0
$\begingroup$

I have a bi-objective problem: $minimize (Z_1(X) and Z_2(X))$

$Z(X)=w_1*Z_1(X)+w_2*Z_2(X)$ is the weighted sum objective function that is minimized. $Z_1(X)$ and $Z_2(X)$ are two objective functions.

I want to know if there is a method or formulation to determine $w_1$ and $w_2$ such that solving the weighted sum optimization problem results in $lexmin(Z_1(X),Z_2(X))$ and $lexmin(Z_2(X),Z_1(X))$ as lexicographic optimum solutions to the bi-objective problem.

$\endgroup$
0
$\begingroup$

You cannot obtain a lexicographically ordered solution with just one optimization. You first have to minimize $Z_1(X)$. If the optimal value is $c$, you then minimize $Z_2(X)$ such that $Z_1(X) \leq c$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.