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

Table 24

MBO using parallel merge sort algorithm with 4 threads.

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	216	109.1743	2	6	3.6142	9	42	25.9406
B2	11	11	11.0000	0.0000	0.00	152	157	6.6604	2	4	1.2365	10	18	7.4686
B3	11	11	11.0000	0.0000	0.00	152	166	47.4789	1	4	1.2960	4	18	8.4496
B4	11	11	11.0000	0.0000	0.00	152	155	2.5716	1	5	2.6331	4	20	10.8924
B5	11	11	11.3871	1.4984	0.00	153	167	45.7047	1	6	3.3085	4	29	18.6757
B6	7	7	7.0000	0.0000	0.00	154	162	9.6934	2	9	5.7726	8	40	24.3002
B7	6	6	6.0000	0.0000	0.00	154	167	41.5747	3	6	2.6845	12	26	10.8095
B8	4	4	4.3226	0.7478	0.00	153	155	2.5003	2	11	9.7807	8	49	39.5824
B9	3	3	3.0645	0.2497	0.00	152	168	58.7230	2	6	2.9494	8	27	17.1893
B10	3	3	3.0000	0.0000	0.00	152	166	41.0109	2	4	1.9355	8	20	9.1206
B11	4	4	4.1290	0.3408	0.00	155	160	4.3005	2	10	6.9986	8	43	29.6649
B12	4	4	4.0000	0.0000	0.00	153	166	41.1127	1	4	1.8044	4	19	7.2704
B13	4	4	4.0000	0.0000	0.00	152	155	2.5059	2	6	4.9324	8	25	20.2386
B14	3	3	3.1935	0.4016	0.00	152	167	46.3310	1	5	2.2269	4	26	14.4843
B15	1	1	1.3548	0.8386	0.00	152	154	2.6249	2	5	3.1356	8	24	12.8711
B16	14	14	14.0000	0.0000	0.00	154	171	46.8582	3	8	4.1048	12	36	19.3441
B17	13	13	13.0000	0.0000	0.00	154	157	4.7342	2	5	1.9903	8	21	8.5249
B18	13	13	13.0000	0.0000	0.00	152	166	40.2106	3	5	1.9210	12	26	11.5105
B19	13	13	13.1935	0.7492	0.00	152	157	9.6044	2	7	4.3160	8	29	17.8754
B20	13	13	13.0000	0.0000	0.00	152	165	54.4453	2	7	3.8504	8	32	17.1361
B21	9	9	9.2258	0.4250	0.00	154	173	54.5359	2	11	7.4947	10	51	32.7887
B22	6	6	6.0968	0.3005	0.00	154	160	5.8877	3	5	2.8044	12	24	11.6705
B23	6	6	6.0645	0.2497	0.00	152	169	48.5055	2	7	4.5711	8	35	21.3986
B24	5	5	5.2581	0.5755	0.00	152	154	2.3010	2	6	2.7875	8	25	11.3416
B25	4	4	4.1935	0.4016	0.00	152	167	46.4296	2	6	2.6644	8	27	23.6771
B26	5	5	5.0000	0.0000	0.00	154	158	3.7574	3	8	6.3478	15	37	26.7206
B27	3	3	3.0323	0.1796	0.00	154	168	47.1433	2	5	3.5903	9	26	19.3762
B28	3	3	3.3226	0.4752	0.00	152	158	19.6735	1	5	3.6966	4	23	15.3801
B29	3	3	3.1613	0.4544	0.00	152	163	41.5225	2	5	3.3315	8	25	35.7845
B30	2	2	2.4839	0.5699	0.00	152	165	44.6843	2	7	5.1800	8	30	22.1249
B31	7	7	7.0000	0.0000	0.00	153	161	6.9997	3	8	4.2651	12	37	18.4910
B32	4	4	4.2903	0.9016	0.00	155	205	147.1775	1	8	5.0298	5	40	29.8585
B33	4	4	4.0645	0.3592	0.00	153	172	25.2682	2	5	3.2974	8	25	13.9995
B34	4	4	4.3226	0.7478	0.00	152	155	3.4554	1	6	6.1399	4	28	24.5491
B35	4	4	4.3871	0.8032	0.00	152	157	7.2196	2	5	2.8979	8	23	11.7220
B36	13	13	13.0000	0.0000	0.00	158	172	15.0594	3	10	5.7384	12	46	26.7314
B37	10	10	10.4516	0.8500	0.00	154	166	14.1400	2	8	6.8311	8	38	28.5876
B38	8	8	8.0323	0.1796	0.00	155	164	12.4326	2	8	5.6068	8	37	23.8998
B39	5	5	5.3548	1.3796	0.00	154	163	12.5069	2	5	2.0884	8	22	9.4440
B40	5	5	5.2581	0.6816	0.00	153	165	16.5927	2	5	3.6106	8	24	15.9870
B41	8	8	8.1613	0.8980	0.00	156	166	9.9435	1	10	8.3483	4	47	36.1707
B42	8	8	8.0000	0.0000	0.00	155	174	34.2187	2	4	1.6350	8	19	8.1873
B43	8	8	8.0000	0.0000	0.00	153	198	46.1624	1	4	2.1423	4	24	13.0368
B44	5	5	5.7742	1.3344	0.00	156	183	32.3323	2	5	1.6919	10	25	9.0367
B45	5	5	5.8065	1.4005	0.00	152	157	4.5948	2	5	2.8658	9	24	12.1692
