An Exact Algorithm for Bilevel 0-1 Knapsack Problems

Table 8

Comparison between MACH2′ and MACH2.

𝑛^1	𝑛^2	𝛼	UC						C
			qualℎ	𝑡ℎ	fix	int𝑧	𝑡MACH2′	𝑡MACH2	qualℎ	𝑡ℎ	fix	int𝑧	𝑡MACH2′	𝑡MACH2
			%		%	%			%		%	%
500	500	0.5	99.0	3.0	9.8	8.51	21.0	12.6	99.2	0.8	0	45.5	21.4	15.8
500	1000	0.5	99.0	2.6	0.0	9.98	50.2	35.8	99.0	1.4	0	48.9	51.0	44.8
1000	500	0.5	99.0	3.8	8.0	6.85	43.0	25.6	99.0	1.0	0	34.47	44.2	31.8
1000	1000	0.5	99.0	2.4	0.0	9.39	82.8	49.6	99.0	1.4	0	44.5	85.2	65.2
500	500	0.75	99.2	2.2	12.6	6.22	30.8	15.8	99.0	1.0	0	25.5	31.2	21.4
500	1000	0.75	99.0	1.6	0.0	5.78	74.6	49.8	99.4	1.2	0	24.3	75.0	56.6
1000	500	0.75	99.0	2.4	19.2	4.36	63.0	26.6	99.0	1.2	0	18.7	64.0	41.2
1000	1000	0.75	99.0	2.8	0.0	5.63	122.0	69.8	99.0	1.0	0	25.7	124.0	81.4