	77.6
250	5	50	15.68	14.83	6.57	6.54	38.7	172.1	7.87	1.74	1.73	20.3	78.0
250	5	75	17.48	16.98	7.42	7.39	36.6	165.3	10.45	2.58	2.56	22.5	87.5
250	10	25	4.53	3.98	6.17	6.15	17.5	128.7	1.83	1.51	1.50	10.4	49.7
250	10	50	4.48	4.11	6.52	6.48	17.4	130.8	1.60	1.49	1.48	8.4	46.2
250	10	75	5.03	4.73	8.54	8.51	18.5	141.3	2.10	2.12	2.11	9.5	51.4
500	5	25	13.80	11.75	10.37	10.31	42.0	182.9	5.96	2.84	2.81	20.9	78.4
500	5	50	11.91	11.17	17.41	17.35	45.2	199.2	5.02	5.21	5.19	21.5	84.0
500	5	75	13.70	11.75	22.53	22.48	41.5	190.0	5.62	7.63	7.60	22.4	85.4
Table 3: Detailed statistics for a branch-and-cut run with three different algorithm variants for the multi-dimensional knapsack instances; each line represents shifted geometric means over 10 instances.
n	m	α	default	lc0-nc-lifting	lc1-nc-uplift
#solved	time	sep time	#solved	time	sep time	#solved	time	sep time
100	5	25	10	11.76	5.11	10	5.89	1.45	10	24.41	18.95
100	5	50	10	7.61	3.32	10	5.27	1.57	10	19.62	16.00
100	5	75	10	4.88	2.39	10	3.67	1.70	10	9.62	7.74
100	10	25	10	47.49	10.83	10	32.67	2.27	10	347.27	308.99
100	10	50	10	44.48	11.49	10	30.04	2.77	10	360.69	325.67
100	10	75	10	16.44	5.20	10	11.33	2.80	10	112.23	102.36
100	30	25	10	558.98	18.90	10	458.22	2.07	3	3288.89	3095.03
100	30	50	10	497.33	20.35	10	413.70	1.63	1	3057.23	2870.52
100	30	75	10	118.77	12.38	10	92.87	1.91	7	1986.30	1892.20
250	5	25	10	83.72	12.55	10	63.59	2.50	10	267.26	195.77
250	5	50	10	125.84	10.07	10	104.14	3.54	10	636.25	493.87
250	5	75	10	53.20	7.89	10	42.53	4.08	10	231.73	188.66
250	10	25	0	3600.01	906.72	2	3419.56	4.13	0	3600.01	2992.23
250	10	50	1	3528.15	1033.57	1	3483.90	4.03	0	3600.00	3326.01
250	10	75	6	2062.86	346.76	7	1645.50	5.10	1	3482.48	3138.87
500	5	25	8	1883.73	218.06	10	1539.94	5.07	3	3056.45	1962.73
500	5	50	7	1422.77	206.38	10	1083.33	7.73	5	2963.75	2068.72
500	5	75	9	676.14	70.40	10	548.03	9.43	7	2039.17	1368.61
there is no clear advantage of the Frank-Wolfe approach, but for larger sizes, it solves more instances and is faster.