Robust Parallel Machine Scheduling Problem with Uncertainties and Sequence-Dependent Setup Time

Table 3

The best computational performance for robust parallel machine scheduling using modified ABC algorithm.

			MIP w/Cplex						Modified ABC algorithm
			Optimal	Iteration	CPU	Regret; UB	Regret; LB	Regret; gap	Best	Best	CPU	# best	DFB
21	3	20	368.4	2	1.46	0.00	0.00	0.00	368.40	4.00	381.22	7	0.00
		40	363.6	2	TL	41.50	6.30	84.82	363.60	2.00	246.51	3	0.00
		60	346.2	0	TL	119.90	0.00	100.00	368.40	7.00	702.52	1	6.03
		80	400.2	1	TL	96.10	0.00	100.00	404.60	10.00	1225.68	2	1.09
		100	378	0	TL	174.50	0.00	100.00	394.00	10.00	1167.61	1	4.06
21	4	20	332	3	63.15	0.00	0.00	0.00	332.00	1.00	126.41	7	0.00
		40	338.4	3	58.35	0.00	0.00	0.00	338.40	1.00	258.02	4	0.00
		60	346.2	5	119.16	15.90	36.40	0.00	346.20	7.00	1359.59	5	0.00
		80	342.6	4	298.16	22.00	45.00	0.00	342.60	10.00	1730.55	2	0.00
		100	350.6	4	TL	43.90	3.30	92.48	350.60	10.00	1821.72	7	0.00
21	5	20	332	0	7.43	0.00	0.00	0.00	332.00	0.00	184.60	5	0.00
		40	332	9	91.40	21.50	31.60	0.00	332.00	0.00	215.59	3	0.00
		60	332	8	82.64	27.20	36.40	0.00	334.60	10.00	3020.11	4	0.78
		80	342.6	8	110.42	8.20	22.00	0.00	342.60	10.00	2351.84	4	0.00
		100	332	8	90.58	56.20	62.00	0.00	332.00	10.00	2704.27	1	0.00
27	3	20	442	1	TL	67.70	0.00	100.00	474.20	4.00	733.30	0	6.79
		40	446.8	0	TL	102.80	0.00	100.00	511.00	6.00	1112.00	0	12.56
		60	487.4	0	TL	118.40	0.00	100.00	465.80	2.00	2140.45	2	−4.64
		80	498.8	0	TL	163.20	0.00	100.00	501.60	10.00	2084.83	0	0.56
		100	514.6	0	TL	218.80	0.00	100.00	499.00	10.00	2084.33	2	−3.13
27	4	20	463	2	TL	28.80	10.00	65.28	418.00	0.00	252.50	6	−10.77
		40	469.4	2	TL	55.10	10.00	81.85	434.00	0.00	253.65	10	−8.16
		60	435.4	1	TL	84.30	0.00	100.00	426.00	10.00	3576.53	4	−2.21
		80	482.2	2	TL	108.30	0.00	100.00	440.40	10.00	3570.41	10	−9.49
		100	488.6	2	TL	127.70	0.00	100.00	439.30	10.00	3588.61	10	−11.22
27	5	20	418	3	TL	22.10	2.70	87.78	418.00	0.00	296.45	9	0.00
		40	418	2	TL	32.30	6.00	81.42	418.00	10.00	3511.84	3	0.00
		60	418	3	TL	31.20	4.40	85.90	418.00	10.00	4067.50	8	0.00
		80	435.4	3	TL	57.20	21.30	62.76	422.40	10.00	4393.53	4	−3.08
		100	429	10	TL	59.50	70.60	0.00	418.00	10.00	4433.44	2	−2.63
33	3	20	575.6	0	3541.30	0.00	0.00	0.00	575.60	6.00	1930.36	3	0.00
		40	585	1	TL	118.50	26.20	77.89	596.50	5.00	1866.59	0	1.93
		60	560.2	0	TL	0.00	0.00	0.00	584.80	10.00	4416.73	0	4.21
		80	618.9	1	TL	215.20	17.50	91.87	614.80	7.00	3997.03	2	−0.67
		100	602	0	TL	293.50	0.00	100.00	575.90	8.00	4318.77	2	−4.53
33	4	20	556.5	8	TL	18.80	0.00	100.00	519.00	1.00	1209.28	8	−7.23
		40	562.9	4	TL	89.30	66.00	26.09	527.00	5.00	4797.14	6	−6.81
		60	540.2	2	TL	115.80	13.20	88.60	557.60	6.00	4299.88	6	3.12
		80	519	2	TL	194.90	0.00	100.00	524.20	6.00	4707.69	2	0.99
		100	519	2	TL	152.00	34.70	77.17	542.00	6.00	4430.14	0	4.24
33	5	20	556.5	2	463.82	0.00	0.00	0.00	556.50	0.00	925.34	10	0.00
		40	562.9	8	1614.77	15.40	33.80	0.00	566.20	0.00	976.70	10	0.58
		60	519	11	2449.81	48.40	50.30	0.00	519.00	5.00	4530.66	8	0.00
		80	519	9	TL	88.00	41.40	52.95	519.00	5.00	4811.97	8	0.00
		100	519	8	TL	58.50	14.90	74.53	523.50	5.00	5248.92	0	0.86

percentage gap between regret lower bound value and regret upper bound value.
deviation in percentage between the average optimal value using modified ABC algorithm and the optimal value using MIP.
best solution (in terms of objective value and CPU time) obtained by MABC algorithm in 10 run times.