Originally posted by: DavidGravot

Hi

I'm doing multi-objective in CP with staticLex expression for the objective function

I'm wondering if there exist some parameters to control the time limit spent in each part of the lexicographic objective function 

Suppose I minimize staticLex(obj1, obj2) , is the time limit split into some time for first order criterion obj1 and some remaining time for obj2 ?

Thanks

David

Originally posted by: PhilippeLaborie

Hi David,

CPO does not use specific time-limits for each of the objectives in a multi-objective like staticLex.

If you really want to do that and more generally if you want to have more control on how the multi-objective problem is solved (for instance time limit t1 for objective 1, then do not deteriorate more than x1% objective 1 while optimizing objective2 with time limit t2, etc.), then you can use starting points to restart from the solution of the previous step (typically after having changed the objective function and added some constraints).

Philippe

Originally posted by: DavidGravot

Thanks Philippe,

two related questions :

1. Assume I have a first criterion which is bounded to be positive and that the staticLex finds its optimal value 0. I guess we can assume than CP will now focus only on the remaining criteria, since there is no use to improve anymore the first one, right ?
2. In an other use case, if cp cannot prove optimality for the first criterion, I would like to be sure that much of the effort is not only kept on it, while we could improve the remaining ones. I understand everything could be controlled accurately with 2-steps optimization , but this is clearly something I would rather avoid

Thanks

David

Originally posted by: PhilippeLaborie

> Assume I have a first criterion which is bounded to be positive and that the staticLex finds its optimal value 0. I guess we can assume than CP will now focus only on the remaining criteria, since there is no use to improve anymore the first one, right ?

Yes. although the search may be slightly different than if you would only minimize the second criterion in a second step.

> In an other use case, if cp cannot prove optimality for the first criterion, I would like to be sure that much of the effort is not only kept on it, while we could improve the remaining ones. I understand everything could be controlled accurately with 2-steps optimization , but this is clearly something I would rather avoid

With staticLex, if the search opportunistically improves the second criterion (while of course not deteriorating the first one), it will keep it as the incumbent solution. So in a sense, not all the effort is spent at improving the first criterion. If you want to completely focuse on the first criterion and then on the second one, you should use two steps.