Discrete Bat Algorithm for Optimal Problem of Permutation Flow Shop Scheduling

Table 2

Statistical performances of DBA, PSOMA, PSOVNS, and OSA.

Problem	DBA					PSOVNS			PSOMA			OSA
		BRE	ARE	WRE	Std	BRE	ARE	WRE	BRE	ARE	WRE	BRE	ARE	Std
Car1	7038	0	0	0	0	0	0	0	0	0	0	0	0	0
Car2	7166	0	0	0	0	0	0	0	0	0	0	0	0	0
Car3	7312	0	0.397	1.190	42.45	0	0.420	1.189	0	0	0	0	0.625	47.19
Car4	8003	0	0	0	0	0	0	0	0	0	0	0	0	0
Car5	7720	0	0	0	0	0	0.039	0.389	0	0.018	0.375	0	0.801	50.73
Car6	8505	0	0	0	0	0	0.076	0.764	0	0.114	0.764	0	2.093	274.71
Car7	6590	0	0	0	0	0	0	0	0	0	0	0	1.483	114.21
Car8	8366	0	0	0	0	0	0	0	0	0	0	0	2.297	254.63
Rec1	1247	0	0.080	0.160	0.85	0.160	0.168	0.321	0	0.144	0.160	0.160	0.160	0
Rec3	1109	0	0.081	0.180	0.88	0	0.158	0.180	0	0.189	0.721	0	0.189	1.85
Rec5	1245	0.242	0.242	0.242	0	0.242	0.249	0.420	0.242	0.249	0.402	0.242	0.588	4.62
Rec7	1566	0	0.575	1.149	9.40	0.702	1.095	1.405	0	0.986	1.149	0	0.434	11.59
Rec9	1537	0	0.638	2.407	15.00	0	0.651	1.366	0	0.621	1.691	0	0.690	12.39
Rec11	1431	0	1.167	2.655	11.17	0.071	1.153	2.656	0	0.129	0.978	0	2.215	37.60
Rec13	1938	0.415	1.461	3.782	19.01	1.036	1.790	2.643	0.259	0.893	1.502	0.311	1.793	14.69
Rec15	1953	0.154	1.226	2.103	7.97	0.769	1.487	2.256	0.051	0.628	1.076	0.718	1.569	16.07
Rec17	1909	0.368	1.277	2.154	41.65	0.999	2.453	3.365	0	1.330	2.155	1.840	3.796	36.72
Rec19	2105	0.573	0.929	2.023	33.06	1.529	2.099	2.532	0.430	1.313	2.102	0.287	0.803	9.48
Rec21	2046	1.438	1.671	2.231	4.04	1.487	1.671	2.033	1.437	1.596	1.636	1.438	1.477	1.69
Rec23	2027	0.796	1.173	2.381	39.27	1.343	2.106	2.884	0.596	1.310	2.038	0.497	0.854	10.82
Rec25	2554	1.632	2.921	3.940	18.96	2.388	3.166	3.780	0.835	2.085	3.233	1.194	1.938	15.06
Rec27	2397	1.011	1.419	2.298	21.35	1.728	2.463	3.203	1.348	1.605	2.402	0.843	1.845	21.06
Rec29	2311	1.049	2.580	3.935	22.84	1.968	3.109	4.067	1.442	1.888	2.492	0.612	2.882	38.83
Rec31	3115	2.299	3.392	4.532	23.66	2.594	3.232	4.237	1.510	2.254	2.692	0.296	1.333	30.39
Rec33	3133	0.610	0.728	1.734	39.40	0.835	1.007	1.477	0	0.645	0.834	0.128	0.732	7.32
Rec35	3277	0	0.037	0.092	1.52	0	0.038	0.092	0	0	0	0	0	0
Rec37	5118	3.373	4.872	5.979	40.31	4.383	4.949	5.736	2.101	3.537	4.039	2.000	2.751	25.43
Rec39	5203	2.280	3.851	5.347	45.97	2.850	3.371	5.585	1.553	2.426	2.830	0.767	1.240	12.31
Rec41	5149	3.810	5.095	6.532	42.89	4.173	4.867	5.585	2.641	3.684	4.052	1.734	2.726	39.38