Table 2 Statistical results for SP of the investigated techniques.

Benchmark problems	Approaches	Mean	Median	STDDev.	Worst	Best
UF1	MOPSO	0.009	0.009	0.003	0.015	0.007
	MOEA/D	0.004	0.004	0.002	0.007	0.002
	MOGWO	0.013	0.005	0.015	0.047	0.001
	Proposed IMOWOA	0.013	0.012	0.004	0.021	0.010
UF2	MOPSO	0.008	0.008	0.002	0.013	0.006
	MOEA/D	0.009	0.009	0.001	0.011	0.008
	MOGWO	0.010	0.008	0.003	0.016	0.007
	Proposed IMOWOA	0.011	0.010	0.004	0.018	0.008
UF3	MOPSO	0.007	0.007	0.002	0.010	0.005
	MOEA/D	0.027	0.025	0.021	0.064	0.001
	MOGWO	0.047	0.049	0.015	0.072	0.016
	Proposed IMOWOA	0.053	0.056	0.017	0.081	0.018
UF4	MOPSO	0.007	0.007	0.001	0.008	0.006
	MOEA/D	0.007	0.007	0.001	0.009	0.006
	MOGWO	0.010	0.009	0.004	0.017	0.006
	Proposed IMOWOA	0.011	0.010	0.004	0.020	0.007
UF5	MOPSO	0.005	0.005	0.004	0.012	0.000
	MOEA/D	0.003	0.000	0.006	0.016	0.000
	MOGWO	0.155	0.089	0.165	0.520	0.009
	Proposed IMOWOA	0.173	0.100	0.185	0.583	0.010
UF6	MOPSO	0.021	0.013	0.033	0.113	0.002
	MOEA/D	0.006	0.000	0.013	0.031	0.000
	MOGWO	0.015	0.011	0.013	0.042	0.002
	Proposed IMOWOA	0.017	0.013	0.014	0.048	0.002
UF7	MOPSO	0.007	0.007	0.003	0.013	0.003
	MOEA/D	0.005	0.004	0.003	0.012	0.001
	MOGWO	0.008	0.006	0.009	0.032	0.000
	Proposed IMOWOA	0.009	0.006	0.010	0.036	0.000
UF8	MOPSO	0.027	0.027	0.008	0.045	0.016
	MOEA/D	–	–	–	–	–
	MOGWO	0.007	0.005	0.005	0.019	0.004
	Proposed IMOWOA	0.030	0.029	0.009	0.050	0.017
UF9	MOPSO	0.024	0.024	0.004	0.031	0.017
	MOEA/D	–	–	–	–	–
	MOGWO	0.018	0.019	0.006	0.029	0.007
	Proposed IMOWOA	0.020	0.021	0.007	0.032	0.007
UF10	MOPSO	0.020	0.021	0.004	0.027	0.016
	MOEA/D	–	–	–	–	–
	MOGWO	0.026	0.024	0.015	0.055	0.000
	Proposed IMOWOA	0.022	0.023	0.004	0.030	0.017

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