Solving the Bilevel Facility Location Problem under Preferences by a Stackelberg-Evolutionary Algorithm

Table 5

Results for the large-size instances.

Instance size	Instance ID	Optimal value	Average value	Best value	Worst value	Gap (%)	Time (sec)	Number of opt
300×1000	big_a_1	22,255,196*	22,463,397.9	22,255,196	23,011,264	0.935	137.294	7
300×1000	big_a_2	22,189,452*	22,203,899.7	22,189,452	22,406,168	0.065	136.519	14
300×1000	big_a_3	22,765,286*	22,930,434.2	22,765,286	23,615,044	0.725	136.765	9
300×1000	big_a_4	22,799,540*	22,888,083.0	22,799,540	23,186,908	0.388	136.618	6
300×1000	big_b_1	22,475,276*	22,693,778.4	22,475,276	23,597,092	0.972	136.842	4
300×1000	big_b_2	21,988,192*	22,368,965.6	21,988,192	24,321,834	1.732	136.854	7
300×1000	big_b_3	22,919,924*	23,276,402.6	22,919,924	24,159,568	1.555	136.714	6
300×1000	big_b_4	22,442,388*	22,528,429.8	22,442,388	22,660,422	0.383	137.477	8
300×1000	big_c_1	21,207,902*	21,213,366.2	21,207,902	21,215,708	0.026	138.299	5
300×1000	big_c_2	21,199,978*	21,411,178.8	21,199,978	22,758,784	0.996	137.756	12
300×1000	big_c_3	21,404,592*	21,439,839.4	21,404,592	21,748,904	0.165	137.719	4
300×1000	big_c_4	21,896,128*	22,000,610.0	21,896,128	22,228,388	0.477	137.965	8
500×1000	large_a_1	38,635,228*	44,263,374.8	38,635,228	47,614,256	14.567	246.448	2
500×1000	large_a_2	34,642,732*	37,575,132.3	34,642,732	54,083,736	8.465	245.541	4
500×1000	large_a_3	37,365,008*	52,054,726.0	37,365,008	53,931,292	12.551	247.318	2
500×1000	large_a_4	36,443,660*	41,851,030.5	36,443,660	48,943,700	14.838	247.371	4
500×1000	large_b_1	30,678,758*	34,006,518.8	30,678,758	38,201,136	10.847	247.373	4
500×1000	large_b_2	30,304,860*	32,972,009.2	30,304,860	36,488,528	8.801	248.489	3
500×1000	large_b_3	30,870,146*	34,027,882.8	30,870,146	38,467,564	10.229	258.161	1
500×1000	large_b_4	30,330,226*	31,763,682.9	30,330,226	36,202,968	4.726	248.756	3
500×1000	large_c_1	30,354,964*	31,914,530.3	30,354,964	36,746,900	5.138	250.254	3
500×1000	large_c_2	30,341,740*	32,659,784.3	30,341,740	36,388,612	7.639	248.719	1
500×1000	large_c_3	30,281,492*	31,677,372.4	30,281,492	34,613,144	4.609	249.228	1
500×1000	large_c_4	24,334,680*	30,592,168.1	24,334,680	34,946,604	15.714	248.388	2