Optimizing task scheduling in cloud computing: a hybrid artificial intelligence approach

Figures & data

Figure 1. Task scheduling model through cloud computing.

Table

j = job index	u = preceding operation
i = operation index	RTk j = Ij ∩ Ark, $I\in k,j$
J = job set	xj = job j ready time
nj = operation number in job j	xij = job j on machine i steady time.
n = $\sum _{j\in J}{n}_{j,}$ job set J total operations in	yk = ready time of vehicle k
I = {1, 2, 3……n} operation number	R(g) = machine ready time denoted by g
Ij = {Nj + 1, Nj + 2, ……Nj + nj}, I linked with j	R(i) = operation i machine ready time
IDi = I − {h; h ≥ i}, i without operation	mi = machine for operation
IDh = I − {i, i ≤ h} h without operation	S = {max[R(g), bk]}
TT = { } tool to carry out the job’s	OCT = {m1, m2, m4, m3} machines for operations
Tk = { } indices set in I linked with tool k in TT, $k\in \mathit{\text{TT}}$	Pti = operation i processing time
v = operation 1st	Cti = operation i completion time.

Figure 2. State-space vs objective function.

Figure 3. Hybrid hill climbing algorithm.

Table 1. Cost function calculation for J1 and L1 benchmark problems.

O_No	M_No	V_No	T_T	J_R	JRH	OCT
O4	M1	V1	0	6	6	26
O5	M3	V2	26	34	34	44
O6	M2	V1	44	50	50	68
O1	M1	V2	42	48	48	56
O2	M2	V2	56	62	68	84
O3	M4	V1	84	92	92	104
O12	M3	V2	72	82	82	92
O13	M1	V2	92	100	100	115
O10	M4	V1	98	110	110	124
O11	M2	V1	124	132	132	150
O7	M3	V2	112	122	122	134
O8	M4	V2	134	140	140	148
O9	M1	V1	148	158	158	173

Figure 4. Population, chromosome, and genes in the genetic algorithm.

Figure 5. The crossover position within the genetic algorithm.

Figure 6. The mutation process within a GA.

Table 2. Benchmark problems calculation for neighbor sequence.

O_No	M_No	V_No	T_T	J_R	JR_H	OC_T
O7	M3	V1	0	10	10	22
O8	M4	V2	22	28	28	36
O9	M1	V1	36	46	46	61
O10	M4	V2	34	46	46	60
O11	M2	V2	60	68	68	86
O4	M1	V1	58	64	64	84
O5	M3	V1	84	92	92	102
O6	M2	V2	102	108	108	126
O1	M1	V1	100	106	106	114
O2	M2	V1	114	120	126	142
O3	M4	V2	142	150	150	162
O12	M3	V1	130	140	140	150
O13	M1	V1	150	158	158	173

Table 3. Cost function through hill-climbing algorithm.

J.No	t/p	HCA	J.No	t/p	HCA	J.No	t/p	HCA	J.No	t/p	HCA
1.1	0.59	107	1.2	0.47	92	1.3	0.52	92	1.4	0.74	118
2.1	0.61	116	2.2	0.49	94	2.3	0.54	96	2.4	0.77	126
3.1	0.59	121	3.2	0.47	101	3.3	0.51	98	3.4	0.74	135
4.1	0.91	127	4.2	0.73	107	4.3	0.8	106	4.4	1.14	144
5.1	0.85	95	5.2	0.68	76	5.3	0.74	81	5.4	1.06	103
6.1	0.78	129	6.2	0.54	111	6.3	0.54	112	6.4	0.78	140
7.1	0.78	136	7.2	0.62	100	7.3	0.68	108	7.4	0.97	151
8.1	0.58	170	8.2	0.46	151	8.3	0.5	155	8.4	0.72	190
9.1	0.61	133	9.2	0.49	124	9.3	0.53	127	9.4	0.76	138
10.1	0.55	166	10.2	0.44	157	10.3	0.49	167	10.4	0.69	194

Table 4. Cost function through the hybrid algorithm.

F(xi)	ti/pi	GAHCA	F(xi)	ti/pi	HCA	F(xi)	ti/pi	HCA	F(xi)	ti/pi	HCA
1.1	0.59	102	1.2	0.47	84	1.3	0.52	88	1.4	0.74	111
2.1	0.61	112	2.2	0.49	89	2.3	0.54	94	2.4	0.77	122
3.1	0.59	116	3.2	0.47	95	3.3	0.51	97	3.4	0.74	127
4.1	0.91	125	4.2	0.73	100	4.3	0.8	102	4.4	1.14	141
5.1	0.85	89	5.2	0.68	73	5.3	0.74	76	5.4	1.06	101
6.1	0.78	125	6.2	0.54	110	6.3	0.54	108	6.4	0.78	139
7.1	0.78	130	7.2	0.62	93	7.3	0.68	100	7.4	0.97	135
8.1	0.58	165	8.2	0.46	151	8.3	0.5	153	8.4	0.72	175
9.1	0.61	131	9.2	0.49	112	9.3	0.53	117	9.4	0.76	133
10.1	0.55	167	10.2	0.44	153	10.3	0.49	154	10.4	0.69	191

Table 5. Percentage improvement between CDS and HCS.

