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General Constraints: Representations and Information Retrieval

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Minshuo Li
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  • First Question

Hi all,

I have two questions ragarding Gurobi's general constraints when using Gurobi's Python API.

1. I've noticed that nonlinear expressions can be added to the model in several ways. For example, to represent the constraint y=x^3, I can use

model.addConstr(x**3 == y[0], name='c0')
model.addGenConstrNL(y[1], x**3, name='c_nl')
model.addGenConstrPoly(x, y[2], [1,0,0,0], name='c_poly')
model.addGenConstrPow(x, y[3], 3, name='c_pow')

The resulting .lp file shows these constraints stored in three different formats:

General Constraints
\ y[0] = x ^ 3
 c0: y[0] = NL : ( POW , -1 , -1 ) ( VARIABLE , x , 0 ) 
  ( CONSTANT , 3 , 0 )
\ y[1] = x ^ 3
 c_nl: y[1] = NL : ( POW , -1 , -1 ) ( VARIABLE , x , 0 ) 
  ( CONSTANT , 3 , 0 )
 c_poly: y[2] = POLY ( 1 x ^ 3 )
 c_pow: y[3] = POW ( x ^ 3 )

While these constraints are mathematically equivalent, they're stored in three different representations in the model. Are these different representations treated identically during the solving process, or might there be performance implications depending on which form is used?

2. When loading a MINLP model from a .lp file, I'd like to retrieve information about the nonlinear expressions in its general constraints (e.g., variables involved, coefficients, nonlinear operators). I've checked Gurobi's documentation but couldn't find direct methods for examining general expressions (both GenExpr and NLExpr). Is it possible to extract this information in the current version of Gurobi? If so, what would be the recommended approach?

Thanks a lot for your assistance.

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3 comments

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  • Matthias Miltenberger
    • Gurobi Staff Gurobi Staff

    Hi!

    That is a very good question and our custom ChatGPT - Gurobot provides a really good and comprehensive answer:

    1. Performance Implications of Different General Constraint Representations

    Gurobi treats general constraints differently depending on their type and representation. Here's how these representations impact performance:

    • Nonlinear Constraints (GenConstrNL): These constraints are handled using Gurobi's spatial branch-and-bound method, which can be computationally expensive. The solver constructs linear outer approximations dynamically to refine the solution space.
    • Polynomial Constraints (GenConstrPoly): This method uses explicit polynomial coefficients and can be more efficient when the polynomial degree is low. It allows Gurobi to use predefined strategies for handling polynomial constraints, avoiding the overhead of dynamically approximating nonlinear terms.
    • Power Constraints (GenConstrPow): When raising a variable to a power, Gurobi can apply either nonlinear branching (if nonlinear optimization is enabled) or piecewise-linear approximations (if the model is solved as a MIP). The performance depends on the chosen method: piecewise-linear approximations introduce more constraints but keep the problem linear, whereas nonlinear constraints increase computational complexity.
    • Directly Adding Nonlinear Expressions (e.g., x**3 == y): These constraints are automatically recognized as nonlinear and processed accordingly. While functionally equivalent to addGenConstrNL, this approach can sometimes be more intuitive but may not explicitly use Gurobi's specialized constraint-handling features.

    Best Practices for Performance:

    • If you are solving a purely nonlinear problem, using addGenConstrNL ensures that the solver is aware of the nonlinear nature of the constraint and can handle it using appropriate global optimization techniques.
    • If the problem can be linearized, then addGenConstrPoly or addGenConstrPow can be preferable, as they help Gurobi optimize the constraint using piecewise-linear approximations.
    • If numerical stability is a concern, function constraints (addGenConstrPow) can help maintain accuracy without requiring explicit auxiliary variables.

    In general, function constraints (GenConstrPow, GenConstrPoly) are more efficient than general nonlinear constraints (GenConstrNL) because they allow Gurobi to leverage dedicated approximation methods instead of relying on a full nonlinear branch-and-bound approach.

    2. Extracting Nonlinear Expressions from General Constraints in a Loaded Model

    As of Gurobi 12.0, there is no direct API method to extract the full expression tree of a nonlinear general constraint (GenConstrNL). However, you can retrieve information about these constraints using the following methods:

    • Retrieve General Constraint Type:

      for gc in model.getGenConstrs():
    print(gc.ConstrName, gc.GenConstrType)

      This helps determine whether the constraint is polynomial, power, or a general nonlinear constraint.

    • Retrieve Function Approximation Parameters:

      func_error = gc.getAttr(GRB.DoubleAttr.FuncPieceError)
func_pieces = gc.getAttr(GRB.IntAttr.FuncPieces)
print(f"Function Approximation Error: {func_error}, Pieces: {func_pieces}")

      This is useful for function constraints like GenConstrPow and GenConstrPoly, which use piecewise approximations.

    • Retrieve the Expression Structure for Nonlinear Constraints: Gurobi internally represents nonlinear constraints as expression trees. The expression tree consists of:

      • Opcode array (operation types like addition, multiplication, sine, etc.).
      • Data array (constants and variable indices).
      • Parent array (hierarchical structure).

      Example:

      nl_expr_tree = model.getAttr("NLExpr", gc)
print(nl_expr_tree)

      However, this method is not yet documented for public API usage. Instead, users typically need to analyze the .lp file manually or reconstruct expressions based on constraint structure.

    Alternative Workarounds:

    • Parsing an .lp File: Since .lp files explicitly list general constraints, you can inspect them externally.
    • Using addGenConstrPoly or addGenConstrPow instead of addGenConstrNL, as these constraints have more structured retrieval options.

    Summary:

    1. Performance of Different General Constraints:

      • GenConstrNL (Nonlinear Constraints) → Computationally expensive, uses spatial branch-and-bound.
      • GenConstrPoly (Polynomial) → More efficient if the polynomial degree is low.
      • GenConstrPow (Power) → Uses function approximation or MIP methods, efficient for known exponentiation functions.
      • x**3 == y (Direct Expression) → Can be recognized as nonlinear but may not use Gurobi’s specialized constraint handlers.

    2. Extracting Nonlinear Expressions:

      • Gurobi does not provide a direct way to extract full nonlinear expressions.
      • You can retrieve the constraint type, approximation settings, and expression tree using attributes.
      • If full expression extraction is necessary, parsing an .lp file may be the best workaround.

    I hope this answers your questions fully. Please feel free to reach out if you need further assistance.

    Cheers,
    Matthias

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  • David Torres Sanchez
    • Gurobi Staff Gurobi Staff

    However, this method is not yet documented for public API usage. Instead, users typically need to analyze the .lp file manually or reconstruct expressions based on constraint structure.

    To correct the API question, we do have a method to obtain the expression tree, using the model.getGenConstrNLAdv.

    >>> m.getGenConstrNLAdv(c)
    (<gurobi.Var C0>, [12, 1, 0], [-1.0, <gurobi.Var C1>, 3.0], [-1, 0, 0])

    Please see the docs for more info on what these represent.

    Cheers, 
    David

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  • Minshuo Li
    • First Comment
    • First Question

    Very helpful information! Thank you Matthias and David! 

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