B46	8	8	8.0323	0.1796	0.00	157	176	28.1980	3	10	7.1360	14	50	40.1945
B47	5	5	5.1935	0.7492	0.00	155	183	36.2397	2	6	2.5649	8	31	16.0299
B48	5	5	5.1935	0.6011	0.00	152	166	23.6329	2	5	2.2832	8	24	10.1954
B49	5	5	5.2581	0.6816	0.00	152	155	2.8071	2	5	2.4613	8	22	10.1229
B50	5	5	5.1290	0.4995	0.00	152	155	4.6881	2	7	5.3336	8	30	25.5601
B51	27	27	28.2903	1.0064	0.00	159	164	4.3110	4	22	9.2894	16	98	40.3385
B52	18	18	19.0645	1.0935	0.00	154	159	5.8249	5	22	9.8280	22	95	42.6600
B53	11	11	11.0000	0.0000	0.00	153	178	32.7949	4	11	3.7102	19	51	18.7233
B54	11	11	11.0000	0.0000	0.00	153	164	19.9278	3	7	2.7140	12	34	14.0533
B55	7	7	7.0000	0.0000	0.00	155	160	3.4790	2	10	4.3510	8	46	18.3698
B56	6	6	6.0000	0.0000	0.00	154	156	1.7121	2	10	3.2772	8	42	13.7300
B57	6	6	6.0323	0.1796	0.00	153	160	16.4040	4	10	3.8788	17	45	16.0311
B58	6	6	6.0323	0.1796	0.00	154	168	26.7755	3	10	3.9119	12	45	16.9634
B59	9	9	9.2258	0.4973	0.00	155	194	38.6829	3	15	8.8444	13	76	44.3162
B60	4	4	4.9032	1.7001	0.00	154	169	24.2931	3	12	6.6625	13	54	30.0641
B61	4	4	4.1290	0.5623	0.00	155	268	200.8557	4	12	7.0176	16	109	179.0541
B62	4	4	4.0000	0.0000	0.00	153	157	4.2149	3	9	3.8691	13	40	15.6801
B63	27	27	27.2581	0.5143	0.00	154	165	10.6263	6	16	9.2118	24	71	40.8554
B64	18	18	18.4516	0.8099	0.00	154	178	18.2276	7	19	9.1876	31	91	45.9490
B65	14	14	14.0323	0.1796	0.00	155	161	7.8149	6	15	7.3228	25	68	30.9394
B66	13	13	13.0000	0.0000	0.00	155	194	41.5668	6	10	3.4251	24	52	21.8884
B67	11	11	11.0323	0.1796	0.00	158	210	67.1852	1	13	6.8971	4	72	42.9510
B68	8	8	8.3226	1.2751	0.00	153	197	51.5259	4	13	7.9708	16	68	52.5572
B69	8	8	8.5806	0.6720	0.00	155	208	84.9156	5	11	5.6323	21	60	31.5805
B70	6	6	6.5484	0.8884	0.00	154	231	66.9705	4	15	8.5271	29	91	56.9068
B71	6	6	6.0645	0.3592	0.00	157	217	70.6903	3	12	6.9808	14	71	46.9560
B72	4	4	4.2258	0.4250	0.00	161	189	40.5461	5	13	7.1670	24	68	41.0736
B73	4	4	4.4516	0.6239	0.00	156	177	29.4202	4	13	5.3836	20	59	23.6061
B74	3	3	3.3871	0.5584	0.00	154	161	4.3200	3	13	7.5998	12	55	32.4734
B75	11	11	11.7742	1.0866	0.00	155	172	13.9606	4	15	9.4963	16	69	45.7583
B76	5	5	5.1935	0.6011	0.00	154	159	4.2812	4	13	6.7199	16	55	28.2946
B77	5	5	5.9677	1.1968	0.00	154	157	3.0589	4	12	7.3398	16	54	30.8010
B78	4	4	4.6452	1.1120	0.00	153	156	2.6757	1	13	7.3425	4	56	30.7701
B79	14	14	14.0000	0.0000	0.00	154	161	5.2525	4	10	2.9487	18	43	12.1078
B80	11	11	11.0000	0.0000	0.00	155	202	147.0668	3	11	5.4449	16	50	26.2353
B81	11	11	11.4516	0.9605	0.00	155	208	59.8935	7	13	4.7648	28	74	32.8557
B82	10	10	10.6452	0.7978	0.00	155	190	37.9565	4	13	7.3710	20	68	41.9503
B83	12	12	12.0000	0.0000	0.00	155	162	6.1394	3	10	5.8394	12	48	28.0464
B84	12	12	12.1935	0.6011	0.00	154	158	2.8090	7	12	6.3531	28	53	25.9466
B85	8	8	9.1613	1.7146	0.00	154	156	1.8346	4	13	6.5165	16	57	27.0130
B86	8	8	8.0000	0.0000	0.00	153	157	3.0107	3	11	3.7543	14	47	15.8781
B87	10	10	10.8065	1.0462	0.00	156	168	14.7487	6	17	9.3396	24	78	43.8068
B88	8	8	8.1935	1.0776	0.00	154	157	2.8132	4	10	5.2145	16	44	21.6391
B89	8	8	8.0000	0.0000	0.00	154	157	2.5607	3	10	4.7956	13	44	20.3743
B90	5	5	5.3871	1.0223	0.00	154	156	2.1397	4	11	4.6769	16	46	19.3850
		AVG	8.1183	0.4847	0.00	153	170	28.8802	2	9	4.9501	12	43	25.6019