Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems

Table 22

MBO using sequential merge sort algorithm.

ID	OPT	Optimum				Execution time			Cycle			Time cycle
		MBO	AVG	SD	RPD%	BET	AVG	ST	BC	AVG	SD	BTC	AVG	SD
B1	11	11	11.0000	0.0000	0.00	158	251	171.6413	4	7	2.4350	17	53	34.2198
B2	11	11	11.0000	0.0000	0.00	157	263	84.9052	1	3	1.1575	4	31	23.2120
B3	11	11	11.0000	0.0000	0.00	153	209	47.3905	2	4	1.4984	9	24	10.2378
B4	11	11	11.0000	0.0000	0.00	155	160	4.7848	2	4	1.9449	8	20	8.5007
B5	11	11	11.0000	0.0000	0.00	155	160	4.4053	2	4	2.0723	8	20	9.2034
B6	7	7	7.0000	0.0000	0.00	165	172	5.9968	2	8	5.4244	10	40	25.3084
B7	6	6	6.0000	0.0000	0.00	158	165	10.2942	2	5	2.6567	9	24	10.9301
B8	4	4	4.1935	0.6011	0.00	154	226	63.7678	3	10	8.5001	13	59	55.3723
B9	3	3	3.1935	0.4016	0.00	152	157	3.4802	2	5	2.5686	8	24	10.5719
B10	3	3	3.0000	0.0000	0.00	152	183	41.7133	2	4	1.5422	8	21	10.5715
B11	4	4	4.1613	0.3739	0.00	155	233	66.3620	2	11	9.9109	9	73	63.6411
B12	4	4	4.0000	0.0000	0.00	153	235	86.2169	2	4	1.6643	11	29	18.5750
B13	4	4	4.0000	0.0000	0.00	152	161	30.0537	3	6	3.6577	12	27	14.8101
B14	3	3	3.3548	0.4864	0.00	152	159	26.0370	2	6	3.7006	8	26	15.6561
B15	1	1	1.6452	0.9504	0.00	152	155	2.6176	2	5	2.3505	8	22	9.6363
B16	14	14	14.0000	0.0000	0.00	155	182	48.3518	3	8	3.5493	12	43	25.2893
B17	13	13	13.0000	0.0000	0.00	152	174	35.1554	2	5	2.1717	8	26	9.4585
B18	13	13	13.0000	0.0000	0.00	152	177	41.1985	2	4	1.8275	8	21	8.6059
B19	13	13	13.0968	0.5388	0.00	153	218	62.5518	1	6	4.0377	4	39	26.7267
B20	13	13	13.0000	0.0000	0.00	155	225	138.3519	3	7	4.5423	13	41	21.4062
B21	9	9	9.1935	0.4016	0.00	153	172	43.6026	2	9	5.2990	8	41	26.7630
B22	6	6	6.1290	0.3408	0.00	152	155	2.0494	1	5	3.1326	4	23	12.9070
B23	6	6	6.1290	0.3408	0.00	152	153	2.0489	2	7	4.8491	8	31	19.7735
B24	5	5	5.2581	0.5755	0.00	152	153	1.6409	2	6	2.4012	8	24	9.6949
B25	4	4	4.1290	0.3408	0.00	152	154	6.0300	3	6	5.4158	12	27	22.1520
B26	5	5	5.0000	0.0000	0.00	154	157	2.3372	2	8	6.0393	8	37	24.7760
B27	3	3	3.0323	0.1796	0.00	152	154	2.2017	2	7	4.8524	8	30	19.3886
B28	3	3	3.2903	0.5884	0.00	152	155	4.7996	1	5	3.2670	4	24	13.9205
B29	3	3	3.0968	0.3005	0.00	152	156	7.3660	3	5	2.0447	12	23	8.2142
B30	2	2	2.4516	0.5680	0.00	152	153	1.7289	2	7	6.5031	8	28	26.3895
B31	7	7	7.0000	0.0000	0.00	153	157	2.7615	4	8	3.2156	19	37	13.2221
B32	4	4	4.2903	0.9016	0.00	152	155	4.1960	3	7	3.7805	13	31	15.0563
B33	4	4	4.1290	0.4995	0.00	152	154	3.7868	2	6	3.0154	8	26	12.7931
B34	4	4	4.3226	0.7478	0.00	152	153	1.2835	2	6	4.2925	8	27	17.1088
B35	4	4	4.7097	0.9727	0.00	152	153	1.6468	1	5	2.0723	4	21	8.5183
B36	13	13	13.0000	0.0000	0.00	154	158	3.8763	3	9	4.9110	13	39	19.3956
B37	10	10	10.3226	0.7478	0.00	152	155	2.5387	2	6	5.4497	9	28	22.2304
B38	8	8	8.0968	0.3005	0.00	152	154	3.3601	2	8	5.6323	8	34	22.8731
B39	5	5	5.1935	1.0776	0.00	152	166	20.9165	2	6	3.5493	8	27	15.7638
B40	5	5	5.0000	0.0000	0.00	152	162	16.8069	2	4	1.8357	8	19	7.9044
B41	8	8	8.0000	0.0000	0.00	155	158	2.9064	1	10	5.2974	4	42	22.2617
B42	8	8	8.0000	0.0000	0.00	152	198	70.2758	1	4	2.0718	8	24	17.2073
B43	8	8	8.0000	0.0000	0.00	152	154	1.7221	1	4	2.2818	4	19	9.3681
B44	5	5	5.9677	1.4256	0.00	152	154	3.8616	2	5	2.5264	8	24	10.1847
B45	5	5	6.1935	1.5366	0.00	152	153	1.3536	2	6	4.6467	8	26	19.1860
