dtlz7.mw

restart; 1 

DTLZ7 


`:=`(f, proc (x) options operator, arrow; `+`(4, `-`(`*`(x, `*`(`+`(1, sin(`+`(`*`(3, `*`(Pi, `*`(x)))))))))) end proc); -1; 'f(x)' = f(x)
 

f(x) = `+`(4, `-`(`*`(x, `*`(`+`(1, sin(`+`(`*`(3, `*`(Pi, `*`(x)))))))))) (1)
 

`:=`(xmin, [0, .6316265307, 1.3596178367, 2.0518383519]) 

[0, .6316265307, 1.3596178367, 2.0518383519] (2)
 

`:=`(xmax, [.2514118360, .8594008566, 1.5148392681, 2.116426807]) 

[.2514118360, .8594008566, 1.5148392681, 2.116426807] (3)
 

`:=`(C, sum(int(sqrt(`+`(`-`(diff(f(x), x)))), x = xmin[i] .. xmax[i]), i = 1 .. 4)) 

1.523012492 (4)
 

`:=`(delta, proc (x) options operator, arrow; `/`(`*`(sqrt(`+`(`-`(`/`(`*`(diff(f(x), x)), `*`(`+`(1, `*`(`^`(diff(f(x), x), 2))))))))), `*`(C)) end proc); -1; 'delta(x)' = simplify(delta(x), size, sy... 

delta(x) = `+`(`*`(.6565934326, `*`(`^`(`+`(`-`(`/`(`*`(`+`(`-`(1), `-`(sin(`+`(`*`(3, `*`(Pi, `*`(x)))))), `-`(`*`(3, `*`(x, `*`(cos(`+`(`*`(3, `*`(Pi, `*`(x))))), `*`(Pi))))))), `*`(`+`(1, `*`(`^`(`... (5)
 

 

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

`:=`(R1, Optimization:-Maximize(H1(x), x = xmin[4] .. xmax[4])); -1; 'R[1]' = R1 

R[1] = [2.48053273481787828, [x = 2.11642680699999985]] (6)
 

`:=`(H2, proc (x) options operator, arrow; `+`(`*`(diff(f(x), x), `*`(`+`(x, `-`(xmax[4])))), f(x)) end proc); -1 

`:=`(R2, Optimization:-Maximize(H2(x), x = xmin[1] .. xmax[4])); -1; 'R[2]' = R2 

R[2] = [13.3720460488617405, [x = 1.32017238890039956]] (7)
 

 

(8)