Table 2 Statistical results over 10 repetitions of proposed Kriging-GWO (hybrid surrogate-metaheuristic) approach in robust optimal placement of two, three, and four transmitting antennas for different "\(\alpha\)" values in Eq. (19).

\(\alpha\)	%Coverage_Mean				%Coverage_Std				SNR				TPT (mW)
\(\alpha\)	Avg	Std	Max	Min	Avg	Std	Max	Min	Avg	Std	Max	Min	Avg	Std	Max	Min
\(\#{\varvec{B}}{\varvec{S}}=2\)
− 2	52.47	1.41	49.95	55.66	14.17	0.45	13.44	15.28	− 5.68	0.22	− 6.09	− 5.18	2.01	0.05	1.94	2.10
− 1	60.16	1.81	56.47	62.15	15.41	0.59	14.51	16.53	− 4.53	0.27	− 5.08	− 4.25	2.53	0.10	2.39	2.69
0	68.05	2.17	65.04	70.32	14.91	0.69	13.70	16.23	− 3.48	0.28	− 3.87	− 3.18	3.07	0.18	2.82	3.32
+ 1	69.32	1.68	66.43	71.60	15.39	1.24	13.64	17.90	− 3.33	0.21	− 3.68	− 3.03	3.26	0.20	2.83	3.50
+ 2	69.52	1.90	66.16	71.65	15.81	0.83	14.52	17.33	− 3.32	0.24	− 3.74	− 3.07	3.34	0.21	2.91	3.62
\(\#{\varvec{B}}{\varvec{S}}=3\)
− 2	69.93	9.00	45.05	78.96	14.94	1.86	11.96	18.86	− 3.34	1.28	− 6.96	− 2.20	3.07	0.08	2.96	3.23
− 1	82.28	2.46	77.49	84.62	14.04	0.81	12.30	15.29	− 1.87	0.26	− 2.38	− 1.61	3.76	0.19	3.42	4.06
0	88.77	2.32	83.26	91.38	11.28	1.25	9.87	13.75	− 1.17	0.24	− 1.75	− 0.89	4.71	0.17	4.39	4.98
+ 1	89.52	4.42	76.39	91.86	11.21	1.19	9.60	13.92	− 1.10	0.47	− 2.48	− 0.84	4.73	0.14	4.52	4.91
+ 2	90.09	1.73	87.42	92.41	10.09	0.83	9.20	11.97	− 1.01	0.17	− 1.31	− 0.79	4.95	0.37	4.53	5.76
\(\#{\varvec{B}}{\varvec{S}}=4\)
− 2	82.87	4.64	71.59	88.45	12.47	1.64	10.14	15.11	− 1.78	0.52	− 3.05	− 1.17	4.03	0.15	3.84	4.34
− 1	88.78	5.49	74.53	93.60	9.35	1.82	7.24	13.02	− 1.14	0.59	− 2.67	− 0.63	5.08	0.22	4.65	5.37
0	92.40	6.31	75.24	97.83	7.46	2.22	4.25	12.01	− 0.77	0.66	− 2.58	− 0.21	6.18	0.28	5.65	6.55
+ 1	96.60	1.10	93.98	98.15	5.06	0.56	4.27	5.97	− 0.33	0.10	− 0.58	− 0.19	6.47	0.19	6.26	6.94
+ 2	96.48	0.89	94.95	97.90	5.42	0.67	4.59	6.95	− 0.35	0.09	− 0.49	− 0.21	6.67	0.20	6.36	7.07

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