A Hybrid Algorithm Based on ACO and PSO for Capacitated Vehicle Routing Problems

Table 7

Comparison of PACO with three ACO-based algorithms.

Prob.	𝑁	𝐾	BKS	IACS [12]	SS_ACO [13]	EACO [15]	PACO
C1	50	5	524.61	524.61 */3	524.61 */55.23	524.61 */—	524.61 */0.79
C2	75	10	835.26	836.18/26	835.26 */70.43	835.26 */—	835.26 */163.44
C3	100	8	826.14	835.6/101	830.14/120.25	826.14 */—	829.92/183.08
C4	150	12	1028.42	1038.22/617	1038.20/250.76	1041.83/—	1040.23/547.88
C5	199	17	1291.45	1327.07/3080	1307.18/707.80	1338.48/—	1348.73/1455.64
C6	50	6	555.43	555.43 */5	559.12/65.17	555.43 */—	555.43 */7.72
C7	75	11	909.68	909.68 */41	912.68/90.42	909.68 */—	909.68 */66.68
C8	100	9	865.94	865.94 */115	869.34/210.46	865.94 */—	868.61/146.5
C9	150	14	1162.55	1173.76/853	1179.4/520.52	1168.81/—	1171.94/614.53
C10	199	18	1395.85	1413.83/4223	1410.26/1012.23	1413.69/—	1454.81/1114.21
C11	120	7	1042.11	1042.11 */204	1044.12/232.46	1045.5/—	1042.11 */95.33
C12	100	10	819.56	832.67/88	824.31/156.47	819.56 */—	819.56 */122.87
C13	120	11	1541.14	1547.07/428	1556.52/467.24	1554.93/—	1562.64/156.32
C14	100	11	866.37	866.37 */125	870.26/368.72	866.37 */—	866.37 */32.75

Notes: 𝑥/𝑦 = f(best solution)/shortest CPU Time (s), BKS is the best-known solution provided by published papers, —denotes that the data is not available, IACS used Intel Pentium III CPU 1000 MHz with 128 MB RAM, SS_ACO used IBM computer CPU 1600 MHz with 512 MB RAM, and EACO used Pentium IV CPU 3.0 GHz.