Table 4.

The output of the algorithms for solving the small-sized instances

Problem	Exact (MCGP-UF)				SA-GP				GA-GP				PSO-GP				HSAMCGP
	Z1 $\times {10}^6$	Z2	Z3	CPU time (s)	Z1 $\times {10}^6$	Z2	Z3	CPU time	Z1 $\times {10}^6$	Z2	Z3	CPU time	Z1 $\times {10}^6$	Z2	Z3	CPU time	Z1 $\times {10}^6$	Z2	Z3	CPU time
1	8837.2	0.082	1.825	26.3	8837.2	0.082	1.825	16.8	8837.2	0.082	1.825	31.5	8837.2	0.082	1.825	29.3	8837.2	0.082	1.825	23.7
2	9246.6	0.144	1.749	37.5	9246.6	0.144	1.749	19.5	9246.6	0.144	1.749	38.2	9246.6	0.144	1.749	35.6	9246.6	0.144	1.749	27.5
3	9675.4	0.195	1.864	94.6	9740.2	0.196	1.852	23.4	9735.0	0.196	1.862	46.1	9742.8	0.196	1.852	42.9	9675.4	0.195	1.863	32.9
4	9943.2	0.278	1.754	175.1	10,035.7	0.280	1.738	26.8	10,028.3	0.280	1.752	52.3	10,039.4	0.280	1.738	48.7	9943.2	0.278	1.753	37.7
5	10,488.7	0.251	1.766	238.5	10,635.5	0.254	1.742	30.2	10,623.8	0.254	1.763	59.5	10,641.4	0.254	1.742	55.4	10,488.7	0.251	1.765	42.5
6	10,843.1	0.366	1.857	482.8	11,038.3	0.371	1.841	34.1	11,022.7	0.371	1.854	66.7	11,046.1	0.372	1.827	62.1	10,936.4	0.368	1.856	48.0
7	11,164.5	0.485	1.799	682.8	11,421.3	0.495	1.782	39.4	11,400.7	0.494	1.795	72.4	11,431.6	0.496	1.761	67.4	11,309.6	0.490	1.798	55.5
8	11,495.3	0.337	1.725	951.3	11,713.7	0.342	1.722	44.7	11,696.2	0.342	1.721	79.1	11,722.4	0.343	1.693	73.6	11,713.7	0.342	1.723	62.9
9	12,072.5	0.568	1.738	1706.5	12,374.3	0.581	1.720	49.5	12,350.2	0.580	1.733	87.5	12,386.4	0.582	1.696	81.5	12,253.6	0.575	1.737	69.7
10	12,368.1	0.715	1.779	2646.2	12,726.8	0.734	1.755	56.3	12,698.1	0.732	1.774	96.3	12,741.1	0.734	1.729	89.7	12,590.7	0.725	1.777	79.3
11	12,953.8	0.626	1.616	4085.9	13,381.3	0.645	1.595	61.2	13,347.1	0.644	1.610	102.8	13,398.4	0.646	1.564	95.7	13,225.8	0.637	1.614	86.2
12	14,066.2	0.884	1.748	6428.5	14,572.6	0.912	1.723	67.6	14,532.1	0.910	1.741	110.1	14,592.8	0.913	1.688	102.5	14,403.8	0.901	1.745	95.2
13	14,859.9	0.912	1.745	9067.1	15,320.6	0.938	1.733	72.3	15,283.7	0.935	1.739	118.6	15,339.0	0.939	1.692	110.4	15,261.1	0.933	1.743	101.8
14	15,724.7	0.857	1.778	12,796.3	16,385.1	0.890	1.744	77.8	16,332.3	0.887	1.769	125.3	16,411.6	0.891	1.705	116.7	16,117.8	0.875	1.775	109.5
15	16,158.2	0.925	1.766	15,449.5	16,901.5	0.964	1.736	83.6	16,842.0	0.961	1.757	134.5	16,931.2	0.965	1.687	125.2	16,659.1	0.950	1.763	117.7