Large-Scale Storage/Retrieval Requests Sorting Algorithm for Multi-I/O Depots Automated Storage/Retrieval Systems

Table 6

Comparisons of existing methods with the proposed method.

Studies	N_r	N_d	CR	T_NN	Contrastive algorithm			GAP
					Algorithm	T _A	CPU
Gharehgozli et al. [27]	20	10	2	1113.10	TPHA	976.42	0.0177	136.68 s
Gharehgozli et al. [27]	50	10	2	2730.60	TPHA	2325.7	0.0397	404.90 s
Gharehgozli et al. [27]	100	10	2	5406.32	TPHA	4650.2	0.1321	756.12 s
Gharehgozli et al. [27]	150	10	2	8006.24	TPHA	6965.1	0.2973	1041.14 s
Gharehgozli et al. [27]	200	10	2	10692.10	TPHA	9190.7	0.5462	1501.4 s
Gharehgozli et al. [27]	100	10	1	6312.60	TPHA	6130.3	0.1147	182.30 s
Gharehgozli et al. [27]	100	10	1	6219.10	TPHA	6197.7	0.0942	21.40 s
Van den Berg and Gademann [28]	10	1	2	7.80	PA	7.3	—	0.5 UT
Van den Berg and Gademann [28]	20	1	2	14.70	PA	14.0	—	0.7 UT
Van den Berg and Gademann [28]	40	1	2	28.30	PA	27.1	—	1.2 UT
Van den Berg and Gademann [28]	10	2	1or2	11.30	PA	11.1	—	0.2 UT
Van den Berg and Gademann [28]	20	2	1or2	22.60	PA	22.4	—	0.2 UT
Van den Berg and Gademann [28]	40	2	1or2	45.40	PA	45.0	—	0.4 UT
Gharehgozli et al. [27]	10	2	2	544.69	PA	449.06	0.61	95.63 s
Gharehgozli et al. [27]	20	2	2	1048.19	PA	820.91	20.27	227.28 s
Gharehgozli et al. [27]	30	2	2	1609.64	PA	1240.39	187.04	369.25 s
Gharehgozli et al. [27]	40	2	2	2146.66	PA	1633.73	776.24	512.93 s
Gharehgozli et al. [27]	50	2	2	2603.50	PA	2005.75	1811.57	597.75 s
Popovic et al. [21]	12	1	6	343.60	ISL	312.84	—	30.76 s
Popovic et al. [21]	12	1	6	343.60	BH	307.81	<1	35.79 s
Popovic et al. [21]	12	1	6	343.60	GA	282.21	<20	61.39 s
Popovic et al. [21]	24	1	6	660.87	ISL	593.20	—	67.67 s
Popovic et al. [21]	24	1	6	660.87	BH	588.66	<16	72.21 s
Popovic et al. [21]	24	1	6	660.87	GA	521.09	<60	139.78 s
This paper	15	15	—	800.78	HA	760.96	0.0204	39.82 s
This paper	20	15	—	1088.40	HA	1057.70	0.0158	30.70 s
This paper	30	15	—	1588.88	HA	1557.38	0.0291	31.50 s
This paper	50	15	—	2647.08	HA	2604.80	0.0626	42.28 s
This paper	80	15	—	4134.93	HA	4089.18	0.1646	45.76 s
This paper	100	15	—	5360.85	HA	5295.70	0.3083	65.15 s

Note. N_r: number of S/R requests; N_d: number of I/O depots; CR: number of command cycle; T_NN: completion time obtained by nearest neighbor algorithm (sec); T_A: completion time obtained by specified algorithm (sec); CPU: computation time (sec); GAP: T_NN-T_A (sec); TPHA: Two-phase heuristic algorithm; PA: polynomial algorithm; ISL: improved shortest leg heuristic; BH: best heuristic; GA: genetic algorithm; HA: heuristic algorithm based on assignment.