An Improved Discrete Artificial Bee Colony Algorithm for Flexible Flowshop Scheduling with Step Deteriorating Jobs and Sequence-Dependent Setup Times

Table 3

Comparison of the four algorithms for small and medium instances.

n × S × mk × h	GA			GH			VNS			IDABC			CPU time
	Avg	Min	ARPI	Avg	Min	ARPI	Avg	Min	ARPI	Avg	Min	ARPI
n × S × mk × H1
10 × 2 × X × H1	1754.4	1710	3.32	1735.8	1704	2.23	1725.6	1704	1.63	1709.4	1698	0.07	25.52
10 × 2 × Y × H1	778.2	765	2.74	787.8	765	2.98	776.7	765	1.53	765.3	765	0.04	27.19
10 × 3 × X × H1	1081.8	1065	1.73	1081.2	1053	2.67	1130.4	1071	7.35	1056.9	1053	0.37	49.66
10 × 3 × Y × H1	1592.8	1552	3.32	1594.4	1572	2.73	1577.2	1552	1.62	1564.8	1552	0.82	42.11
10 × 5 × X × H1	4236.1	4135	2.62	4225.1	4119	3.05	4225.9	4101	3.07	4216.0	4100	2.83	78.03
10 × 5 × Y × H1	4430.3	4354	1.75	4435.9	4368	1.88	4363.8	4354	0.22	4358.2	4354	0.10	81.33
40 × 2 × X × H1	17268.0	16626	3.35	17857.8	17622	11.01	17208.6	16836	6.98	16736.4	16808	4.04	146.63
40 × 2 × Y × H1	16813.6	16192	4.14	17879.2	17480	10.75	17276.0	16872	7.01	16409.6	16144	1.65	139.72
40 × 3 × X × H1	39717.0	38140	4.55	40121.3	39170	5.61	40267.2	38860	5.99	38991.2	37990	2.63	262.19
40 × 3 × Y × H1	16295.5	15995	3.39	16700.5	16345	5.97	16326.0	15875	3.59	15999.5	15760	1.52	189.74
40 × 5 × X × H1	17268.0	16060	7.52	17357.8	16626	8.08	17208.6	16836	7.15	16736.4	16086	4.21	346.06
40 × 5 × Y × H1	45633.6	44064	6.29	45929.7	44784	6.99	44965.8	44379	4.74	44474.4	42930	3.60	482.23
70 × 2 × X × H1	7312.4	7115	8.70	7445.0	7204	10.67	7397.3	7247	9.96	7163.6	6727	6.49	294.42
70 × 2 × Y × H1	42046.9	40474	8.64	43504.3	41874	12.41	43201.9	42287	11.62	40496.4	38703	4.63	281.67
70 × 3 × X × H1	39585.9	38406	8.68	39309.6	38298	7.93	39376.8	37869	8.11	37216.2	36423	2.18	496.63
70 × 3 × Y × H1	67027.4	64744	6.36	67655.0	65840	7.35	66655.0	64952	5.76	63835.7	63033	1.29	429.50
70 × 5 × X × H1	51786.4	50873	7.44	51987.9	51003	7.84	51972.9	51030	7.81	48987.1	48201	1.61	734.33
70 × 5 × Y × H1	81461.2	80544	7.00	81714.2	80664	7.33	81300.2	80210	6.79	77476.8	76134	1.76	789.32
Average	25338.3	24601	5.09	25629.0	25027	6.53	25386.4	24822	5.61	24344.1	23803	2.21	272.02
n × S × mk × H2
10 × 2 × X × H2	1126.0	1108	1.62	1120.0	1108	1.08	1122.4	1108	1.30	1108.4	1108	0.04	25.52
10 × 2 × Y × H2	1020.6	999	2.47	1029.6	1011	3.37	1020.9	1014	2.50	1001.7	996	0.58	27.19
10 × 3 × X × H2	469.9	461	2.37	470.5	461	2.51	468.0	459	1.96	460.4	459	0.31	49.66
10 × 3 × Y × H2	3003.0	2926	2.63	2974.0	2926	0.71	2946.3	2926	0.69	2926.4	2926	0.01	42.11
10 × 5 × X × H2	4823.6	4802	2.02	4831.9	4801	2.20	4856.8	4802	2.72	4804.1	4728	1.61	78.03
10 × 5 × Y × H2	4261.6	4200	2.05	4274.4	4200	2.36	4215.2	4176	0.94	4176.8	4176	0.02	81.33
40 × 2 × X × H2	8677.2	8304	4.76	8999.1	8607	8.65	8837.4	8676	6.69	8530.8	8232	2.99	146.63
40 × 2 × Y × H2	6795.0	6507	5.30	7229.7	7050	12.04	6890.4	6711	6.78	6614.4	6453	2.50	139.72
40 × 3 × X × H2	22859.4	22218	7.41	25345.8	22872	10.64	22761.0	22110	6.95	21937.8	21282	3.08	262.19
40 × 3 × Y × H2	3179.7	3090	3.30	3248.5	3195	5.54	3196.8	3127	3.86	3122.6	3078	1.45	189.74
40 × 5 × X × H2	39642.2	39099	4.21	39505.9	38739	3.89	39667.5	39494	4.32	38536.0	38025	1.34	346.06
40 × 5 × Y × H2	34203.4	33327	4.14	34980.4	34174	6.50	34365.8	33782	4.63	33717.6	32884	2.66	482.23
70 × 2 × X × H2	52081.9	50935	5.76	53207.0	52353	8.05	52888.6	52086	7.40	50476.3	49245	2.50	294.42
70 × 2 × Y × H2	68669.4	65230	7.97	68177.7	66990	7.20	68780.6	66240	8.14	66003.8	63600	3.78	281.67
70 × 3 × X × H2	50135.6	48936	4.57	51162.1	49422	6.71	50552.6	49806	5.44	48794.7	47946	1.77	496.63
70 × 3 × Y × H2	24507.3	24162	5.15	24948.9	24729	7.04	24859.2	24399	6.66	24277.6	23308	4.15	429.50
70 × 5 × X × H2	61215.0	60342	7.73	61804.5	61083	8.77	61518.9	60497	8.26	57294.3	56823	0.83	734.33
70 × 5 × Y × H2	54368.4	53136	5.93	55100.4	53332	7.35	54555.6	53724	6.29	52626.0	51328	2.53	789.32
Average	24502.2	23877	4.32	24911.7	24281	5.81	24639.1	24174	4.75	23689.4	23144	1.79	272.02