A Chaotic Particle Swarm Optimization-Based Heuristic for Market-Oriented Task-Level Scheduling in Cloud Workflow Systems

Table 2

Iteration processes of PSO and CPSO algorithms.

(a) PSO Initialization

Search variable	Tasks					ET	Cost
	A	B	C	D	E
	0.6	0.8	0.4	0.2	0.9	11.1	5.6
	0.2	−0.3	0.1	0.4	−0.2
	2	3	2	1	3
	0.8	0.7	0.1	0.3	0.9	10	5.5
	0	0.2	0.5	0.1	−0.2
	3	3	1	1	3
	0.3	0.8	0.7	0.5	0.9	20.5	6.0
	0.5	−0.4	−0.3	0	−0.3
	1	3	3	2	3
	3	3	1	1	3	10	5.5

(b) CPSO initialization

Search variable	Tasks					ET	Cost
	A	B	C	D	E
	0.5	0.9	0.7	0.6	0.8	20.5	6.0
	0.2	−0.3	−0.6	−0.2	−0.6
	1	3	3	2	3
	0.3	0.5	0.7	0.6	0.1	15.8	4.3
	0.5	0.1	−0.4	−0.2	0
	1	2	3	2	1
	0.2	0.3	0.7	0.5	0.3	17.3	4.5
	0.5	0.1	−0.1	−0.2	0.4
	1	1	3	2	1
	1	3	3	2	1	15.8	4.3

(c) PSO first iteration

Search variable	Tasks					ET	Cost
	A	B	C	D	E
	0.8	0.5	0.5	0.6	0.7	16.7	4.3
	0.1	0.2	−0.2	−0.3	0.1
	3	2	2	2	3
	0.8	0.5	0.6	0.4	0.7	16.7	4.3
	−0.1	0.1	0	0.2	0.2
	3	2	2	2	3
	0.8	0.4	0.4	0.5	0.6	18.7	4.7
	0.1	0.2	0.1	−0.1	0.2
	3	2	2	2	2
	3	2	2	2	3	16.7	4.3

(d) CPSO first iteration

Search variable	Tasks					ET	Cost
	A	B	C	D	E
	0.7	0.6	0.1	0.4	0.2	14.6	3.9
	0.1	0	0	0.2	0
	3	2	1	2	1
	0.8	0.6	0.3	0.4	0.1
	−0.1	0	−0.2	0.2	0	14.6	3.9
	3	2	1	2	1
	0.7	0.4	0.6	0.4	0.7
	0.2	0	−0.4	0.2	−0.6	16.7	4.3
	3	2	2	2	3
	3	2	1	2	1	14.6	3.9

(e) PSO last iteration

Search variable	Tasks					ET	Cost
	A	B	C	D	E
	0.9	0.7	0.3	0.3	0.8	16.7	4.3
	−0.1	−0.1	0	0.1	0.2
	3	2	2	2	3
	0.7	0.6	0.6	0.6	0.9	16.7	4.3
	0.7	0.1	−0.2	−0.3	0.1
	3	2	2	2	3
	0.9	0.6	0.5	0.4	0.8
	0.1	0.4	−0.2	−0.1	−0.3	16.7	4.3
	3	2	2	2	3
	3	2	2	2	3	16.7	4.3

(f) CPSO last iteration

Search variable	Tasks					ET	Cost
	A	B	C	D	E
	0.8	0.6	0.1	0.6	0.2	14.6	3.9
	−0.1	−0.2	0.1	0	0.2
	3	2	1	2	1
	0.7	0.6	0.1	0.6	0.1	14.6	3.9
	0.1	0	0.2	−0.1	0.1
	3	2	1	2	1
	0.9	0.4	0.3	0.6	0.1	14.6	3.9
	0.1	0	−0.2	−0.2	0
	3	2	1	2	1
	3	2	1	2	1	14.6	3.9