Solvers

This section provides an overview of using and configuring solvers for IDAES. In general, standard Pyomo solver interfaces and features are used in IDAES, but IDAES provides a few extensions to make working with solvers slightly easier. Some IDAES solver features are documented in other sections, so references are provided as appropriate.

Default Solver Config

The global solver settings can be set via the IDAES configuration system. This feature is handy in IDAES where multiple solver objects are used for initialization before finally solving a problem. Since IDAES default solver settings differ from Pyomo, users must explicitly enable the IDAES solver configuration system with the use_idaes_solver_configuration_defaults() function.

idaes.core.solvers.config.use_idaes_solver_configuration_defaults(b=True)[source]

This function enables (or disables if given False as the argument) solvers getting default settings from the IDAES configuration. When enabled this allows global configuration of solvers.

Parameters

b – True to use default solver configurations from the IDAES configuration False to use standard Pyomo solver factories. Default is True.

Returns

None

Getting a Solver

Typically users can use the standard Pyomo SoverFactory to get a solver. If a solver is needed in a general model or utility, a utility function (idaes.core.solvers.get_solver) provides a default or user configured solver at runtime. This is used by IDAES core models and tests.

Solver Logging

A logger for solver-related log messages can be obtained from the idaes.logger.getSolveLogger() function (documented here). IDAES also has features for redirecting solver output to a log (see Logging Solver Output).

Solver Feature Checking

There are some functions available to check what features are available to solvers and to help with basic solver testing.

idaes.core.solvers.ipopt_has_linear_solver(linear_solver)[source]

Check if IPOPT can use the specified linear solver.

Parameters

linear_solver (str) – linear solver in {“ma27”, “ma57”, “ma77”, “ma86”, “ma97”, “pardiso”, “pardisomkl”, “spral”, “wsmp”, “mumps”} or other custom solver.

Returns

True if Ipopt is available with the specified linear solver or False if either Ipopt or the linear solver is not available.

Return type

(bool)

PETSc Utilities

IDAES provides an AMPL solver interface for the PETSc solver suite, (see the PETSc website). PETSc provides nonlinear equation (NLE) and differential algebraic equation (DAE) solvers. Both NLE and DAE solvers are capable of solving simulation problems with zero degrees of freedom. These solvers may be useful for initial model development, initialization, and running simulation cases without optimization.

PETSc includes optimization solvers, but they are not currently supported by the IDAES AMPL solver wrapper. Optimization support will likely be added in the future.

DAE Terminology

For the following discussion regarding the PETSc solver interface, the following terminology is used.

  • Derivative variable: a time derivative

  • Differential variable: a variable that is differentiated with respect to time

  • Algebraic variable: a variable with no explicit time derivative appearing in the problem

  • State variables: the set of algebraic and differential variables

  • Time variable: a variable representing time

DAE problems do not need to include a time variable, but, if they do, there can only be one. Differential variables do not need to explicitly appear in constraints, but their time derivatives do. DAE problems must have zero degrees of freedom, which means the number of constraints must equal the number of state variables.

Installing PETSc

The PETSc solver is an extra binary package, and not installed by default. If you are using a supported platform, you can use the command idaes get-extensions --extra petsc to install it.

Registered Solvers

Importing idaes.core.solvers.petsc registers two new solvers “petsc_snes” and “petsc_ts.” The “petsc_snes” solver provides nonlinear equation solvers. The SNES (Scalable Nonlinear Equation Solvers) solvers are strictly nonlinear equations solvers, so they cannot directly handle optimization problems and the problem must have zero degrees of freedom. The TS (time-stepping) solvers require specialized suffixes to designate derivative, differential, algebraic, and time variables and the associations between derivative and differential variables. Both the SNES and TS solvers accept the standard scaling factor suffixes, but for TS solvers, derivatives and differential variables cannot be scaled independently, so the differential variable scale is used. Currently, time cannot be scaled for TS solvers.

Standard PETSc command line options are available to the solvers except that for compatibility reasons, they are specified with a double dash instead of single. Command line options can be used to set up the SNES and TS solvers. Currently only implicit TS solvers are supported. Commonly used TS types are:

  • “beuler”, implicit Euler,

  • “cn”, Crank-Nicolson, and

  • “alpha”, generalized-alpha method.

To get started, important command line options are for SNES solvers are described https://petsc.org/release/docs/manualpages/SNES/SNESSetFromOptions.html and TS options are described https://petsc.org/release/docs/manualpages/TS/TSSetFromOptions.html. Remember that options specified through the IDAES AMPL interface use a double dash rather than the single dash shown in the PETSc documentation. Users can also set linear solver and preconditioner options, and are encouraged to read the PETSc documentation if needed.

