A Hybrid Multiobjective Differential Evolution Algorithm and Its Application to the Optimization of Grinding and Classification

Table 3

Test functions.

Test function	Objective function; min𝐹(𝑋)=min[𝑓1(𝑋),𝑓2(𝑋)]	Constraints	Range of variable
CTP	𝑓1(𝑋)=𝑥1,𝑓2(𝑋)−𝑓=exp^1(𝑋)𝑐(𝑋)×41+∑^5𝑖=2𝑥𝑖^2−10cos2𝜋𝑥𝑖	𝑔1(𝑋)=cos(𝜃)𝑓2(𝑋)−𝑒−sin(𝜃)𝑓1(𝑋),𝑔2(𝑋)=𝑎sin𝑏𝜋sin(𝜃)𝑓2(𝑋)(𝜃)𝑓−𝑒+cos1(𝑋)^𝑐𝑑,𝑔1(𝑋)≥𝑔2(𝑋)	0≤𝑥1≤1−5≤𝑥𝑖≤5𝑖=2,3,4,5
BNH	𝑓1(𝑋)=4𝑥1^2+4𝑥2^2,𝑓2(𝑋)=(𝑥1−5)^2+(𝑥2−5)^2	𝑔1(𝑋)=(𝑥1−5)^2+𝑥2^2𝑔−25,2(𝑋)=−(𝑥1−8)^2+(𝑥2𝑔+3)+7.7,1(𝑋)≤0,𝑔2(𝑋)≤0	0≤𝑥1≤50≤𝑥2≤3
TNK	𝑓1(𝑋)=𝑥1,𝑓2(𝑋)=𝑥2	𝑔1(𝑋)=−𝑥1^2−𝑥2^2𝑥+1+0.1cos16arctan^1𝑥2,𝑔2(𝑋)=(𝑥1−0.5)^2+𝑥2,𝑔−0.51(𝑋)≤0,𝑔2(𝑋)−0.5≤0	0≤𝑥𝑖≤𝜋𝑖=1,2