mixed integer nonlinear optimization

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hossam eldakroury 2019-10-6

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评论： Walter Roberson 2019-10-6

Hi everyone,

Consider i have an [objective function = A(X1)+B(X2)+C(X3)+.... ] where X1,X2,X3,... are the inputs,

where A,B,C,.. are not constants and non-linear but their values changes according the X1,X2,X3,... values,

X1,X2,X3,... are binary values either 1 or 0,

So can i still use any of mathematical optimization methods in optimization tool box to solve this kind of problem ? considering it should be a mathematical method and not heuristic such GA,

and what is the best method to solve this kind of problem ?

N.B: am not very expert at using matlab

Thanks.

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Walter Roberson 2019-10-6

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You X values are binary, 0 or 1. Your A, B, C, etc., you say are non-linear. But there are only two possible inputs for them, so they are each implicitly

input is 0: constant1
input is 1: constant2

which can also be expressed as

constant1 + input * (constant2-constant1)

which is linear. Your formula can be rewritten as

A_constant1 + B_constant1 + C_constant1 ... + (A_constant2-A_constant1)*X1 + (B_constant2-B_constant1)*X2 + ...
    

and you consolidate the values to arrive at

constant + Adiff * X1 + Bdiff * X2 + Cdiff * X3 ....

If you do not have any constraints, this can be minimized immediately by setting the X* for a negative difference to 1 and setting the X* for a positive difference to 0.

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