Utilities for DAEs with Pyomo.DAE

The easiest way to use the “petsc_ts” solver is to use the utility method that converts a standard Pyomo.DAE to the form used by the solver.

Discretization

The utility for solving Pyomo.DAE problems uses the PETSc TS solvers to integrate between selected time points in the Pyomo.DAE discretization. The results for each time point integrated between are stored in the Pyomo model. Optionally the skipped time points can be interpolated from the PETSc solver trajectory data. This can be used to initialize and verify the results of the full time-discretized model. For example, this could be used to determine if the time steps used in the discretization are too big by comparing the integrator solution to the fully discretized solution. To quickly run a DAE model, you can integrate between the first and last time points.

Time Variable

Although it is probably not typical of Pyomo.DAE models, a time variable can be specified. Constraints can be written as explicit functions of time. For example, some model input could be ramped up or down as a function of time.

Limitations

The integrator approach does not support some constraints that can be solved using the full discretized model. For example, you can have constraints to calculate initial conditions, but cannot have constraints that specify final or intermediate conditions. Optimization is not directly possible, but future implementation of optimization solvers in combination with adjoint sensitivity calculations may enable optimization.

Non-time-indexed variables and constraints should usually be solved with the initial conditions in the first step. Non-time-indexed variables can optionally be detected and added to the equations solved for the initial conditions, or explicitly specified by the user. Users will have to take care not to include non-time indexed constraints that contain time-indexed variables at times other than the initial time. If such constraints exist for the fully discretized model users should deactivate them as appropriate.

Solving

The following function can be used to solve the DAE.

idaes.core.solvers.petsc.petsc_dae_by_time_element(m, time, timevar=None, initial_constraints=None, initial_variables=None, detect_initial=True, skip_initial=False, snes_options=None, ts_options=None, keepfiles=False, symbolic_solver_labels=True, between=None, interpolate=True, calculate_derivatives=True)[source]

Solve a DAE problem step by step using the PETSc DAE solver. This integrates from one time point to the next.

Parameters

  • m (Block) – Pyomo model to solve

  • time (ContinuousSet) – Time set

  • timevar (Var) – Optional specification of a time variable, which can be used to write constraints that are an explicit function of time.

  • initial_constraints (list) – Constraints to solve in the initial condition solve step. Since the time-indexed constraints are picked up automatically, this generally includes non-time-indexed constraints.

  • initial_variables (list) – This is a list of variables to fix after the initial condition solve step. If these variables were originally unfixed, they will be unfixed at the end of the solve. This usually includes non-time-indexed variables that are calculated along with the initial conditions.

  • detect_initial (bool) – If True, add non-time-indexed variables and constraints to initial_variables and initial_constraints.

  • skip_initial (bool) – Don’t do the initial condition calculation step, and assume that the initial condition values have already been calculated. This can be useful, for example, if you read initial conditions from a separately solved steady state problem, or otherwise know the initial conditions.

  • snes_options (dict) – PETSc nonlinear equation solver options

  • ts_options (dict) – PETSc time-stepping solver options

  • keepfiles (bool) – pass to keepfiles arg for solvers

  • symbolic_solver_labels (bool) – pass to symbolic_solver_labels argument for solvers. If you want to read trajectory data from the time-stepping solver, this should be True.

  • between (list or tuple) – List of time points to integrate between. If None use all time points in the model. Generally the list should start with the first time point and end with the last time point; however, this is not a requirement and there are situations where you may not want to include them. If you are not including the first time point, you should take extra care with the initial conditions. If the initial conditions are already correct consider using the skip_initial option if the first time point is not included.

  • interpolate (bool) – if True and trajectory is read, interpolate model values from the trajectory

  • calculate_derivatives – (bool) if True, calculate the derivative values based on the values of the differential variables in the discretized Pyomo model.

Returns (PetscDAEResults):

See PetscDAEResults documentation for more informations.

Reading Trajectory Data

By specifying the --ts_save_trajectory=1 option the trajectory information will be saved. The idaes.core.solvers.petsc.petsc_dae_by_time_element function returns trajectory data if saved as a PetscTrajectory class, which has methods to load, save, and interpolate.

class idaes.core.solvers.petsc.PetscTrajectory(stub=None, vecs=None, json=None, pth=None, vis_dir='Visualization-data', delete_on_read=False, unscale=None, model=None, no_read=False)[source]
delete_files()[source]

Delete the trajectory data and variable information files.

