Table AI. The Objective values and...

Table AI.

The Objective values and computational times by CPLEX, UIMA, and the candidate population-based algorithms for the small-size problem instances

Problem instance	No. of vessels	No. of berths	CPLEX		UIMA		EA		PSO		EDA		DE
Problem instance	No. of vessels	No. of berths	Objective value, 10⁷ (US$)	CPU time, (sec)	Objective value, 10⁷ (US$)	CPU time, (sec)	Objective value, 10⁷ (US$)	CPU time, (sec)	Objective value, 10⁷ (US$)	CPU time, (sec)	Objective value, 10⁷ (US$)	CPU time, (sec)	Objective value, 10⁷ (US$)	CPU time, (sec)
P1	5	2	0.49	0.56	0.49	27.52	0.49	8.38	0.49	9.73	0.49	11.61	0.49	22.28
P2	5	3	0.46	0.90	0.46	27.45	0.46	8.36	0.46	9.70	0.46	11.58	0.46	22.38
P3	5	4	0.44	1.59	0.44	27.51	0.44	8.39	0.44	9.79	0.44	11.69	0.44	22.35
P4	7	2	0.80	3.31	0.80	31.12	0.80	9.51	0.80	11.07	0.80	13.02	0.80	23.68
P5	7	3	0.73	5.21	0.73	31.05	0.73	10.22	0.73	11.05	0.73	13.11	0.73	23.81
P6	7	4	0.70	5.69	0.70	31.61	0.70	9.98	0.70	11.08	0.70	13.18	0.70	23.83
P7	9	2	1.02	25.36	1.02	34.79	1.02	10.84	1.02	12.45	1.02	14.57	1.02	25.20
P8	9	3	0.93	50.74	0.93	34.95	0.93	11.04	0.93	12.44	0.93	14.80	0.93	25.22
P9	9	4	0.87	20.03	0.87	35.38	0.87	10.87	0.87	12.50	0.87	15.00	0.87	25.39
P10	11	2	1.22	79.46	1.22	38.10	1.22	12.02	1.24	13.73	1.24	16.18	1.24	26.75
P11	11	3	1.15	88.67	1.15	38.19	1.15	12.29	1.16	13.80	1.18	16.56	1.18	26.78
P12	11	4	1.06	59.65	1.06	38.66	1.08	12.65	1.09	13.83	1.09	16.99	1.07	26.77
P13	13	2	1.42	391.33	1.42	42.18	1.47	13.38	1.49	15.06	1.47	17.82	1.47	28.06
P14	13	3	1.36	679.36	1.39	42.09	1.43	13.34	1.44	15.10	1.44	17.82	1.42	28.25
P15	13	4	1.28	704.26	1.29	42.18	1.31	13.30	1.31	15.28	1.32	18.13	1.30	28.43
P16	15	2	1.56	326.48	1.59	45.37	1.62	14.43	1.64	16.49	1.63	19.15	1.62	29.63
P17	15	3	1.50	1393.49	1.53	45.47	1.56	14.56	1.56	16.47	1.58	19.52	1.58	30.34
P18	15	4	1.47	2348.76	1.50	45.78	1.53	14.57	1.54	16.68	1.55	19.85	1.55	30.25
P19	17	2	1.77	1461.42	1.81	49.20	1.85	15.92	1.87	17.87	1.88	20.83	1.87	31.52
P20	17	3	1.85	7237.00	1.76	49.41	1.82	15.86	1.84	17.91	1.89	21.20	1.88	31.31
P21	17	4	1.78	7225.15	1.71	49.58	1.73	15.91	1.75	18.12	1.76	21.68	1.75	31.36
P22	20	3	2.31	7277.19	2.25	54.62	2.29	17.91	2.31	19.93	2.35	24.53	2.36	34.26
P23	20	4	2.26	7303.72	2.05	54.85	2.07	17.62	2.09	20.10	2.07	24.66	2.06	33.85
P24	20	5	1.97	7328.10	1.88	55.14	1.91	17.76	1.93	20.10	1.92	25.81	1.92	33.92
Average			1.27	1834.06	1.25	40.51	1.27	12.88	1.28	14.59	1.28	17.47	1.28	27.73

