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I have a set of close mixed-integer programming problems. More exactly, all the problems share the same set of (binary and continuous) variables, the same set of linear inequality constraints, and the same linear objective function. However, linear equality constraints are specific to each problem.

Is there an algorithm to solve the set of problems that is more efficient than separate solving of each of the problems?

Both algorithms and references to solvers that do this are interesting. Thanks in advance.

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  • $\begingroup$ Is everything linear (MILP)? One equality constraint per problem? $\endgroup$
    – RobPratt
    Commented Aug 15, 2020 at 12:45
  • $\begingroup$ Yes, linear (fixed title and description), No, typically multiple equality constraints. $\endgroup$
    – Nikolay
    Commented Aug 15, 2020 at 13:15

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You could dualize the (complicating) equality constraints and use the branch-and-price algorithm. The resulting problems all have the same subproblem, and so you can use a common pool of columns. More explicitly, solve the first problem, use the resulting columns as an initial pool for the second problem, and repeat for each subsequent problem.

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