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 "Optimization Solution" Differential Evolution Optimization Method
 MIN: Iterations + BestValue 50, f(x) = -6.53425765992309 100, f(x) = -6.53333982271925 150, f(x) = -6.21052326440253 200, f(x) = -6.5311036869851 MINIMUM: -6.54589200375742 New Iteration = 0, f(x) = -6.19529495815637 BestMember x = (0.259520727591366, -1.63623497579914) x = (0.222742638654422, -1.65603761540672) x = (0.0372447678992733, -1.65828996192986) x = (0.268501347353915, -1.62332177318526) AT: (0.268501347353915, -1.62332177318526) x = (0.315631360893897, -1.76181688148613)

 MAX: 50, f(x) = -8.05777094137129 100, f(x) = -8.1033827974068 150, f(x) = -7.95388694651982 200, f(x) = -7.99593245779207 MAXIMUM: 9.43139241663182E-08 New Iteration = 0, f(x) = -5.50631151970504 x = (-0.0820359129691665, 1.61184189772591) x = (-0.0239642040915622, 1.60704877936847) x = (-0.150779409106252, 1.58963111068481) x = (-0.131828877204949, 1.58353739155079) AT: (-0.131828877204949, 1.58353739155079) x = (0.390176109219983, 1.93508462977367)

 Enter new iteration: Iteration =

IMPLEMENTATION
Differential Evolution Method Optimization

This method may be considered as a random-search technique. Stochastic methods are efficient techniques for finding the global minimum of a function with multiple variables. In general, thse type of optimization techniques are inspired by biological processes and are called evolutionary algorithms.

Several advantages of using evolutionary algorithms over the traditional optimization methods include:

• Optimize with continous or discrete variables.
• Usually do not require derivative information.
• Deal with a large number of variables.
• Work with numerically generated data, experimental data, or analytical functions.

Algorithm Creation

Using the "peaks" function, which is used extensively in Matlab:

 f(x,y) = 3(1-x)2 e-x2 - (y + 1)2 - 10( 1/5x - x3 - y5) e-x2

This function has several local minima and maxima. It is also possible to find the global maximum for the peaks function by simply returning the negative value of the function.

Testing the Differential Evolution Method

To test it out we find the the minimum and maximum points of the peaks function. We ran the program using different iteration parameters(4). The user can manipulate and test it further by manually entering new iterations.

Supporting code and methods are not shown.

 Other Implementations...

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Math, Analysis,
expertise..."

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