Multi-Objective Reentrant Hybrid Flowshop Scheduling with Machines Turning on and off Control Strategy Using Improved Multi-Verse Optimizer Algorithm

Table 6

Comparisons of IMOMVO and the four algorithms for small-sized problems.

Test problems	Performance measures		IMOMVO	MOMVO	MOPSO	MOALO	NSGA-II
Sproblem-01-20	SP	Min	4.2538	3.3425	2.6581	4.8011	3.4495
		Avg	5.5441	6.1904	6.7477	9.2005	5.4655
		Std	1.2617	2.8282	2.9487	3.1855	1.5064
	GD	Min	0.4243	1.0905	1.7217	1.4066	1.3952
		Avg	0.9150	2.0821	2.2098	5.1492	2.0520
		Std	0.3053	1.1803	0.4345	2.3362	0.3902
	IGD	Min	1.1835	1.9842	2.2384	2.7163	2.1045
		Avg	0.2990	0.7035	0.4396	0.6491	0.5931
		Std	1.0887	1.0087	1.6941	1.6562	1.3959
Sproblem-02-20	SP	Min	6.4828	6.0011	7.8466	3.8277	3.9211
		Avg	9.7764	15.8743	14.8757	9.0176	14.3121
		Std	4.0321	9.8391	5.0085	2.6563	5.4210
	GD	Min	0.8724	1.5297	2.1647	3.3802	2.5898
		Avg	1.9700	4.0680	3.6181	5.3739	3.8907
		Std	0.9110	1.8535	1.2529	1.3984	1.3274
	IGD	Min	1.0842	2.6203	2.6529	3.3949	3.2842
		Avg	2.4374	5.1764	4.6116	6.1921	4.7595
		Std	1.4366	2.8636	1.5003	2.7036	2.1415
Sproblem-03-20	SP	Min	2.567	0.8237	2.7398	4.4499	2.3531
		Avg	4.9246	4.9596	4.3365	6.1176	6.0466
		Std	2.0407	2.2553	1.4207	1.9027	3.0756
	GD	Min	0	0.5079	1.5609	1.8643	0.9265
		Avg	0.9232	2.4554	2.1164	2.9399	1.8288
		Std	0.8034	1.4898	0.4847	0.7599	0.5991
	IGD	Min	1.0441	2.0295	1.3708	2.1544	1.4214
		Avg	1.4052	3.1044	2.7329	2.7603	2.5920
		Std	0.2756	1.0239	1.3596	0.5844	1.1414
Sproblem-04-20	SP	Min	4.4390	3.0618	4.1757	6.0383	5.036
		Avg	6.4714	6.7734	7.4176	9.9239	7.5878
		Std	1.1955	1.8944	2.2194	2.6719	2.4746
	GD	Min	0.5672	2.0327	1.9053	4.3381	1.8788
		Avg	1.2277	2.8152	3.5303	7.1940	3.0729
		Std	0.5413	0.6537	2.9476	2.2363	0.8076
	IGD	Min	0.8572	1.2991	2.1892	3.399	2.1246
		Avg	1.5798	2.4576	3.0508	5.4666	2.8488
		Std	0.4280	0.7041	0.7275	1.1314	0.7762
Sproblem-05-20	SP	Min	1.9556	3.7677	2.5162	3.8762	3.4323
		Avg	5.3309	8.5614	7.9275	7.2344	6.4903
		Std	2.0804	3.7584	9.4040	3.0191	3.3006
	GD	Min	0.4654	2.7581	0	4.2029	3.5653
		Avg	1.7576	4.3472	3.8166	8.6313	4.5525
		Std	0.9737	2.0990	1.9706	3.5671	0.9877
	IGD	Min	1.4727	2.0496	3.0676	5.155	2.7927
		Avg	2.0439	3.5092	3.8419	7.9333	4.0812
		Std	0.5769	1.1922	0.8280	2.9383	1.0016
Sproblem-06-20	SP	Min	5.6331	7.7566	5.1192	7.3206	5.7043
		Avg	10.1854	13.3589	9.5592	12.1647	8.7989
		Std	3.58811	5.2599	4.1399	3.5184	2.8420
	GD	Min	0	2.8996	3.3732	5.2997	3.1649
		Avg	1.5256	5.1802	5.5500	14.7124	5.1470
		Std	0.9362	1.9553	2.3292	7.9477	1.5420
	IGD	Min	1.1463	3.067	3.0608	4.3261	3.0502
		Avg	2.2706	4.6015	5.2186	12.3180	4.5948
		Std	0.6253	1.1447	1.3723	5.1917	0.8459