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

Table 4

Results for the medium-size instances.

Instance size	Instance ID	Optimal value	Average value	Best value	Worst value	Gap (%)	Time (sec)	Number of opt
75×100	a100_75_1	2,286,397	2,305,392.47	2,286,397	2,407,972	0.831	3.4230	11
75×100	a100_75_2	2,463,187	2,466,300.40	2,463,187	2,509,888	0.126	3.3775	14
75×100	a100_75_3	2,415,836	2,439,790.27	2,415,836	2,481,304	0.992	3.3760	6
75×100	a100_75_4	2,380,150	2,386,191.33	2,380,150	2,398,158	0.254	3.4679	7
75×100	b100_75_1	1,950,231	1,968,184.47	1,950,231	1,999,198	0.921	3.5263	8
75×100	b100_75_2	2,023,097	2,043,233.40	2,023,097	2,067,532	0.995	3.5099	6
75×100	b100_75_3	2,062,595	2,082,063.53	2,062,595	2,142,439	0.944	3.5200	2
75×100	b100_75_4	1,865,323	1,883,910.00	1,965,323	1,953,993	0.996	3.4973	3
75×100	c100_75_1	1,843,620	1,851,536.07	1,843,620	1,875,764	0.429	3.5425	7
75×100	c100_75_2	1,808,867	1,826,892.60	1,808,867	1,885,459	0.997	3.5293	8
75×100	c100_75_3	1,820,587	1,829,550.67	1,820,587	1,869,527	0.492	3.4979	10
75×100	c100_75_4	1,839,007	1,856,116.80	1,839,007	1,896,699	0.930	3.5146	4
100×1000	cap_a_1	27,490,608*	27,669,164.8	27,490,608	27,848,872	0.649	49.939	5
100×1000	cap_a_2	27,434,572*	27,620,332.0	27,434,572	27,909,206	0.677	49.662	5
100×1000	cap_a_3	27,435,430*	27,639,741.2	27,435,430	27,792,660	0.745	49.241	5
100×1000	cap_a_4	27,804,896*	27,813,746.1	27,804,896	27,937,648	0.032	51.115	14
100×1000	cap_b_1	24,449,922*	24,449,922.0	24,449,922	24,449,922	0.000	51.631	15
100×1000	cap_b_2	24,532,388*	24,556,056.3	24,532,388	24,708,592	0.096	50.304	12
100×1000	cap_b_3	24,318,664*	24,331,881.6	24,318,664	24,351,708	0.054	51.039	9
100×1000	cap_b_4	24,526,456*	24,535,120.8	24,526,456	24,591,442	0.035	50.444	13
100×1000	cap_c_1	23,095,054*	23,321,130.5	23,095,054	23,740,388	0.979	50.557	4
100×1000	cap_c_2	23,368,530*	23,447,282.0	23,368,530	23,579,496	0.337	51.621	4
100×1000	cap_c_3	23,237,760*	23,366,553.3	23,237,760	23,502,456	0.554	52.952	6
100×1000	cap_c_4	23,192,496*	23,257,851.5	23,192,496	23,461,264	0.282	52.449	5