A Fast Elitism Gaussian Estimation of Distribution Algorithm and Application for PID Optimization

Table 1

High dimensional benchmarks.

Quadric; 𝑛=10	𝑓4(𝑥)=∑^𝑛∑𝑖=1^𝑖𝑗=1𝑥𝑗^2,  −100≤𝑥𝑖≤100
Rosenbrock; 𝑛=10	𝑓5(𝑥)=∑^𝑛−1𝑖=1100𝑥𝑖+1−𝑥^2𝑖^2+1−𝑥1^2,  −50≤𝑥𝑖≤50
Ackley; 𝑛=10	𝑓6(𝑥)=−20exp−0.2∑^𝑛𝑖=1𝑥^2𝑖𝑛−exp∑^𝑛𝑖=1cos2𝜋𝑥𝑖𝑛+20+𝑒, −30≤𝑥𝑖≤30
Griewank; 𝑛=10	𝑓71(𝑥)=4000^𝑛𝑖∑=1𝑥𝑖^2−∏^𝑛𝑖=1𝑥cos^𝑖√𝑖+1, −300≤𝑥𝑖≤300
Rastrigrin; 𝑛=10	𝑓8(𝑥)=∑^𝑛𝑖=1𝑥^2𝑖−𝐴cos2𝜋𝑥𝑖+𝐴,  −5.12≤𝑥𝑖≤5.12
Schaffer’s 𝑓3; 𝑛=10	𝑓9(𝑥)=∑^𝑛𝑖=1𝑥^2𝑖+𝑥^2𝑖+1^0.25×sin50×𝑥^2𝑖+𝑥^2𝑖+1^0.1+1.0,  −100≤𝑥𝑖≤100