dtlz2.mw

restart; 1 

DTLZ2 


`:=`(f, proc (x) options operator, arrow; sqrt(`+`(1, `-`(`*`(`^`(x, 2))))) end proc); -1; 'f(x)' = f(x); 1; `:=`(x[min], 0); -1; `:=`(x[max], 1); -1; 'x[min]' = x[min], 'x[max]' = x[max]
 

 

f(x) = `*`(`^`(`+`(1, `-`(`*`(`^`(x, 2)))), `/`(1, 2)))
x[min] = 0, x[max] = 1 (1)
 

`:=`(delta, proc (x) options operator, arrow; `/`(`*`(sqrt(`+`(`-`(`/`(`*`(diff(f(x), x)), `*`(`+`(1, `*`(`^`(diff(f(x), x), 2))))))))), `*`(int(sqrt(`+`(`-`(diff(f(x), x)))), x = x[min] .. x[max]))) ... 

delta(x) = `+`(`/`(`*`(2, `*`(`^`(`+`(1, `-`(`*`(`^`(x, 2)))), `/`(1, 4)), `*`(`^`(x, `/`(1, 2))))), `*`(Beta(`/`(3, 4), `/`(3, 4))))) (2)
 

`:=`(H1, proc (x) options operator, arrow; `+`(x, `/`(`*`(`+`(f(x), `-`(f(x[min])))), `*`(diff(f(x), x)))) end proc); -1 

`:=`(R1, Optimization:-Maximize(H1(x), x = x[min] .. x[max])); -1; 'R[1]' = R1 

R[1] = [1.17995967957098591, [x = .930604860898754382]] (3)
 

`:=`(H2, proc (x) options operator, arrow; `+`(`*`(diff(f(x), x), `*`(`+`(x, `-`(x[max])))), f(x)) end proc); -1 

`:=`(R2, Optimization:-Maximize(H2(x), x = x[min] .. x[max])); -1; 'R[2]' = R2 

R[2] = [1.17995967957098591, [x = .366025393639890506]] (4)