An Endosymbiotic Evolutionary Algorithm for the Hub Location-Routing Problem

Table 1

Computational results from ACO and EEA.

Problem; number	Number of; customers	Number of; candidate hubs	Number; of clusters	Clustering; ratio	ACO		EEA
					Cost	CPU	Cost	CPU	Improvement ratio (%)
1	100	10	0	—	1523.7	2.66	1453.2	3.88	4.85
2	100	10	3	0.5	1497.3	2.37	1436.5	4.25	4.23
3	100	10	3	1.0	1473.5	3.12	1438.1	3.69	2.46
4	100	10	5	0.5	1383.9	3.55	1328.8	4.72	4.15
5	100	10	5	1.0	1358.6	2.78	1315.0	3.55	3.32
6	100	20	0	—	1465.8	2.94	1408.5	3.90	4.07
7	100	20	3	0.5	1429.2	3.48	1366.3	4.84	4.60
8	100	20	3	1.0	1392.0	4.25	1321.5	4.62	5.33
9	100	20	5	0.5	1277.4	3.83	1236.9	5.02	3.27
10	100	20	5	1.0	1261.5	4.33	1218.4	5.73	3.54
11	200	10	0	—	2858.3	10.38	2710.7	15.58	5.45
12	200	10	3	0.5	2644.0	13.73	2518.3	14.25	4.99
13	200	10	3	1.0	2569.8	12.92	2496.4	15.39	2.94
14	200	10	5	0.5	2378.2	12.80	2272.9	14.26	4.63
15	200	10	5	1.0	2318.7	13.19	2258.5	13.81	2.67
16	200	20	0	—	2749.0	13.05	2567.3	16.35	7.08
17	200	20	3	0.5	2562.6	15.06	2418.6	18.29	5.95
18	200	20	3	1.0	2461.9	14.77	2319.1	17.72	6.16
19	200	20	5	0.5	2146.2	15.20	2045.8	18.30	4.91
20	200	20	5	1.0	2123.7	14.58	2037.5	16.08	4.23