`NMinimize` provides wrong answer when `WorkingPrecision` is specified

Question

I'm trying to use NMinimize to solve the 4th question of Hundred-dollar, Hundred-digit Challenge problems

What is the global minimum of the function $\exp(\sin(50x))+\sin(60e^y)+\sin(70\sin x)+\sin(\sin(80y))-\sin(10\left(x+y\right))+1/4\left(x^2+y^2\right)$ ?

The mathematica codes are as following:

f[x_, y_] := 
 Exp[Sin[50 x]] + Sin[60  Exp[y]] + Sin[70  Sin[x]] + Sin[Sin[80 y]] -
   Sin[10 (x + y)] + (x^2 + y^2)/4

NMinimize[f[x, y], {x, y}]

The above codes give the correct answer {-3.30687, {x -> -0.0244036, y -> 0.210625}}

However, when I tried to specify the option WorkingPrecision to obtain a higher precision answer, NMinimize gave me a wrong answer:

NMinimize[f[x, y], {x, y}, WorkingPrecision -> 30]

(*{-3.14407941031143614721780738981, {x -> -0.0231677594567431947167213562978, 
  y -> -0.494212878682625029250540893094}}*)

So how to obtain the true answer when specifying the WorkingPrecision option?

Answer 1

Use different Method:

NMinimize[f[x, y], {x, y}, WorkingPrecision -> 30, 
 Method -> "DifferentialEvolution"]
(* or *)
NMinimize[f[x, y], {x, y}, WorkingPrecision -> 30, 
 Method -> {"RandomSearch", "SearchPoints" -> 500}]

(* {-3.30686864747523728007611377090, 
    {x -> -0.0244030796943751719036133083297, 
     y -> 0.210612427155355770591591100555}} *)

Suggested reading: Numerical Nonlinear Global Optimization.