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

Table 6

Comparison of PACO with three PSO-based algorithms.


No.	Problem			BKS	DPSO-SA [18]	SR-2 [20]	CPSO-SA [19]	PACO

1	A-n33-k5	32	5	661	661 */32.2	661 */13	661 */0.7	661 */0.12
2	A-n46-k7	45	7	914	914 */128.9	914 */23	917/2.4	914 */0.16
3	A-n60-k9	59	9	1354	1354 */308.8	1355/40	1354 */6.5	1354 */14.15
4	B-n35-k5	34	5	955	955 */37.6	955 */14	955 */1.2	955 */0.06
5	B-n45-k5	44	5	751	751 */134.2	751 */20	751 */4.8	751 */1.12
6	B-n68-k9	67	9	1272	1272 */344.2	1274/50	1274/27.2	1275/87.19
7	B-n78-k10	77	10	1221	1239/429.4	1223/64	1237/24	1221 */54.38
8	E-n30-k3	29	3	534	534 */28.4	534 */16	534 */0.3	534 */0.05
9	E-n51-k5	50	5	521	528/300.5	521 */22	521 */4.6	521 */0.51
10	E-n76-k7	75	7	682	688/526.5	682 */60	692/9.5	685/18.95
11	F-n72-k4	71	4	237	244/398.3	237 */53	237 */5.3	237 */6.28
12	F-n135-k7	134	7	1162	1215/1526.3	1162 */258	1200/202.8	1170/246.85
13	M-n101-k10	100	10	820	824/874.2	820 */114	825/6.1	820 */66.02
14	M-n121-k7	120	7	1034	1038/1733.5	1036/89	1039/51.5	1034 */8.18
15	P-n76-K4	75	4	593	602/496.3	594/48	596/27.6	593 */8.61
16	P-n101-k4	100	4	681	694/977.5	683/86	691/29.4	683/25.7

Notes: = f(best solution)/shortest CPU Time (s), BKS is the best-known solution provided by published papers, DPSO-SA used Intel Pentium IV CPU 1.8 GHz with 256 M RAM, SR-2 used Intel Pentium IV CPU 3.4 GHz with 1 GB RAM, and CPSO-SA used Intel Core 2 CPU E8400 3 GHz with 3.5 G RAM.

Mathematical Problems in Engineering

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

Table 6