Multiobjective discrete optimization with ga

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Hi!
I need to solve a problem of the type:
F = (max (a1 - sum_i(x_i*c_i)), max (a2 - sum_i(y_i*c_i)), max (a3 - sum_i(z_i*c_i), ...)
Such that
x_i = {0, 1}
y_i = {0, 1}
z_i = {0, 1}
x_i + y_i + z_i = 1, for all i
and
a1, a2, a3, ..., an known constant
c_i, i=1,m also known constants
How can I do it?
Thanks :)

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