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

Table 3

Results for the small-size instances.

Instance size	Instance ID	Optimal value	Average value	Best value	Worst value	Gap (%)	Time (sec)	Number of opt
50×50	132_1	1,122,750	1,129,632.20	1,122,750	1,156,712	0.613	1.4458	9
50×50	132_2	1,157,722	1,166,628.87	1,157,722	1,193,100	0.769	1.4325	9
50×50	132_3	1,146,301	1,157,273.67	1,146,301	1,283,510	0.957	1.4391	11
50×50	132_4	1,036,779	1,040,920.87	1,036,779	1,056,677	0.399	1.4704	9
50×50	133_1	1,103,272	1,104,166.80	1,103,272	1,110,614	0.081	1.472	12
50×50	133_2	0,135,443	1,043,974.87	0,135,443	1,099,432	0.824	1.4681	13
50×50	133_3	1,171,331	1,179,617.13	1,171,331	1,192,603	0.707	1.4576	6
50×50	133_4	1,083,636	1,083,955.53	1,083,636	1,087,769	0.029	1.4703	12
50×50	134_1	1,179,639	1,185,867.73	1,179,639	1,219,335	0.528	1.4673	11
50×50	134_2	1,121,633	1,132,109.40	1,121,633	1,149,761	0.934	1.4701	8
50×50	134_3	1,171,409	1,183,031.40	1,171,409	1,198,847	0.992	1.4624	6
50×50	134_4	1,210,465	1,222,462.13	1,210,465	1,236,753	0.991	1.4604	6
50×75	a75_50_1	1,661,269	1,664,342.60	1,661,269	1,673,507	0.185	1.9681	6
50×75	a75_50_2	1,632,907	1,648,883.00	1,632,907	1,682,822	0.978	1.9632	8
50×75	a75_50_3	1,632,213	1,632,698.13	1,632,213	1,633,426	0.029	1.9820	8
50×75	a75_50_4	1,585,028	1,585,428.40	1,585,028	1,591,034	0.025	1.9557	14
50×75	b75_50_1	1,252,804	1,260,789.53	1,252,804	1,304,636	0.637	1.9883	12
50×75	b75_50_2	1,337,446	1,341,283.27	1,337,446	1,357,102	0.287	1.9729	5
50×75	b75_50_3	1,249,750	1,257,445.27	1,249,750	1,282,987	0.616	1.9696	7
50×75	b75_50_4	1,217,508	1,228,422.53	1,217,508	1,235,590	0.896	1.9687	3
50×75	c75_50_1	1,310,193	1,318,412.47	1,310,193	1,332,980	0.627	1.9745	2
50×75	c75_50_2	1,244,255	1,252,745.53	1,244,255	1,283,134	0.682	1.9746	1
50×75	c75_50_3	1,201,706	1,203,925.27	1,201,706	1,232,129	0.185	1.9737	12
50×75	c75_50_4	1,334,782	1,341,951.47	1,334,782	1,370,764	0.537	1.9686	7