B46	8	8	8.0645	0.2497	0.00	154	158	3.4348	3	10	6.7563	12	42	27.9592
B47	5	5	5.0000	0.0000	0.00	152	155	4.1228	2	5	2.9256	8	22	13.0905
B48	5	5	5.4839	2.0145	0.00	152	153	1.3897	2	5	2.8931	8	22	11.7203
B49	5	5	5.1935	0.6011	0.00	152	152	1.1704	3	6	3.1819	12	26	12.7969
B50	5	5	5.3226	0.7478	0.00	152	153	1.4473	2	6	3.4529	8	26	14.0041
B51	27	27	28.1613	0.9694	0.00	154	159	4.7774	5	21	9.0993	21	92	39.5406
B52	18	18	18.9355	1.0307	0.00	154	156	2.2785	2	19	9.3341	8	80	38.7324
B53	11	11	11.0000	0.0000	0.00	153	155	1.5889	4	10	2.8815	16	42	12.1075
B54	11	11	11.0000	0.0000	0.00	152	154	1.6277	3	7	2.4596	12	32	10.2627
B55	7	7	7.0000	0.0000	0.00	154	158	4.4897	4	11	5.5967	16	48	22.6364
B56	6	6	6.0000	0.0000	0.00	153	155	1.9233	4	10	3.4112	16	44	13.9193
B57	6	6	6.0968	0.3962	0.00	153	154	1.3552	6	12	5.2644	24	52	21.4015
B58	6	6	6.0645	0.3592	0.00	152	155	4.0377	3	9	3.7643	14	38	14.9752
B59	9	9	9.1290	0.3408	0.00	154	158	2.6825	5	15	6.7165	21	64	28.5839
B60	4	4	4.3871	1.2021	0.00	152	156	2.3145	6	13	5.7136	24	56	23.8186
B61	4	4	4.1290	0.3408	0.00	152	155	2.0394	4	13	6.7101	16	54	27.4017
B62	4	4	4.0000	0.0000	0.00	152	155	4.1824	4	9	3.4273	18	40	13.6191
B63	27	27	27.2581	0.5143	0.00	155	165	11.2005	4	21	11.4243	16	90	48.4598
B64	18	18	18.3871	0.9549	0.00	155	167	14.2569	7	19	9.3371	28	86	39.7379
B65	14	14	14.0645	0.2497	0.00	153	161	9.3472	6	15	7.5537	25	65	31.4611
B66	13	13	13.0000	0.0000	0.00	154	247	97.6943	6	11	3.3020	24	81	67.8854
B67	11	11	11.0323	0.1796	0.00	156	209	33.3034	4	14	7.7241	19	77	43.7733
B68	8	8	8.8065	2.3154	0.00	156	179	30.7013	2	13	7.7239	9	63	40.9466
B69	8	8	8.5161	0.6256	0.00	154	190	35.2266	5	12	5.7914	20	64	35.7448
B70	6	6	6.4839	0.6256	0.00	152	167	16.6121	5	12	5.6220	22	57	26.9089
B71	6	6	6.0000	0.0000	0.00	155	176	15.3473	6	11	5.4370	29	54	24.4164
B72	4	4	4.2258	0.5603	0.00	155	168	21.0614	6	12	4.0783	28	55	23.1119
B73	4	4	4.4516	0.6752	0.00	152	173	15.2415	4	11	6.4611	16	52	28.1919
B74	3	3	3.3226	0.4752	0.00	153	166	14.9468	4	13	8.6221	20	60	35.3722
B75	11	11	11.6774	0.9794	0.00	156	169	8.4222	4	17	10.5949	17	77	47.6167
B76	5	5	5.2581	0.6816	0.00	154	167	23.7204	3	12	5.0513	14	56	26.0949
B77	5	5	5.3871	0.8032	0.00	165	174	8.3753	6	14	8.1313	27	66	37.9381
B78	4	4	4.9355	1.2093	0.00	163	176	12.2235	5	13	4.7399	22	60	25.3983
B79	14	14	14.0323	0.1796	0.00	156	181	28.4157	5	10	3.2965	25	47	16.9919
B80	11	11	11.0000	0.0000	0.00	171	190	20.4805	3	10	4.6704	17	53	23.3860
B81	11	11	11.3871	0.8032	0.00	159	186	24.6086	7	14	7.1159	34	70	35.5031
B82	10	10	10.3548	0.6607	0.00	153	169	25.0386	4	12	6.0875	16	55	29.4125
B83	12	12	12.2258	1.2572	0.00	154	167	8.4371	4	12	6.3860	18	57	29.6714
B84	12	12	12.0000	0.0000	0.00	155	165	13.7350	6	11	3.8852	31	52	17.8962
B85	8	8	8.9355	1.4361	0.00	153	170	23.4146	4	14	7.3518	17	64	33.0030
B86	8	8	8.1613	0.5829	0.00	156	177	15.4220	3	10	3.7814	13	47	18.0706
B87	10	10	10.4839	1.0605	0.00	156	184	20.5574	4	18	9.4481	19	89	50.8878
B88	8	8	8.0000	0.0000	0.00	155	194	109.8234	4	9	3.1995	20	61	96.8101
B89	8	8	8.0000	0.0000	0.00	153	159	8.7550	4	10	3.7275	17	42	15.4842
B90	5	5	5.2903	0.9016	0.00	152	156	2.2509	4	11	5.6435	17	49	22.9895
		AVG	8.1025	0.4576	0.00	153	171	21.1539	3	9	4.7263	13	43	23.8747