A New Multiobjective Evolutionary Algorithm Based on Decomposition of the Objective Space for Multiobjective Optimization

Table 1

Multiobjective benchmark functions.

Instance	Objective function
F1	𝑓1(𝑥)=1+𝑔(𝑥)𝑥1
	𝑓2(𝑥)=1+𝑔(𝑥)1−√𝑥1
	𝑔(𝑥)=2sin𝜋𝑥1𝑛−1+∑^𝑛𝑖=2𝑡^2𝑖−cos2𝜋𝑡𝑖
	𝑡𝑖=𝑥𝑖−sin0.5𝜋𝑥𝑖
F2	𝑓1(𝑥)=1+𝑔(𝑥)𝑥1
	𝑓2(𝑥)=1+𝑔(𝑥)1−𝑥^21
	𝑔(𝑥)=2sin𝜋𝑥1𝑛−1+∑^𝑛𝑖=2𝑡^2𝑖−cos2𝜋𝑡𝑖
	𝑡𝑖=𝑥𝑖−sin0.5𝜋𝑥𝑖
F3	𝑓1(𝑥)=1+𝑔(𝑥)cos𝜋𝑥12
	𝑓2(𝑥)=1+𝑔(𝑥)sin𝜋𝑥12
	𝑔(𝑥)=2sin𝜋𝑥1𝑛−1+∑^𝑛𝑖=2𝑡^2𝑖−cos2𝜋𝑡𝑖
	𝑡𝑖=𝑥𝑖−sin0.5𝜋𝑥𝑖
F4	𝑓1(𝑥)=1+𝑔(𝑥)𝑥1
	𝑓2(𝑥)=1+𝑔(𝑥)1−𝑥1^0.5cos^22𝜋𝑥1
	𝑔(𝑥)=2sin𝜋𝑥1𝑛−1+∑^𝑛𝑖=2𝑡^2𝑖−cos2𝜋𝑡𝑖
	𝑡𝑖=𝑥𝑖−sin0.5𝜋𝑥𝑖
F5	𝑓1(𝑥)=1+𝑔(𝑥)𝑥1𝑥2
	𝑓2(𝑥)=1+𝑔(𝑥)𝑥11−𝑥2
	𝑓3(𝑥)=1+𝑔(𝑥)1−𝑥1
	𝑔(𝑥)=2sin𝜋𝑥1𝑛−1+∑^𝑛𝑖=3𝑡^2𝑖−cos2𝜋𝑡𝑖
	𝑡𝑖=𝑥𝑖−𝑥1𝑥2
F6	𝑓1(𝑥)=1+𝑔(𝑥)cos(0.5𝜋𝑥1)cos(0.5𝜋𝑥2)
	𝑓2(𝑥)=1+𝑔(𝑥)cos(0.5𝜋𝑥1)sin(0.5𝜋𝑥2)
	𝑓3(𝑥)=1+𝑔(𝑥)sin(0.5𝜋𝑥1)
	𝑔(𝑥)=2sin𝜋𝑥1𝑛−1+∑^𝑛𝑖=3𝑡^2𝑖−cos2𝜋𝑡𝑖
	𝑡𝑖=𝑥𝑖−𝑥1𝑥2