MIP API Reference

MIP uses the shared Java problem construction and solve APIs documented in Convex Optimization API Reference. The following features are particularly relevant to mixed-integer problems.

Variable Types

Use VariableType when adding a variable or updating an existing variable:

Variable integer = problem.addVariable(
    0.0, 100.0, 3.0,
    VariableType.INTEGER, "integer");

Variable semiContinuous = problem.addVariable(
    0.0, 100.0, 1.0,
    VariableType.SEMI_CONTINUOUS, "semi");

The supported values are CONTINUOUS, INTEGER, and SEMI_CONTINUOUS. Problem.isMIP() and Solution.isMIP() report whether a problem or result contains a noncontinuous variable.

MIP Starts

MIP starts can be provided per variable through Variable.setMIPStart. The high-level Problem.solve collects defined variable starts and passes them to the native solver. A complete start can also be supplied directly through SolverSettings.addMIPStart(double[]).

x.setMIPStart(3.0);
y.setMIPStart(2.0);

Passing a complete start directly means building the array yourself. It is indexed by Variable.getIndex(), which is the order getVariables returns, so build it from that list rather than by hand:

Map<Variable, Double> start = Map.of(x, 3.0, y, 2.0);

double[] values = new double[problem.getNumVariables()];
for (Variable variable : problem.getVariables()) {
  values[variable.getIndex()] = start.getOrDefault(variable, 0.0);
}

try (SolverSettings settings = new SolverSettings()) {
  settings.addMIPStart(values);
  try (Solution solution = problem.solve(settings)) {
    System.out.println(solution.getMIPGap());
  }
}

MIP Settings

All solver settings are set through SolverSettings. Use the overloaded setSetting methods for string, integer, floating-point, and Boolean values. MIP-relevant settings include time and node limits, MIP tolerances, presolve, heuristics, scaling, determinism, and cut controls. The generated CuOptConstants class contains the string and integer constants from the cuOpt public constants header, including every setting name.

MIP Callbacks

SolverSettings.setMIPCallback accepts either callback interface:

MIPSolutionCallback receives each incumbent solution:

settings.setMIPCallback(
    (solution, objectiveValue, solutionBound, userData) -> {
      System.out.println("incumbent objective = " + objectiveValue);
    },
    "my-user-data",
    problem.getNumVariables());

MIPSetSolutionCallback runs in the other direction: the solver asks your code for a solution to try, and the MIPCallbackSolution you return carries it back. Use it to feed in a solution found elsewhere — a heuristic of your own, or a result carried over from a previous solve. Returning null declines, leaving the search untouched.

The array is in variable-index order and must cover every variable, so build it the same way as a MIP start:

settings.setMIPCallback(
    (solutionBound, userData) -> {
      double[] values = new double[problem.getNumVariables()];
      for (Variable variable : problem.getVariables()) {
        values[variable.getIndex()] = myHeuristic(variable);
      }
      return new MIPCallbackSolution(values, objectiveOf(values));
    },
    null,
    problem.getNumVariables());

Callbacks are native-runtime features. Keep the callback and any user data valid for the duration of the solve, and close the SolverSettings after the solve completes. Registered callbacks can be inspected with getMIPCallbacks.

MIP Solution Fields

For a MIP Solution:

• getPrimalObjective returns the incumbent objective value;

• getMIPGap returns the current relative MIP gap;

• getSolutionBound returns the best bound reported by the solver; and

• getTerminationStatus, getErrorStatus, and getErrorMessage describe the solve.

Incumbent values are read from the model: Variable.getValue after the solve.

LP-only accessors such as getDualSolution and getReducedCost raise IllegalStateException for a MIP result.

MIP statistics — presolve time, node and simplex iteration counts, and the violation magnitudes — are read as solution attributes:

int nodes = solution.getIntAttribute(
    CuOptConstants.CUOPT_SOLUTION_ATTR_MIP_NUM_NODES);
double violation = solution.getFloatAttribute(
    CuOptConstants.CUOPT_SOLUTION_ATTR_MIP_MAX_CONSTRAINT_VIOLATION);

An LP selector on a MIP solution raises CuOptException.

Inspecting a MIP

A problem can be inspected through getConstraintMatrix and getQuadraticObjectiveMatrix. To create an LP relaxation, build the problem with VariableType.CONTINUOUS, or set the types through Variable.setVariableType before solving.