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I have two different optimization models to solve a problem. Both of them work on a graph but the first one leads to optimization with an objective that has two summations:

$\sum \sum x_{ij}$

and the second one leads to optimization with one summation in the objective:

$\sum x_i$

Note that the constraints are almost the same and the difference is just the model that makes different objectives.

The second objective is faster than the first one to solve the same instances of the problem. Is it possible to say that the number of summations is an important parameter that leads to this difference in efficiency?

samie
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No. If it was that simple, you could simply add a new variable $t$ to minimize and the constraint $t = \sum \sum x_{ij}$, and things would run faster.

Johan Löfberg
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  • OP mentions constraints are same/similar in both cases. – Rahul Madhavan Apr 14 '21 at 20:24
  • Yes, similar, so adding a single line with a linear equality would still have it pretty similar assuming a well functioning solver and reasonably generic model. Regardless, the geist of the answer is still that there is no reason to believe that more terms in the objective leads to worse performance. Sometimes it will be slower, sometimes it will be faster, and sometimes it will make no difference, depending on the model. – Johan Löfberg Apr 14 '21 at 20:35