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

Table 1

Test problems.

Test problems	Objective functions; min𝐹(𝑋)=min[𝑓1(𝑋),𝑓2(𝑋)]	Range of variable
ZDT2	𝑓1(𝑋)=𝑥1,𝑓2𝑓(𝑋)=𝑔(𝑋)1−^1𝑔(𝑋)^2,𝑔(𝑋)=1+9∑^𝑛𝑖=2𝑥𝑖𝑛−1	𝑛=300≤𝑥𝑖≤1
ZDT3	𝑓1(𝑋)=𝑥1,𝑓2(𝑋)=𝑔1−𝑓1𝑔−𝑓1𝑔sin10𝜋𝑓1,𝑔(𝑋)=1+9∑^𝑛𝑖=2𝑥𝑖𝑛−1	𝑛=300≤𝑥𝑖≤1
ZDT4	𝑓1(𝑋)=𝑥1,𝑓2(𝑋)=𝑔1−𝑓1𝑔,𝑔(𝑋)=1+10(𝑛−1)+∑^𝑛𝑖=2𝑥^2𝑖−10cos4𝜋𝑥𝑖	𝑛=100≤𝑥1≤1−5≤𝑥𝑖≤5,𝑖=2,…,𝑛
ZDT6	𝑓1(𝑋)=1−exp−4𝑥1sin^66𝜋𝑥1,𝑓2(𝑋)𝑓=𝑔1−^1𝑔^2,𝑔(𝑋)=1+9∑^𝑛𝑖=2𝑥𝑖(𝑛−1)^0.25	𝑛=100≤𝑥𝑖≤1