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.