The Scientific World Journal

Research Article

Discrete Bat Algorithm for Optimal Problem of Permutation Flow Shop Scheduling

Table 1

Statistical performances of DBA, DBA_NEH1, and DBA-IVPNS.


Problem		DBA				DBA_NEH1				DBA-IVPNS
Problem		BRE	ARE	WRE	Std	BRE	ARE	WRE	Std	BRE	ARE	WRE	Std

Car1	7038	0	0	0	0	0	0	0	0	0	0	0	0
Car2	7166	0	0.195	2.931	54.22	0	0.391	2.931	73.89	0	0	0	0
Car3	7312	0	0.476	1.190	44.12	0	0.635	1.190	44.93	0	0.397	1.190	42.45
Car4	8003	0	0	0	0	0	0	0	0	0	0	0	0
Car5	7720	0	0.246	1.308	35.70	0	0.664	1.360	45.95	0	0.352	1.308	40.88
Car6	8505	0	0	0	0	0	0	0	0	0	0	0	0
Car7	6590	0	0	0	0	0	0	0	0	0	0	0	0
Car8	8366	0	0	0	0	0	0	0	0	0	0	0	0
Rec1	1247	0.160	0.209	0.722	1.84	0.160	0.241	1.043	2.85	0.160	0.545	1.925	7.92
Rec3	1109	0.090	0.481	2.164	7.09	0	0.499	1.803	6.09	0.180	0.385	1.713	4.51
Rec5	1242	0.242	0.623	2.174	9.49	0.242	0.768	2.496	10.72	0.242	1.100	2.496	10.69
Rec7	1566	1.149	1.443	3.831	11.41	1.149	2.048	3.831	18.33	1.149	1.537	3.831	13.54
Rec9	1537	0	2.420	3.709	13.44	0	2.065	3.318	15.98	1.041	2.728	4.815	13.13
Rec11	1431	0.559	1.975	3.564	13.56	0	2.241	7.617	29.69	0	1.859	4.403	16.64
Rec13	1930	0.415	2.394	3.938	19.84	0.933	2.525	4.819	19.30	1.762	2.694	4.352	16.29
Rec15	1950	0.154	2.178	4.615	23.43	0.821	2.410	4.615	24.23	1.231	2.903	4.256	19.21
Rec17	1902	0.946	2.685	4.206	19.27	0.894	3.582	5.941	25.20	1.577	5.065	6.730	25.65
Rec19	2093	0.573	2.621	4.252	21.38	1.386	2.599	4.730	19.58	2.484	3.883	5.542	20.28
Rec21	2017	1.438	2.310	4.412	19.89	1.636	2.568	5.702	24.05	1.785	3.543	5.255	19.50
Rec23	2011	0.945	3.216	5.868	23.88	1.591	3.090	4.923	19.22	3.282	4.422	6.266	18.48
Rec25	2513	2.348	3.520	5.213	20.71	1.870	3.489	5.133	23.77	3.780	5.428	6.805	19.57
Rec27	2373	2.402	3.638	5.057	19.03	1.728	3.217	5.900	23.66	2.023	4.374	5.942	23.93
Rec29	2287	1.530	4.323	7.084	33.64	2.186	3.615	5.597	24.60	4.766	6.046	7.521	19.20
Rec31	3045	3.284	4.917	6.502	30.44	3.153	4.926	6.765	38.21	5.353	6.192	7.783	21.95
Rec33	3114	0.835	1.916	4.143	29.20	1.317	2.338	4.528	26.65	1.927	2.899	4.689	25.99
Rec35	3277	0.092	0.484	2.014	18.73	0.092	1.082	3.021	36.89	0.244	1.107	2.563	20.99
Rec37	4951	5.615	7.172	8.140	39.66	5.918	7.387	8.826	37.75	8.503	9.156	10.261	21.68
Rec39	5087	3.696	5.578	6.408	41.52	4.914	6.083	7.529	35.22	6.979	7.629	8.374	23.50
Rec41	4960	6.129	7.435	8.952	33.55	6.573	7.589	8.952	29.22	8.105	9.319	10.726	37.80

Average		1.124	2.154	3.531	20.17	1.261	2.278	3.882	22.62	1.951	2.881	4.095	16.68