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NMinimize -DifferentialEvolution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg113962] NMinimize -DifferentialEvolution
  • From: lightnation <lightnation at naver.com>
  • Date: Fri, 19 Nov 2010 05:10:36 -0500 (EST)

NMinimize[Flatten[{obj,constraints}],var,Method-
>"DifferentialEvolution"];

The sentence above is to solve the optimzation problem whose objective
function and constraints are represented as "obj", "constraints"
respectively, using genetic algorithm built in Mathematica in the name
of "DifferentialEvolution".

This type of command is to solve the complex problem which cannot be
solve in the analytic ways.

The question is,
How can we solve the optimization problem involving the system
which is expressed in "DAE"(Differential and Algebraic Equation) way.
The typical exampe of DAEsystem is the power system.
The structure of electric grid is represented as the algebraic
equation(load+loss=generation),
the dynamics concerning the motion of rotator in generator is
represented in differential equations.

For instance,

letting
constraints=Flatten[{constraint1,constraint2,constraint3,
...........eigconstraint}]

eigconstraint can be represented as,

Max[Re[#]&/@Eigenvalues[DAEsystem_Matrix]]<=0

and DAEsystem_Matrix can be expressed through the system linearization
in the symbolic way.
However, Mathematica does not have the capability
of calculating the large DAEsystem such as power system in the
symbolic way.
(The message meaning "Kernel" has been shut down emerged.
I guess this is related to the capacity of RAM.)
Instead, Mathematica can calculate the DAEsystem_Matrix when given the
initial values.

My question is
How can we formulated this type of problem to the 'NMinmize" command?
I mean
how can I epxress the "eigconstraint" when it is not clearly expressed
in symbolic way as described above?

I am waiting for the wise answer from others.
Thank you.



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