# Looking for Global Optimization Test Problems

Posted 9 years ago
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 I'm working on a new version of MathOptimizer Professional and am looking for test problems. They should be non-linear, with continuous variables and should be expressed symbolically. In other words, no numerical functions as part of the problem definition. Problems can be unconstrained or constrained. There need to be bounds on the ranges of the variables. Here's an example from the Mathematica documentation which I have made more difficult by increasing n from 10 to 50: In[1]:= Needs["MathOptimizerProGCCcallLGO"] In[22]:= n = 50; f = Sum[(x[i] - Sin[i])^2, {i, 1, n}]; c = Table[-0.5 < x[i] < 0.5, {i, n}]; v = Array[x, n]; AbsoluteTiming[ NMinimize[{f, c}, v, Method -> {"RandomSearch", Method -> "InteriorPoint", "SearchPoints" -> 1}]] Out[26]= {6.142542, {4.36464, {x[1] -> 0.5, x[2] -> 0.5, x[3] -> 0.14112, x[4] -> -0.5, x[5] -> -0.5, x[6] -> -0.279416, x[7] -> 0.5, x[8] -> 0.5, x[9] -> 0.412118, x[10] -> -0.5, x[11] -> -0.5, x[12] -> -0.5, x[13] -> 0.420167, x[14] -> 0.5, x[15] -> 0.5, x[16] -> -0.287903, x[17] -> -0.5, x[18] -> -0.5, x[19] -> 0.149877, x[20] -> 0.5, x[21] -> 0.5, x[22] -> -0.00885132, x[23] -> -0.5, x[24] -> -0.5, x[25] -> -0.132352, x[26] -> 0.5, x[27] -> 0.5, x[28] -> 0.270906, x[29] -> -0.5, x[30] -> -0.5, x[31] -> -0.404038, x[32] -> 0.5, x[33] -> 0.5, x[34] -> 0.5, x[35] -> -0.428183, x[36] -> -0.5, x[37] -> -0.5, x[38] -> 0.296369, x[39] -> 0.5, x[40] -> 0.5, x[41] -> -0.158623, x[42] -> -0.5, x[43] -> -0.5, x[44] -> 0.0177019, x[45] -> 0.5, x[46] -> 0.5, x[47] -> 0.123573, x[48] -> -0.5, x[49] -> -0.5, x[50] -> -0.262375}}} In[27]:= AbsoluteTiming @ callLGO[f, {}, Thread[{v, -.5, .5}]] Out[27]= {0.816736, {4.36464, {x[1] -> 0.5, x[2] -> 0.5, x[3] -> 0.14112, x[4] -> -0.5, x[5] -> -0.5, x[6] -> -0.279415, x[7] -> 0.5, x[8] -> 0.5, x[9] -> 0.412118, x[10] -> -0.5, x[11] -> -0.5, x[12] -> -0.5, x[13] -> 0.420167, x[14] -> 0.5, x[15] -> 0.5, x[16] -> -0.287903, x[17] -> -0.5, x[18] -> -0.5, x[19] -> 0.149877, x[20] -> 0.5, x[21] -> 0.5, x[22] -> -0.00885131, x[23] -> -0.5, x[24] -> -0.5, x[25] -> -0.132352, x[26] -> 0.5, x[27] -> 0.5, x[28] -> 0.270906, x[29] -> -0.5, x[30] -> -0.5, x[31] -> -0.404038, x[32] -> 0.5, x[33] -> 0.5, x[34] -> 0.5, x[35] -> -0.428183, x[36] -> -0.5, x[37] -> -0.5, x[38] -> 0.296369, x[39] -> 0.5, x[40] -> 0.5, x[41] -> -0.158623, x[42] -> -0.5, x[43] -> -0.5, x[44] -> 0.0177019, x[45] -> 0.5, x[46] -> 0.5, x[47] -> 0.123573, x[48] -> -0.5, x[49] -> -0.5, x[50] -> -0.262375}, "Maximum Constraint Violation" -> 0., "Function Evaluations" -> 275694, "Model Status" -> "Global Search Based Solution", "Solver Status" -> "Resource Interrupt", "Runtime" -> 0.17}} 
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