Solver-independent Callbacks

Many mixed-integer (linear, conic, and nonlinear) programming solvers offer the ability to modify the solve process. Examples include changing branching decisions in branch-and-bound, adding custom cutting planes, providing custom heuristics to find feasible solutions, or implementing on-demand separators to add new constraints only when they are violated by the current solution (also known as lazy constraints).

While historically this functionality has been limited to solver-specific interfaces, JuMP provides solver-independent support for three types of callbacks:

lazy constraints
user-cuts
heuristic solutions

Available solvers

Solver-independent callback support is limited to a few solvers. This includes CPLEX, GLPK, Gurobi, Xpress, and SCIP (SCIP does not support lazy constraints).

Warning

While JuMP provides a solver-independent way of accessing callbacks, you should not assume that you will see identical behavior when running the same code on different solvers. For example, some solvers may ignore user-cuts for various reasons, while other solvers may add every user-cut. Read the underlying solver's callback documentation to understand details specific to each solver.

Tip

This page discusses solver-independent callbacks. However, each solver listed above also provides a solver-dependent callback to provide access to the full range of solver-specific features. Consult the solver's README for an example of how to use the solver-dependent callback. This will require you to understand the C interface of the solver.

Things you can and cannot do during solver-independent callbacks

There is a limited range of things you can do during a callback. Only use the functions and macros explicitly stated in this page of the documentation, or in the Callbacks tutorial.

Using any other part of the JuMP API (for example, adding a constraint with @constraint or modifying a variable bound with set_lower_bound) is undefined behavior, and your solver may throw an error, return an incorrect solution, or result in a segfault that aborts Julia.

In each of the three solver-independent callbacks, there are two things you may query:

callback_node_status returns an MOI.CallbackNodeStatusCode enum indicating if the current primal solution is integer feasible.
callback_value returns the current primal solution of a variable.

If you need to query any other information, use a solver-dependent callback instead. Each solver supporting a solver-dependent callback has information on how to use it in the README of their GitHub repository.

If you want to modify the problem in a callback, you must use a lazy constraint.

Warning

You can only set each callback once. Calling set twice will over-write the earlier callback. In addition, if you use a solver-independent callback, you cannot set a solver-dependent callback.

Lazy constraints

Lazy constraints are useful when the full set of constraints is too large to explicitly include in the initial formulation. When a MIP solver reaches a new solution, for example with a heuristic or by solving a problem at a node in the branch-and-bound tree, it will give the user the chance to provide constraints that would make the current solution infeasible. For some more information about lazy constraints, see this blog post by Paul Rubin.

A lazy constraint callback can be set using the following syntax:

julia> import GLPK

julia> model = Model(GLPK.Optimizer);

julia> @variable(model, x <= 10, Int)
x

julia> @objective(model, Max, x)
x

julia> function my_callback_function(cb_data)
           status = callback_node_status(cb_data, model)
           if status == MOI.CALLBACK_NODE_STATUS_FRACTIONAL
               # `callback_value(cb_data, x)` is not integer (to some tolerance).
               # If, for example, your lazy constraint generator requires an
               # integer-feasible primal solution, you can add a `return` here.
               return
           elseif status == MOI.CALLBACK_NODE_STATUS_INTEGER
               # `callback_value(cb_data, x)` is integer (to some tolerance).
           else
               @assert status == MOI.CALLBACK_NODE_STATUS_UNKNOWN
               # `callback_value(cb_data, x)` might be fractional or integer.
           end
           x_val = callback_value(cb_data, x)
           if x_val > 2 + 1e-6
               con = @build_constraint(x <= 2)
               MOI.submit(model, MOI.LazyConstraint(cb_data), con)
           end
       end
my_callback_function (generic function with 1 method)

julia> set_attribute(model, MOI.LazyConstraintCallback(), my_callback_function)

Info

The lazy constraint callback may be called at fractional or integer nodes in the branch-and-bound tree. There is no guarantee that the callback is called at every primal solution.

