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Speeding up random search

Using an example from the documentation

f[x_, y_] = 
  Exp[Sin[50 x]] + Sin[60 Exp[y]] + Sin[70 Sin[x]] + Sin[Sin[80 y]] - 
   Sin[10 (x + y)] + 1/4 (x^2 + y^2);

 AbsoluteTiming @ NMinimize[f[x, y], {x, y}, Method -> "RandomSearch"]

{0.0919746, {-2.38708, {x -> -0.124868, y -> 0.290932}}}

AbsoluteTiming @ 
 NMinimize[f[x, y], {x, y}, Method -> {"RandomSearch", "SearchPoints" -> 1500}]

{4.19461, {-3.30687, {x -> -0.0244031, y -> 0.210612}}}

 AbsoluteTiming @ (sln = 
   NMinimize[{f[x + dx, y + dy], -0.01 <= dx <= .01 , -.01 <= dy <= .01}, {x, 
     y, dx, dy}, Method -> {"RandomSearch", "SearchPoints" -> 50 }])

{0.432524, {-3.30687, {x -> -0.0156802, y -> 0.212335, dx -> -0.00872292, 
   dy -> -0.00172211}}}

{x + dx, y + dy} /. sln[[2]]

 {-0.0244031, 0.210612}
POSTED BY: Frank Kampas
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In[9]:= AbsoluteTiming @ (sln = 
   NMinimize[{f[x + dx1, y + dy1], -0.1 <= dx1 <= .1 , -.1 <= 
      dy1 <= .1}, {x, y, dx1, dy1}, 
    Method -> {"RandomSearch", "SearchPoints" -> 6 }])

Out[9]= {0.0652766, {-3.30687, {x -> -0.0186475, y -> 0.241002, 
   dx1 -> -0.00575559, dy1 -> -0.0303898}}}

In[10]:= {x + dx1, y + dy1} /. sln[[2]]

Out[10]= {-0.0244031, 0.210612}
POSTED BY: Frank Kampas
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