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This is quite a general question, but I have not been able to find a solution so far.

I am trying to solve a problem of combinatorial optimization in which I have several objective functions to optimize, as well as several constraints to impose. I am thus trying to find some software (an R package preferably) that can solve this problem.

I have explored several options, but none of them seems to be useful for my purpose: lpSolveAPI is aimed for linear programming only, which is not the case; mco can minimize a multidimensional objective function, but does not seem to be able to manage binary (i.e. decision) variables, needed for combinatorial problems; adagio and CEGO can deal with combinatorial optimization problems, but as far as I can see they can only optimize a single unidimensional function.

Is there any other package I am not aware of that can handle this type of problem? Or any of the aforementioned may be useful, though I may be missing the way to the functionality I need?

Thank you so much in advance with this. It is being really a nightmare trying to find this out.

Mori
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    I'm not really sure if I understand the question correctly. maybe this might hint into a helpful direction: http://stackoverflow.com/questions/23808693/how-to-put-mathematical-constraints-with-gensa-function-in-r/23830791#23830791 ; if you have several objective functions you can just calculate the (weighted) sum of the objective values to get a global target value. – Tom Sep 05 '16 at 06:55
  • If the problem is small you can enumerate the Pareto optimal points using a series of MIP problems [(link)](http://yetanothermathprogrammingconsultant.blogspot.com/2010/02/generating-all-non-dominated-solutions.html) – Erwin Kalvelagen Sep 05 '16 at 17:13
  • If you could provide a example, that would be useful. – Emmanuel Hamel Apr 12 '23 at 17:54

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