Problem instance	No. of vessels	No. of berths	CPLEX		UIMA		EA		PSO		EDA		DE
Problem instance	No. of vessels	No. of berths	Objective value, 10⁷ (US$)	CPU time, (sec)	Objective value, 10⁷ (US$)	CPU time, (sec)	Objective value, 10⁷ (US$)	CPU time, (sec)	Objective value, 10⁷ (US$)	CPU time, (sec)	Objective value, 10⁷ (US$)	CPU time, (sec)	Objective value, 10⁷ (US$)	CPU time, (sec)
P1	5	2	0.49	0.56	0.49	27.52	0.49	8.38	0.49	9.73	0.49	11.61	0.49	22.28
P2	5	3	0.46	0.90	0.46	27.45	0.46	8.36	0.46	9.70	0.46	11.58	0.46	22.38
P3	5	4	0.44	1.59	0.44	27.51	0.44	8.39	0.44	9.79	0.44	11.69	0.44	22.35
P4	7	2	0.80	3.31	0.80	31.12	0.80	9.51	0.80	11.07	0.80	13.02	0.80	23.68
P5	7	3	0.73	5.21	0.73	31.05	0.73	10.22	0.73	11.05	0.73	13.11	0.73	23.81
P6	7	4	0.70	5.69	0.70	31.61	0.70	9.98	0.70	11.08	0.70	13.18	0.70	23.83
P7	9	2	1.02	25.36	1.02	34.79	1.02	10.84	1.02	12.45	1.02	14.57	1.02	25.20
P8	9	3	0.93	50.74	0.93	34.95	0.93	11.04	0.93	12.44	0.93	14.80	0.93	25.22
P9	9	4	0.87	20.03	0.87	35.38	0.87	10.87	0.87	12.50	0.87	15.00	0.87	25.39
P10	11	2	1.22	79.46	1.22	38.10	1.22	12.02	1.24	13.73	1.24	16.18	1.24	26.75
P11	11	3	1.15	88.67	1.15	38.19	1.15	12.29	1.16	13.80	1.18	16.56	1.18	26.78
P12	11	4	1.06	59.65	1.06	38.66	1.08	12.65	1.09	13.83	1.09	16.99	1.07	26.77
P13	13	2	1.42	391.33	1.42	42.18	1.47	13.38	1.49	15.06	1.47	17.82	1.47	28.06
P14	13	3	1.36	679.36	1.39	42.09	1.43	13.34	1.44	15.10	1.44	17.82	1.42	28.25
P15	13	4	1.28	704.26	1.29	42.18	1.31	13.30	1.31	15.28	1.32	18.13	1.30	28.43
P16	15	2	1.56	326.48	1.59	45.37	1.62	14.43	1.64	16.49	1.63	19.15	1.62	29.63
P17	15	3	1.50	1393.49	1.53	45.47	1.56	14.56	1.56	16.47	1.58	19.52	1.58	30.34
P18	15	4	1.47	2348.76	1.50	45.78	1.53	14.57	1.54	16.68	1.55	19.85	1.55	30.25
P19	17	2	1.77	1461.42	1.81	49.20	1.85	15.92	1.87	17.87	1.88	20.83	1.87	31.52
P20	17	3	1.85	7237.00	1.76	49.41	1.82	15.86	1.84	17.91	1.89	21.20	1.88	31.31
P21	17	4	1.78	7225.15	1.71	49.58	1.73	15.91	1.75	18.12	1.76	21.68	1.75	31.36
P22	20	3	2.31	7277.19	2.25	54.62	2.29	17.91	2.31	19.93	2.35	24.53	2.36	34.26
P23	20	4	2.26	7303.72	2.05	54.85	2.07	17.62	2.09	20.10	2.07	24.66	2.06	33.85
P24	20	5	1.97	7328.10	1.88	55.14	1.91	17.76	1.93	20.10	1.92	25.81	1.92	33.92
Average			1.27	1834.06	1.25	40.51	1.27	12.88	1.28	14.59	1.28	17.47	1.28	27.73

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