Parameters

None –

Returns

None

from_json(pth)[source]

Read the trajectory data from a json file in the form of a dictionary.

Parameters

pth (str) – path for json file to write

Returns

None

get_dt()[source]

Get a list of time steps

Parameters

None –

Returns

(list)

get_vec(var)[source]

Return the vector of variable values at each time point for var.

Parameters

  • var (str or Var) – Variable to get vector for.

  • time (Set) – Time index set

Retruns (list):

vector of variable values at each time point

interpolate(times)[source]

Create a new vector dictionary interpolated at times. This method will also extrapolate values outside the original time range, so care should be taken not to specify times too far outside the range.

Parameters

times (list) – list of times to interpolate. These must be in increasing order.

Returns (dict):

Dictionary of vectors for values at interpolated points

interpolate_vec(times, var)[source]

Create a new vector dictionary interpolated at times. This method will also extrapolate values outside the original time range, so care should be taken not to specify times too far outside the range.

Parameters

times (list) – list of times to interpolate. These must be in increasing order.

Returns (dict):

Dictionary of vectors for values at interpolated points

to_json(pth)[source]

Dump the trajectory data to a json file in the form of a dictionary with variable name keys and ‘_time’ with vectors of values at each time.

Parameters

pth (str) – path for json file to write

Returns

None

Using TS Solvers without Pyomo.DAE

Most IDAES models use Pyomo.DAE and that is probably the easiest way to set up a DAE problem, however you may directly construct a DAE problem.

There are two suffixes that need to be specified to use the PETSc TS solvers from Pyomo. The first is an integer suffix dae_suffix, which specifies the variable types. The algebraic variables do not need to be included, but 0 specifies algebraic variables, 1 specifies differential variables, 2 specifies derivative variables, and 3 specifies the time variable. A variable for time is optional, and only one time variable can be specified. The other suffix is an integer suffix dae_link which contains differential and derivative variables. The integer in the suffix links the derivative to it’s differential variable, by specifying an integer greater than 0 that is unique to the pair.

If there are differential variables that do not appear in the constraints, they can be supplied to the export_nonlinear_variables argument of solve. For the trajectory data, you will also want to use symbolic_solver_labels.

To solve the problem, start with the initial conditions in the Pyomo model. After the solve the final conditions will be in the Pyomo model. To get intermediate results, you will need to store the solver trajectory as described previously.

Planned Future PETSc Support

This section provides PETSc features that are planned to be supported in the future, but are not currently supported.

  • Enable parallel methods

  • Enable IMEX methods for TS solvers

  • Enable TAO optimization solvers

  • Provide PETSc Python functions for reading trajectory data (rather than requiring users to get them manually).

Test Models

The idaes.core.solvers.features module provides functions to return simple models of various types. These models can be used to test if solvers are available and functioning properly. They can also be used to test that various optional solver features are available. These functions all return a tuple where the first element is a model of the specified type, and the remaining elements are the correct solved values for select variables.

idaes.core.solvers.features.lp()[source]

This provides a simple LP model for solver testing.

Parameters

None –

Returns

Pyomo ConcreteModel, correct solved value for m.x

Return type

(tuple)

idaes.core.solvers.features.milp()[source]

This provides a simple MILP model for solver testing.

Parameters

None –

Returns

Pyomo ConcreteModel, correct solved value for m.x

Return type

(tuple)

idaes.core.solvers.features.nlp()[source]

This provides a simple NLP model for solver testing.

Parameters

None –

Returns

Pyomo ConcreteModel, correct solved value for m.x

Return type

(tuple)

idaes.core.solvers.features.minlp()[source]

This provides a simple MINLP model for solver testing.

Parameters

None –

Returns

Pyomo ConcreteModel, correct solved value for m.x and m.i

Return type

(tuple)

idaes.core.solvers.features.nle()[source]

This provides a simple system of nonlinear equations model for solver testing.

Parameters

None –

Returns

Pyomo ConcreteModel, correct solved value for m.x

Return type

(tuple)

idaes.core.solvers.features.dae(nfe=1)[source]

This provides a DAE model for solver testing.

The problem and expected result are from the problem given here: https://archimede.dm.uniba.it/~testset/report/chemakzo.pdf.

Parameters

None –

Returns

Pyomo ConcreteModel, correct solved value for y[1] to y[5] and y6

Return type

(tuple)