# Tag Info

### Multiple Travelling Salesmen - How to make the second slowest salesman matter?

You are dealing with a multi-objective problem. A common approach is to first consider your main goal, in your case that is $T_{max}$. Once you have found an optimal $T_{max}$, you adjust your ...
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### Problem of scaling or normalizing in multiobjective optimization problem when one objective function is much larger than the other?

I would suggest that you start by asking yourself (or the boss) why you want to reduce delay and why you want to reduce resource use. Ideally, these will translate into some sort of tangible costs. ...
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### Lexicographic objective to maximize the x-th highest value

As Mark L. Stone notes, some solvers (including CPLEX) handle lexicographic optimization directly. If you are using a solver that does not, but does allow you to modify branching, pruning etc. using ...
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### How to use gurobi to describe the process of finding the rank of matrix without objective function？

In theory we can use the fact that rank = the number of non-zero singular values in a singular value decomposition (SVD). ...
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### Exception from IBM ILOG CPLEX: CPLEX Error 5002: 'q1' is not convex.->

You did not identify the variables in your model. Presumably X is a variable. If either M_T or Consumption_M_T_R is a variable, then your objective function is a nonconvex quadratic function. If any ...
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### New considerations for efficient solutions in multiobjective optimization

Years ago two of my colleagues proposed an interactive approach. (This was for LPs, but should generalize to MIPs.) It requires reasonably fast solution time for the model. The gist was to optimize a ...
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### Weighted sum in the objective function

We typically normalize on seconds, minutes xor dollars, for as far as that is possible. And then leave it to a business stakeholder alignment meeting to tweak the weights. But normalization is not ...
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### Problem of scaling or normalizing in multiobjective optimization problem when one objective function is much larger than the other?

You write in a comment that "you want to scale $f_1$ and $f_2$ so that they are as big as the others". If I understand you correctly, this may be impossible if you do not know the range of ...
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### Problem of scaling or normalizing in multiobjective optimization problem when one objective function is much larger than the other?

In my opinion, the problem could be addressed by defining an appropriate reference system or rather an appropriate measurement scale. We can image $f_1$ and $f_2$ to be the coordinate of two vectors: ...

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