Job	t/p	CDS (Prasad et al., 2023)	HCA	% of Improvement
4.3	0.8	234	106	120.75
9.4	0.76	295	138	113.77
4.2	0.73	225	107	110.28
4.4	1.14	299	144	107.64
1.2	0.47	190	92	106.52
4.1	0.91	260	127	104.72
9.2	0.49	249	124	100.81
9.1	0.61	263	133	97.74
9.3	0.53	251	127	97.64
5.2	0.68	149	76	96.05
10.1	0.55	312	166	87.95
10.2	0.44	284	157	80.89
10.4	0.69	348	194	79.38
5.3	0.74	145	81	79.01
5.4	1.06	182	103	76.70
3.3	0.51	173	98	76.53
3.2	0.47	178	101	76.24
1.3	0.52	162	92	76.09
6.1	0.78	225	129	74.42
3.1	0.59	211	121	74.38
6.4	0.78	237	140	69.29
10.3	0.49	279	167	67.07
3.4	0.74	224	135	65.93
1.1	0.59	173	107	61.68
6.2	0.54	179	111	61.26
1.4	0.74	189	118	60.17
5.1	0.85	147	95	54.74
8.1	0.58	261	170	53.53
7.4	0.97	227	151	50.33
8.4	0.72	285	190	50.00
2.1	0.61	172	116	48.28
2.2	0.49	137	94	45.74
7.1	0.78	194	136	42.65
6.3	0.54	156	112	39.29
7.2	0.62	139	100	39.00
2.4	0.77	174	126	38.10
2.3	0.54	130	96	35.42
7.3	0.68	142	108	31.48
8.2	0.46	181	151	19.87
8.3	0.5	183	155	18.06

Table 6. Percentage improvement between HCS and GHCS.

Job	t/p	HCA	GHCA	% Improvement
7.4	0.97	151	135	11.85
9.2	0.49	124	112	10.71
1.2	0.47	92	84	9.52
8.4	0.72	190	175	8.57
9.3	0.53	127	117	8.55
10.3	0.49	167	154	8.44
7.3	0.68	108	100	8.00
7.2	0.62	100	93	7.53
4.2	0.73	107	100	7.00
5.1	0.85	95	89	6.74
5.3	0.74	81	76	6.58
3.2	0.47	101	95	6.32
1.4	0.74	118	111	6.31
3.4	0.74	135	127	6.30
2.2	0.49	94	89	5.62
1.1	0.59	107	102	4.90
7.1	0.78	136	130	4.62
1.3	0.52	92	88	4.55
3.1	0.59	121	116	4.31
5.2	0.68	76	73	4.11
4.3	0.8	106	102	3.92
9.4	0.76	138	133	3.76
6.3	0.54	112	108	3.70
2.1	0.61	116	112	3.57
2.4	0.77	126	122	3.28
6.1	0.78	129	125	3.20
8.1	0.58	170	165	3.03
10.2	0.44	157	153	2.61
2.3	0.54	96	94	2.13
4.4	1.14	144	141	2.13
5.4	1.06	103	101	1.98
4.1	0.91	127	125	1.60
10.4	0.69	194	191	1.57
9.1	0.61	133	131	1.53
8.3	0.5	155	153	1.31
3.3	0.51	98	97	1.03
6.2	0.54	111	110	0.91
6.4	0.78	140	139	0.72
8.2	0.46	151	151	0.00
10.1	0.55	166	167	−0.60

Table 7. Simulation cloud environment 1.

Entity	Constraint	Value	Entity	Constraint	Value
Virtual machine	No of VM	6	Job	No of jobs	40–120
	RAM	512 MB		Length	50–5000
	Bandwidth	1000 MB	Host	No of Hosts	2
	MIPS	100–1000		Bandwidth	10000
	Type of policy	Time share		RAM	2048 MB
	size	10,000		Storage	1,000,000
	OS	Linux	Datacenter		2
	CPU	1
	VVM	Xen

Table 8. Simulation cloud environment 2.

Entity	Constraint	Value	Entity	Constraint	Value
Virtual machine	No Virtual Machines	6	Job	No of jobs	40–120
	RAM	128–15,360 MB		Length	100–10,000
	Bandwidth	128–15,360 MB	Host	No of Hosts	2
	MIPS	256–30,720		Bandwidth	10 GB
	Type of policy	Time share		RAM	20 GB
	size	10 GB		Storage	1TB
	OS	Linux	Datacenter		2
	CPU	1
	VVM	Xen

Table 9. Comparison with the results of CDS, HCA, and GAHCA at a significant level a = 0.05.

