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

Table 8

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

Test problems	Performance measures		IMOMVO	MOMVO	MOPSO	MOALO	NSGA-II
Lproblem-01-20	SP	Min	31.5046	37.9386	39.2627	45.2234	32.5645
		Avg	47.0788	63.0421	48.9852	83.7999	56.2081
		Std	14.6542	24.1826	9.5585	24.5639	19.7613
	GD	Min	9.6393	20.0731	40.3205	58.4695	14.7962
		Avg	15.0285	33.6796	49.1722	87.9470	28.7340
		Std	4.0260	11.0479	8.2321	19.4371	15.4064
	IGD	Min	11.1861	14.2001	32.0123	36.2466	21.3965
		Avg	13.6352	31.7573	49.3988	63.4794	27.3624
		Std	1.6068	11.5299	11.0756	28.5335	4.5460
Lproblem-02-20	SP	Min	39.2138	43.3812	41.9372	43.5818	35.7117
		Avg	48.0512	80.0144	58.5973	78.0675	48.6288
		Std	10.2653	42.4928	11.7668	22.4166	16.4953
	GD	Min	0	13.7379	36.8747	31.5268	25.0612
		Avg	13.0129	53.0043	52.3202	52.7521	35.1891
		Std	6.6623	26.9211	12.8599	11.8538	16.3095
	IGD	Min	0	12.3588	17.6584	31.939	22.0302
		Avg	11.7856	50.5360	52.2226	64.0970	33.5677
		Std	6.5477	32.6129	33.5188	27.0935	19.0259
Lproblem-03-20	SP	Min	12.9284	14.5336	11.0352	17.2225	14.2715
		Avg	17.1909	20.6562	17.6746	28.972	17.6740
		Std	2.6819	5.0773	5.2745	16.9026	2.6553
	GD	Min	0	6.5092	0	20.6104	0.6099
		Avg	1.7627	16.8459	15.5075	32.7396	9.3958
		Std	2.6162	7.7080	7.1737	10.1721	5.5497
	IGD	Min	1.3130	10.1753	11.3452	26.5771	1.3472
		Avg	5.2737	17.9577	24.5695	39.4279	16.1063
		Std	2.1392	7.8994	20.5780	909037	3.9406
Lproblem-04-20	SP	Min	19.7206	16.7344	19.5014	23.1202	22.6913
		Avg	26.3831	31.3330	30.8081	35.5944	27.2626
		Std	4.6792	12.3887	9.3875	5.5558	5.7137
	GD	Min	0	2.0338	6.719	23.9144	8.2262
		Avg	5.0776	13.6868	15.6351	34.7515	15.0124
		Std	3.5823	10.2058	5.1480	5.7331	9.2964
	IGD	Min	0	5.8252	9.7547	20.8213	7.7169
		Avg	5.8495	12.9112	15.1598	33.2070	12.0886
		Std	2.3550	5.3789	4.7880	12.1977	4.7048
Lproblem-05-20	SP	Min	0	0	0	0	0
		Avg	19.7206	26.1458	24.2800	18.4337	21.7567
		Std	31.3350	33.8072	25.3138	31.3129	27.0370
	GD	Min	0	0	5.1640	0	0
		Avg	4.8984	14.9427	19.6865	26.1215	16.9535
		Std	3.3327	8.2743	20.7626	15.1955	8.0954
	IGD	Min	6	0	7	21.7401	11.3529
		Avg	9.1573	22.7388	25.2810	29.1370	27.4365
		Std	1.9291	16.6252	14.5438	3.1175	17.4456
Lproblem-06-20	SP	Min	26.3994	27.5350	29.1025	42.2188	33.6225
		Avg	56.4040	57.7383	47.7134	63.3400	52.4290
		Std	17.8382	19.7179	14.8274	19.3504	14.5233
	GD	Min	0	10.4265	4.7540	18.6695	8.2554
		Avg	4.6472	21.3337	11.9000	27.2603	14.1198
		Std	2.4220	10.5578	8.0866	8.5111	5.9599
	IGD	Min	10.4799	17.6675	17.8134	18.5859	16.1167
		Avg	12.4413	27.938	21.5491	38.2586	23.4192
		Std	1.7633	8.9999	4.1238	17.7398	7.8422