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

Table 4

Comparison of the four algorithms for large 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
100 × 2 × X × H1	85002.6	80394	8.89	86004.0	83364	10.18	86182.8	85224	10.41	81648.6	78060	4.60	563.30
100 × 2 × Y × H1	164413.6	162340	8.69	165181.4	164110	9.20	164004.7	160820	8.42	154190.4	151270	1.93	570.34
100 × 3 × X × H1	46886.7	45298	6.64	47590.7	45573	8.24	47375.1	45339	7.75	44838.0	43968	1.98	674.16
100 × 3 × Y × H1	162497.4	162030	7.42	163215.7	162620	7.90	163404.8	162140	8.02	154372.7	151270	2.05	691.13
100 × 5 × X × H1	111831.0	103973	9.28	113080.3	109763	10.50	111534.2	108734	8.99	105269.5	102336	2.87	800.00
100 × 5 × Y × H1	27299.4	26998	8.45	27476.4	27194	9.15	27325.2	26392	8.55	25724.9	25173	2.19	800.00
120 × 2 × X × H1	67987.9	64257	8.94	69349.3	68724	11.13	68148.8	65922	9.20	64419.3	62406	3.23	755.67
120 × 2 × Y × H1	181648.0	174368	8.44	182875.2	175072	9.18	182338.4	176600	8.86	172412.8	167504	2.93	759.46
120 × 3 × X × H1	250104.5	244510	11.00	254437.3	251670	12.93	249121.0	242280	10.57	232410.3	225310	3.15	800.00
120 × 3 × Y × H1	156395.6	155288	8.31	158088.0	157040	9.48	157724.8	157128	9.23	147907.2	144400	2.43	800.00
120 × 5 × X × H1	353503.5	349220	7.68	355892.7	351950	8.40	534840.2	351250	8.08	331862	328300	1.08	800.00
120 × 5 × Y × H1	317292.8	303048	6.99	318821.6	312832	7.50	314614.4	311240	6.08	302820.8	296576	2.11	800.00
Average	160405.3	155977	8.39	161834.4	159159	9.48	175551.2	157756	8.68	151489.7	148048	2.55	734.51
n × S × mk × H2
100 × 2 × X × H2	30774.4	30210	4.67	31132.6	30408	5.89	30855.8	30238	4.94	30072.0	29402	2.28	563.30
100 × 2 × Y × H2	36300.3	34101	6.45	36957.0	36483	8.38	36704.4	36333	7.63	35929.5	34662	5.36	570.34
100 × 3 × X × H2	46820.3	44035	9.09	48176.5	46020	12.25	47780.5	45895	11.32	42967.4	42920	0.11	674.16
100 × 3 × Y × H2	96520.6	93430	5.07	97543.1	93552	6.18	97208.4	93372	5.82	92908.5	91886	1.13	691.13
100 × 5 × X × H2	233298.4	229788	9.26	235390.2	222711	10.24	233203.8	227548	9.22	215706.6	213516	1.03	800.00
100 × 5 × Y × H2	26102.1	25189	9.10	26158.0	25455	9.33	25978.5	25208	8.58	24693.1	23925	3.21	800.00
120 × 2 × X × H2	146292.3	141300	3.81	150106.5	148113	6.52	148338.0	144729	5.26	143712.9	140992	1.98	755.67
120 × 2 × Y × H2	110558.5	107555	9.29	109579.0	108495	8.32	108672.5	107310	7.42	105177.0	101165	3.97	759.46
120 × 3 × X × H2	244468.6	238810	6.30	248267.6	237611	7.96	246137.8	240340	7.03	235697.3	229970	2.49	800.00
120 × 3 × Y × H2	73899.5	70101	7.02	74268.4	72523	7.55	74104.5	70653	7.31	70228.2	69054	1.70	800.00
120 × 5 × X × H2	282084.6	271104	8.07	283192.5	271120	8.50	279734.2	270824	7.18	266991.9	261000	2.30	800.00
120 × 5 × Y × H2	258686.4	245560	7.55	267808.8	264159	11.34	264243.0	257390	9.86	247565.3	240536	2.92	800.00
Average	132150.5	127599	7.14	134048.4	129721	8.54	132746.8	129153	7.63	125970.8	123252	2.37	734.51