Chaotic Multiobjective Evolutionary Algorithm Based on Decomposition for Test Task Scheduling Problem

Table 1

The list of chaotic maps.

Chaotic map	Formula	Dimensions	Range
Baker’s map	𝐵𝑥,𝑦=𝑦2𝑥,2𝑦for0≤𝑥<0.52−2𝑥,1−2for0.5≤𝑥<1	2	𝑥∈(0,1)
Arnold’s cat map	𝑥𝑘+1=𝑥𝑘+𝑦𝑘(1)𝑦mod𝑘+1=𝑥𝑘+2𝑦𝑘mod(1)	2	𝑥𝑘∈(0,1)
Circle map	𝑥𝑘+1=𝑥𝑘𝑎+𝑏−2𝜋sin2𝜋𝑥𝑘mod(1)	1	(0, 1)
	𝑎=0.5 𝑏=0.2
Cubic map	𝑥𝑘+1=𝜌𝑥𝑘1−𝑥^2𝑘,𝑥𝑘∈(0,1)	1	(0, 1)
	𝜌=2.59
Gauss map	𝑥𝑘+1=0𝑥𝑘1=0𝑥𝑘mod(1)otherwise	1	(0, 1)
ICMIC map	𝑥𝑘+1𝑎=sin𝑥𝑘,𝑎∈(0,∞),𝑥𝑘∈(−1,1)	1	[−1,1]
	𝑎=2
Logistic map	𝑥𝑘+1=𝑎𝑥𝑘1−𝑥𝑘	1	(0, 1)
	𝑎=4
Sinusoidal map	𝑥𝑘+1=sin𝜋𝑥𝑘,𝑥𝑘∈(0,1)	1	(0, 1)
Tent map	𝑥𝑘+1=𝑥𝑘𝑥0.7^𝑘<0.7103𝑥𝑘1−𝑥𝑘otherwise	1	(0, 1)
Zaslavskii map	𝑥𝑘+1=𝑥𝑘+𝑣+𝑎𝑦𝑘+1(1)𝑦mod𝑘+1=cos2𝜋𝑥𝑘+𝑒^−𝑟𝑦𝑘	2	𝑦𝑘∈[−1.0512,1.0512]
	𝑣=400 𝑟=3 𝑎=12.6695