Warning

Only add a lazy constraint if your primal solution violates the constraint. Adding the lazy constraint irrespective of feasibility may result in the solver returning an incorrect solution, or lead to many constraints being added, slowing down the solution process.

model = Model(GLPK.Optimizer)
@variable(model, x <= 10, Int)
@objective(model, Max, x)
function bad_callback_function(cb_data)
    # Don't do this!
    con = @build_constraint(x <= 2)
    MOI.submit(model, MOI.LazyConstraint(cb_data), con)
end
function good_callback_function(cb_data)
    if callback_value(x) > 2
        con = @build_constraint(x <= 2)
        MOI.submit(model, MOI.LazyConstraint(cb_data), con)
    end
end
set_attribute(model, MOI.LazyConstraintCallback(), good_callback_function)

Warning

During the solve, a solver may visit a point that was cut off by a previous lazy constraint, for example, because the earlier lazy constraint was removed during presolve. If this happens, you must re-add the lazy constraint.

User cuts

User cuts, or simply cuts, provide a way for the user to tighten the LP relaxation using problem-specific knowledge that the solver cannot or is unable to infer from the model. Just like with lazy constraints, when a MIP solver reaches a new node in the branch-and-bound tree, it will give the user the chance to provide cuts to make the current relaxed (fractional) solution infeasible in the hopes of obtaining an integer solution. For more details about the difference between user cuts and lazy constraints see the aforementioned blog post.

A user-cut callback can be set using the following syntax:

julia> import GLPK

julia> model = Model(GLPK.Optimizer);

julia> @variable(model, x <= 10.5, Int)
x

julia> @objective(model, Max, x)
x

julia> function my_callback_function(cb_data)
           x_val = callback_value(cb_data, x)
           con = @build_constraint(x <= floor(x_val))
           MOI.submit(model, MOI.UserCut(cb_data), con)
       end
my_callback_function (generic function with 1 method)

julia> set_attribute(model, MOI.UserCutCallback(), my_callback_function)

Warning

User cuts must not change the set of integer feasible solutions. Equivalently, user cuts can only remove fractional solutions. If you add a cut that removes an integer solution (even one that is not optimal), the solver may return an incorrect solution.

Info

The user-cut callback may be called at fractional nodes in the branch-and-bound tree. There is no guarantee that the callback is called at every fractional primal solution.

Heuristic solutions

Integer programming solvers frequently include heuristics that run at the nodes of the branch-and-bound tree. They aim to find integer solutions quicker than plain branch-and-bound would to tighten the bound, allowing us to fathom nodes quicker and to tighten the integrality gap.

Some heuristics take integer solutions and explore their "local neighborhood" (for example, flipping binary variables, fix some variables and solve a smaller MILP) and others take fractional solutions and attempt to round them in an intelligent way.

You may want to add a heuristic of your own if you have some special insight into the problem structure that the solver is not aware of, for example, you can consistently take fractional solutions and intelligently guess integer solutions from them.

A heuristic solution callback can be set using the following syntax:

julia> import GLPK

julia> model = Model(GLPK.Optimizer);

julia> @variable(model, x <= 10.5, Int)
x

julia> @objective(model, Max, x)
x

julia> function my_callback_function(cb_data)
           x_val = callback_value(cb_data, x)
           status = MOI.submit(
               model, MOI.HeuristicSolution(cb_data), [x], [floor(Int, x_val)]
           )
           println("I submitted a heuristic solution, and the status was: ", status)
       end
my_callback_function (generic function with 1 method)

julia> set_attribute(model, MOI.HeuristicCallback(), my_callback_function)

The third argument to submit is a vector of JuMP variables, and the fourth argument is a vector of values corresponding to each variable.

MOI.submit returns an enum that depends on whether the solver accepted the solution. The possible return codes are:

MOI.HEURISTIC_SOLUTION_ACCEPTED
MOI.HEURISTIC_SOLUTION_REJECTED
MOI.HEURISTIC_SOLUTION_UNKNOWN

Warning

Some solvers may accept partial solutions. Others require a feasible integer solution for every variable. If in doubt, provide a complete solution.

Info

The heuristic solution callback may be called at fractional nodes in the branch-and-bound tree. There is no guarantee that the callback is called at every fractional primal solution.