Change the objective function and resolve?

[Frank Olaf Sem-Jacobsen]

Hi guys,

I have a problem which I want to optimise along two different axis in sequence. E.g., first I want to minimise costs, and I then want to add this cost as a constraint and try to maximise some other parameter of the same problem. This would give me the best possible solution for the minimal cost.

This could be quite easily done by simply  building the first problem and solving it, and then building the second problem with a modified objective function (to minimise a different combination of parameters) and adding the solution of the first problem as a constraint to the second. However, I find that most of my time is spent generating the problem. Building the constraints appears to be quite expensive, so I would prefer to find some solution that allows me to reuse the existing problem. This requires me to be able to change the objective function, i.e. replace it with something different, as well as adding the cost result from the first solution as a constraint to the existing problem and solve it again. I would suspect that this also would decrease the solution time for the second problem since we are starting with a valid but suboptimal solution.

Alternatively, is there perhaps a way to build these two requirements into a single LP? I have both targets as part of the objective function already, combined with a weight parameter, but tuning this parameter to give me the type of optimal solution that I'm looking for for any combination of input parameters is impossible, I fear.

Do you have any suggestions for how I could move forward with something like this? I have not been able to find any references to replacing the objective function in the documentation, so maybe it is not possible?

Thanks.

[Stuart Mitchell]

You just add a new objective with += in the same way you added it in the beginning the old objective will be replaced.

You can also use LpProblem.set objective() which does the same thing or use the LpProblem.sequentialSolve () function which takes a list of objectives and tolerances and does what you want to do.

Stu

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[Roland Vincze]

Hello!

I would like to use more objectives as well (actually a number of 4), but sometimes minimising sometimes maximising. How does the sequentialSolve function work? How can I add all the objectives to the model? Is there any documentation of this functionality?

Thanks,

Roland

[Stuart Mitchell]

documentation is in https://github.com/coin-or/pulp/blob/master/src/pulp/pulp.py#L1649

the function assumes you want to minimise all objectives. So please multiply all maximise objectives by -1 to convert the objective to a minimise objective.

Stu

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Stuart Mitchell

PhD Engineering Science

Extraordinary Freelance Programmer and Optimisation Guru

www.stuartmitchell.com

[Roland Vincze]

I see. Could you please give me a short example code? I don't know what objects to provide as the 'objectives' argument (I tried LpProblem, but that does not work).

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[Stuart Mitchell]

LpAffineExpression some thing like

>>> a + b + c