 Site Statistics  |   Contact  |   About Us       Thursday, July 29, 2021  ~ Bisection Method ~ Simplex Method ~ Golden Search ~ Newton Method ~ Multi-Newton ~ Evolution Method

 "Optimization Solution" Differential Evolution Optimization Method
 MIN: Iterations + BestValue 50, f(x) = -6.52810298037659 100, f(x) = -6.53270286318908 150, f(x) = -6.40271152348984 200, f(x) = -6.52537906333096 MINIMUM: -6.5458920083748 New Iteration = 0, f(x) = -6.18670859534776 BestMember x = (0.203237359908985, -1.60134573653332) x = (0.251296781865552, -1.64756048679597) x = (0.105002839167138, -1.65292970207557) x = (0.264737347264186, -1.64594677074158) AT: (0.264737347264186, -1.64594677074158) x = (0.422960544015728, -1.57284362594264)

 MAX: 50, f(x) = -8.09463291766526 100, f(x) = -8.00375056917656 150, f(x) = -7.77626119161936 200, f(x) = -8.11506669735273 MAXIMUM: 3.94548306550149 New Iteration = 0, f(x) = -3.51970539178696 x = (0.0369730936535508, 1.5960037673574) x = (-0.127724687255791, 1.572392652007) x = (-0.117233261021428, 1.45449102248378) x = (0.00217678677392064, 1.57811689733384) AT: (0.00217678677392064, 1.57811689733384) x = (1.19072196781203, 0.0252733500792055)

 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...

 Object-Oriented Implementation Graphics and Animation Sample Applications Ore Extraction Optimization Vectors and Matrices Complex Numbers and Functions Ordinary Differential Equations - Euler Method Ordinary Differential Equations 2nd-Order Runge-Kutta Ordinary Differential Equations 4th-Order Runge-Kutta Higher Order Differential Equations Nonlinear Systems Numerical Integration Numerical Differentiation Function Evaluation  Math, Analysis,
expertise..."

EIGENVALUE SOLUTIONS...
Eigen Inverse Iteration
Rayleigh-Quotient Method
Cubic Spline Method

 Applied Mathematical Algorithms A complex number z = x + iy, where... Complex Functions Non-linear system methods... Non Linear Systems Construction of differentiation... Differentiation Consider the function where... Integration
 About Us KMP Engineering is an independent multidisciplinary engineering consulting company specializing in mathematical algorithms.  → ABOUT  → SITE STATISTICS Contact Us KMP ENGINEERING 2461 E Orangethorpe Ave Fullerton, CA 92631 USA info@keystoneminingpost.com Site Map  →  Home  →  Areas of Expertise  →  Reference Items  →  Managed Services  →  Login Mining & Software Engineering 