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

Table 5

Computational results of PACO over 20 runs on two benchmark sets.

		First benchmark set				Second benchmark set
	Best	Avg.	Worst	Std.	AT (s)		Best	Avg.	Worst	Std.	AT (s)
A-n33-k5	661 *	661	661	0	0.87	C1	524.61 *	527.54	543.16	4.98	32.3
A-n46-k7	914 *	914	914	0	6.02	C2	835.26 *	842.71	852.14	4.31	107.91
A-n60-k9	1354 *	1356.4	1369	4.49	52.88	C3	829.92	838.29	844.65	3.76	141.89
B-n35-k5	955 *	955	955	0	2.65	C4	1040.23	1053.22	1077.68	9.31	377.83
B-n45-k5	751 *	751	751	0	5.85	C5	1348.73	1375.05	1392.93	12.73	1048.45
B-n68-k9	1275	1286.25	1288	2.86	62.97	C6	555.43 *	556.72	560.24	1.09	27.09
B-n78-k10	1221 *	1228.1	1252	8.6	98.78	C7	909.68 *	917.93	932.06	7	98.70
E-n30-k3	534 *	534	534	0	4.38	C8	868.61	880.47	895.7	8.37	117.74
E-n51-k5	521 *	522.65	528	2.87	19.46	C9	1171.94	1194.96	1233.9	15.24	505.89
E-n76-k7	685	691.15	694	2.35	46.85	C10	1454.81	1498.23	1577.52	28.8	939.08
F-n72-k4	237 *	237	237	0	30.64	C11	1042.11 *	1045.01	1049.45	2.87	196.49
F-n135-k7	1170	1193.45	1229	15.99	248.77	C12	819.56 *	821.55	825.95	1.91	148.67
M-n101-k10	820 *	822.9	824	1.41	113.28	C13	1562.64	1575.55	1596.63	8.16	320.92
M-n121-k7	1034 *	1039.6	1127	20.12	80.62	C14	866.37 *	866.81	867.77	0.51	173.15
P-n76-K4	593 *	597.95	616	5.72	53.48
P-n101-k4	683	693.35	706	7.21	64.92

* The solution equals the best-known solution.
AT denotes the average CPU time required to reach the final best solution over 20 runs.