User-defined Callbacks
Callbacks are functions defined by the user that allow him to take over part of the default conquer algorithm. The more classical callbacks in Branch-and-Cut and Branch-and-Price solvers are:
- Pricing callback (only in Branch-and-Price solvers) that takes over the procedure to determine whether the current master LP solution is optimum or produces an entering variable with negative reduced cost by solving subproblems
- Separation callback that takes over the procedure to determine whether the current master LP solution is feasible or produces a valid problem constraint that is violated
- Branching callback that takes over the procedure to determine whether the current master LP solution is integer or produces a valid branching disjunctive constraint that rules out the current fractional solution.
You can't change the original formulation in a callback because Coluna does not propagate the changes into the reformulation and does not check if the solutions found are still feasible.
Pricing callbacks
Pricing callbacks let you define how to solve the subproblems of a Dantzig-Wolfe decomposition to generate a new entering column in the master program. This callback is useful when you know an efficient algorithm to solve the subproblems, i.e. an algorithm better than solving the subproblem with a MIP solver.
See the example in the tutorial section.
Errors and Warnings
Coluna.Algorithm.IncorrectPricingDualBound — TypeIncorrectPricingDualBoundError thrown when transmitting a dual bound larger than the primal bound of the best solution to the pricing subproblem found in a run of the pricing callback.
Coluna.Algorithm.MissingPricingDualBound — TypeMissingPricingDualBoundError thrown when the pricing callback does not transmit any dual bound. Make sure you call MOI.submit(model, BD.PricingDualBound(cbdata), db) in your pricing callback.
Coluna.Algorithm.MultiplePricingDualBounds — TypeMultiplePricingDualBoundsError thrown when the pricing transmits multiple dual bound. Make sure you call MOI.submit(model, BD.PricingDualBound(cbdata), db) only once in your pricing callback.
Separation callbacks
Separation callbacks let you define how to separate cuts or constraints.
Facultative & essential cuts (user cut & lazy constraint)
This callback allows you to add cuts to the master problem. The cuts must be expressed in terms of the original variables. Then, Coluna expresses them over the master variables. You can find an example of essential cut separation and facultative cut separation in the JuMP documentation.