Originally posted by: SystemAdmin

Can I use the IloPiecewiseLinear object for a concave piecewise linear function in a LP problem or it will transform my problem into a MIP problem (and slow down resolution)?
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Originally posted by: EdKlotz

> 70DU_Marko_BLAIS wrote:
> Can I use the IloPiecewiseLinear object for a concave piecewise linear function in a LP problem or it will transform my problem into a MIP problem (and slow down resolution)?

Unless you are maximizing it, it will indeed transform it into a MIP problem. But, give it a try nonetheless; even though this probably slows down solve time, you may find that the run times are fast
enough to meet your needs despite your theoretical concerns.
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#DecisionOptimization

Originally posted by: SystemAdmin

Piecewise linear function transform the problem into a MIP if necessary or not necessary.

MB
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Originally posted by: EdKlotz

In the case where it is not necessary, the problem type may still be MIP, and you may see output indicating that the MIP optimizer was invoked. That is to be expected. But, in that case, you should see that the "MIP" solves immediately
with the root node solve, i.e. the root node LP solution has no integer infeasibilities. If so, then everything is to be expected. If not, then additional investigation is required to make sure that you are truly maximizing a concave function. The first step in that regard would involve reproducing the
problematic behavior on as small an example as possible. Then, I would recommend
setting CPLEX's search strategy to traditional branch and cut, so you can see the
branching selections in the log file. Once you have that, check the first few
branching selections; those should identify the parts of the pwl function that CPLEX thinks are not concave.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: EdKlotz

In the case where it is not necessary, the problem type may still be MIP, and you may see output indicating that the MIP optimizer was invoked. That is to be expected. But, in that case, you should see that the "MIP" solves immediately
with the root node solve, i.e. the root node LP solution has no integer infeasibilities. If so, then everything is to be expected. If not, then additional investigation is required to make sure that you are truly maximizing a concave function. The first step in that regard would involve reproducing the
problematic behavior on as small an example as possible. Then, I would recommend
setting CPLEX's search strategy to traditional branch and cut, so you can see the
branching selections in the log file. Once you have that, check the first few
branching selections; those should identify the parts of the pwl function that CPLEX thinks are not concave.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: EdKlotz

In the case where it is not necessary, the problem type may still be MIP, and you may see output indicating that the MIP optimizer was invoked. That is to be expected. But, in that case, you should see that the "MIP" solves immediately
with the root node solve, i.e. the root node LP solution has no integer infeasibilities. If so, then everything is to be expected. If not, then additional investigation is required to make sure that you are truly maximizing a concave function. The first step in that regard would involve reproducing the
problematic behavior on as small an example as possible. Then, I would recommend
setting CPLEX's search strategy to traditional branch and cut, so you can see the
branching selections in the log file. Once you have that, check the first few
branching selections; those should identify the parts of the pwl function that CPLEX thinks are not concave.
#CPLEXOptimizers
#DecisionOptimization