Table 7.

The average results of objective functions and CPU times (based on seconds) of the method developed

Problem size	Objective function	LP-metric	CPU	GWO	CPU	MGWO	CPU	VNS	CPU
S1	$Z_1$ $Z_2$ $Z_3$ $Z_4$	374,125.4 1035 58.73 237.05	6	374,125.4 1035 58.73 237.05	6	374,125.4 1035 58.73 237.05	6	374,125.4 1035 58.73 237.05	7
S2	$Z_1$ $Z_2$ $Z_3$ $Z_4$	389,209.3 1108 84.52 318.47	159	389,238.9 1123 85.29 320.98	11	389,233.3 1114 84.86 319.73	11	389,245.7 1127 85.33 322.15	13
S3	$Z_1$ $Z_2$ $Z_3$ $Z_4$	467,910.2 1433 127.94 485.34	479	467,978.7 1439 128.89 487.30	54	467,965.0 1436 128.23 486.46	38	467,989.4 1442 129.32 489.19	66
S4	$Z_1$ $Z_2$ $Z_3$ $Z_4$	609,198.5 2674 177.84 539.47	703	609,209.4 2682 183.93 545.48	68	609,203.7 2678 179.23 542.40	49	609,211.0 2688 186.09 549.08	74
S5	$Z_1$ $Z_2$ $Z_3$ $Z_4$	769,428.6 3002 298.67 723.31	1454	769,444.7 3015 303.25 735.39	78	769,435.3 3009 300.44 728.14	55	769,449.1 3021 311.69 738.08	83
M1	$Z_1$ $Z_2$ $Z_3$ $Z_4$	– – – –	–	1,012,524.0 3877 411.5 816.32	99	1,012,508.3 3875 408.9 811.56	68	1,012,538.3 3881 417.2 821.55	103
M2	$Z_1$ $Z_2$ $Z_3$ $Z_4$	– – – –	–	1,014,025.3 3909 463.5 871.19	110	1,013,988.0 3901 459.1 866.04	82	1,014,036.4 3914 468.9 880.25	122
M3	$Z_1$ $Z_2$ $Z_3$ $Z_4$	– – – –	–	1,015,589.6 3998 504.4 940.10	135	1,015,573.6 3995 499.3 931.11	98	1,015,573.6 4006 514.4 949.68	151
M4	$Z_1$ $Z_2$ $Z_3$ $Z_4$	– – – –	–	1,222,556.4 4219 562.6 1035.08	149	1,222,539.5 4210 557.2 1026.75	115	1,222,566.2 4222 565.3 1042.61	179
M5	$Z_1$ $Z_2$ $Z_3$ $Z_4$	– – – –	–	1,319,439.1 4435 5816.9 1267.03	173	1,319,428.4 4426 5810.3 1256.08	144	1,319,445.9 4441 5826.6 1274.11	188