F(x)	CDS (Alla et al., 2023)	HCA	GAHCA	F(x)	CDS	HCA	GAHCA
F1	234	106 +	135−	F21	237	140−	102+
F2	295	138−	112+	F22	279	167−	133+
F3	225	107−	84+	F23	224	135	108+
F4	299	144+	175−	F24	173	107+	112−
F5	190	92+	117−	F25	179	111+	122−
F6	260	127+	154−	F26	189	118+	125−
F7	249	124−	100+	F27	147+	95+	165−
F8	263	133−	93+	F28	261	170−	153+
F9	251	127−	100+	F29	227	151−	94+
F10	149	76+	89−	F30	285	190−	141+
F11	312	166−	76+	F31	172	116-	101+
F12	284	157−	95+	F32	137	94+	125−
F13	348	194−	111+	F33	194	136+	191−
F14	145	81+	127−	F34	156	112+	131−
F15	182	103−	89+	F35	139+	100+	153−
F16	173	98+	102−	F36	174	126−	97+
F17	178	101+	130−	F37	130	96+	110−
F18	162	92−	88+	F38	142	108+	139−
F19	225	129−	116+	F39	181	151≈	151≈
F20	211	121−	73+	F40	183	155+	167−

Table 10. Ranks according to Friedman test.

F(x)	RANK	RANK	RANK	F(x)	RANK	RANK	RANK
F1	R3	R2	R1	F21	R3	R1	R2
F2	R3	R1	R2	F22	R3	R1	R2
F3	R3	R1	R2	F23	R3	R1	R2
F4	R3	R2	R1	F24	R3	R2	R1
F5	R3	R2	R1	F25	R3	R2	R1
F6	R3	R2	R1	F26	R3	R2	R1
F7	R3	R1	R2	F27	R2	R3	R1
F8	R3	R1	R2	F28	R3	R1	R2
F9	R3	R1	R2	F29	R3	R1	R2
F10	R3	R2	R1	F30	R3	R1	R2
F11	R3	R1	R2	F31	R3	R1	R2
F12	R3	R1	R2	F32	R3	R2	R1
F13	R3	R1	R2	F33	R3	R2	R1
F14	R3	R2	R1	F34	R3	R2	R1
F15	R3	R1	R2	F35	R2	R3	R1
F16	R3	R2	R1	F36	R3	R1	R2
F17	R3	R2	R1	F37	R3	R2	R1
F18	R3	R1	R2	F38	R3	R2	R1
F19	R3	R1	R2	F39	R3	R1.5	R1.5
F20	R3	R1	R2	F40	R3	R2	R1
					∑=118	∑= 61.5	∑= 60.5

Table

S.No	CDS (Prasad et al., 2023)	HCA	GAHCA	Xi	Xi^2
X1	234	106	135	475	225,625
X2	295	138	112	545	297,025
X3	225	107	84	416	173,056
X4	299	144	175	618	381,924
X5	190	92	117	399	159,201
X6	260	127	154	541	292,681
X7	249	124	100	473	223,729
X8	263	133	93	489	239,121
X9	251	127	100	478	228,484
X10	149	76	89	314	98,596
X11	312	166	76	554	306,916
X12	284	157	95	536	287,296
X13	348	194	111	653	426,409
X14	145	81	127	353	124,609
X15	182	103	89	374	139876
X16	173	98	102	373	139,129
X17	178	101	130	409	167,281
X18	162	92	88	342	116,964
X19	225	129	116	470	220,900
X20	211	121	73	405	164,025
X21	237	140	102	479	229,441
X22	279	167	133	579	335,241
X23	224	135	108	467	218,089
X24	173	107	112	392	153,664
X25	179	111	122	412	169,744
X26	189	118	125	432	186,624
X27	147	95	165	407	165,649
X28	261	170	153	584	341,056
X29	227	151	94	472	222,784
X30	285	190	141	616	379,456
X31	172	116	101	389	151,321
X32	137	94	125	356	126,736
X33	194	136	191	521	271,441
X34	156	112	131	399	159,201
X35	139	100	153	392	153,664
X36	174	126	97	397	157,609
X37	130	96	110	336	112,896
X38	142	108	139	389	151,321
X39	181	151	151	483	233,289
X40	183	155	167	505	255,025
Total Xi	8444	4994	4786	18,224	8,587,098
Xi^2	71,301,136	24,940,036	22,905,796

Table

Variation	Squares sum	DOF	Squares mean	F-ratio
Treatments between	94,748	39	2429	F0t = 2429/1180 = 2.05
Blocks between	211,056	2	105528	F0b = 105,528/1180 = 89.43
Error	92,036	78	1180
Total		119

Figure 7. Number of jobs vs performance matrix for layout 1.

Figure 8. Number of jobs vs performance matrix for layout 2.

Figure 9. Number of jobs vs performance matrix for layout 3.

Figure 10. Number of jobs vs performance matrix for layout 4.

Prasad, S., Medikondu, A. V. R. N. R., Reddy, M. B. S. S., Rakesh, K., Shanthi Swaroopini, A., & Sahu, P. K. (2023) Mathematical model for vehicle scheduling [Paper presentation]. In AIP Conference Proceedings (pp 1–8). https://doi.org/10.1063/5.0143073

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Alla, V. R. S. P., Medikondu, N. R., Kanakavalli, P. B., & Ravulapalli, V. P. (2023). Design and development of a mixed integer programming model for scheduling tasks through artificial intelligence. International Journal on Interactive Design and Manufacturing (IJIDeM), https://doi.org/10.1007/s12008-023-01488-1

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Data availability statement

The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.