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Math Help - Optimization problem

  1. #1
    Newbie
    Joined
    Dec 2010
    Posts
    6

    Optimization problem

    Dear all,

    I have the following challenge.

    I have got a three-phase distribution line for electrical power with the lines A,B,C.
    As well, I have a set of loads Li (with i=1...n), which have got the below behaviour over time.
    time: t1 t2 t3 t4 t5 t6
    L1: 1 3 4 5 6 1
    L2: 1 1 1 1 1 1
    L3: 2 1 4 5 6 7
    ...
    Ln: 2 1 4 5 6 7

    I would like to distribute the loads over the three distribution lines in order to achieve the best distribution possible, that is, minimize the difference between phase A,B,C.

    Has anybody a hint which approach is best and better and example application?
    To me it is a optimisation problem, I may solve with something like Newton or so. But I cannot find the solution. The problem is, that in contrast to the following example, I have vector for x and not values:

    min(f(x))=x2+10(x-x^2) ...

    My x in there are vectors again

    Thanks a lot.

    HHsts
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  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
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    someplace
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    14,972
    Thanks
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    Quote Originally Posted by HHsts View Post
    Dear all,

    I have the following challenge.

    I have got a three-phase distribution line for electrical power with the lines A,B,C.
    As well, I have a set of loads Li (with i=1...n), which have got the below behaviour over time.
    time: t1 t2 t3 t4 t5 t6
    L1: 1 3 4 5 6 1
    L2: 1 1 1 1 1 1
    L3: 2 1 4 5 6 7
    ...
    Ln: 2 1 4 5 6 7

    I would like to distribute the loads over the three distribution lines in order to achieve the best distribution possible, that is, minimize the difference between phase A,B,C.

    Has anybody a hint which approach is best and better and example application?
    To me it is a optimisation problem, I may solve with something like Newton or so. But I cannot find the solution. The problem is, that in contrast to the following example, I have vector for x and not values:

    min(f(x))=x2+10(x-x^2) ...

    My x in there are vectors again

    Thanks a lot.

    HHsts
    Most non-linear solvers work with vector design vectors, it is only in beginners calculus that single variable problems are given prominence.

    It makes no sense to code the algorithm yourself, there is a solver in Excel that is suitable for smallish problems, Matlab has a number of optimisation functions that should be suitable (if you are on a budget Octave will do the same things for you).

    Also look in "Numerical Recipes", you will find the Nelder-Mead algorithm there and code in your language of choice (some times called the/a simplex algorithm but that is a cause of confusion with the simplex algorithm of linear programming, which is a completely different beast) which I often use (the algorithm not their code).

    CB
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  3. #3
    Newbie
    Joined
    Dec 2010
    Posts
    6
    Thanks for the reply.
    I will go to this page you mentioned.

    In the meantime, I have found a first approach with the mixed-interger programming based on branch and bound algorithms, I am exploring.
    Looks good. Disadvantage yet, the implementation in Matlab, is still heavy, although Matlab offers a basic function on that.
    May be numerical recepies will help me find another one, as you mentioned, for easier implementation.

    Thanks

    HHsts
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