Constraint Functions

This module provides a library of pre-defined ParMOO constraint function implementations and templates to define your own constraint function.

ConstraintFunction Template (ABC)

An abstract base class (ABC) for ParMOO constraint functions.

class constraints.const_func.ConstraintFunction(des_type, sim_type)

ABC defining ParMOO constraint functions.

Extend this class to create a callable object that matches ParMOO can use as a constraint function, such as an Objective or its Gradient.

Contains 2 methods:

  • __init__(des_type, sim_type)

  • __call__(x, sx)

The __init__ method is already implemented, and is the constructor. It can be overwritten if additional inputs (besides the design variable and simulation output types) are needed.

The __call__ method is left to be implemented, and performs the constraint function evaluation.

__init__(des_type, sim_type)

Constructor for ConstraintFunction class.

Parameters:

  • des_type (np.dtype) – The numpy.dtype of the design variables.

  • sim_type (np.dtype) – The numpy.dtype of the simulation outputs.

Constraint Function Library

This module contains a library of common constraint functions, matching ParMOO’s interface.

The common constraints are:

  • SingleSimBound – bound on a single simulation output’s value

  • SumOfSimSquaresBound – bound on the SOS for several sim outputs

  • SumOfSimsBound – bound on the (abs) sum of several sim outputs

And their corresponding gradient functions are:

  • SingleSimBoundGradient

  • SumOfSimSquaresBoundGradient

  • SumOfSimsBoundGradient

class constraints.const_lib.SingleSimBound(des_type, sim_type, sim_ind, bound_type='upper', bound=0.0)

Class for bounding a single simulation’s output.

If upper-bounding:

``` def ConstraintFunction(x, sx):

return sx[self.sim_ind] - upper_bound

```

If lower-bounding:

``` def ConstraintFunction(x, sx):

return lower_bound - sx[self.sim_ind]

```

Also supports derivative usage.

Contains 2 methods:

  • __init__(des_type, sim_type, sim_ind, bound_type='min', bound=0)

  • __call__(x, sim)

The __init__ method inherits from the ConstraintFunction ABC.

The __call__ returns the slack (negative when feasible).

__init__(des_type, sim_type, sim_ind, bound_type='upper', bound=0.0)

Constructor for SingleSimBound class.

Parameters:

  • des_type (np.dtype) – The numpy.dtype of the design variables.

  • sim_type (np.dtype) – The numpy.dtype of the simulation outputs.

  • sim_ind (str or tuple) – The name (or name, output index pair for simulations with more than one output field) designating the simulation output to minimize or maximize.

  • bound_type (str) – Either ‘lower’ to lower-bound or ‘upper’ to upper-bound. Defaults to ‘upper’.

  • bound (float) – The lower/upper bound for this constraint. Defaults to 0.

__call__(x, sx)

Define constraint evaluation.

Parameters:

  • x (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of a design point to evaluate.

  • sx (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of the simulation output(s) at x.

Returns:

The (negative when feasible) slack in this constraint for the input sx (x is unused).

Return type:

float

class constraints.const_lib.SumOfSimSquaresBound(des_type, sim_type, sim_inds, bound_type='upper', bound=0.0)

Class for constraining the sum-of-squared simulation outputs.

If upper bounding:

``` ConstraintFunction(x, sx):

return sum([sx[i]**2 for all i]) - upper_bound

```

If lower bounding:

``` def ConstraintFunction(x, sx):

return lower_bound - sum([sx[i]**2 for all i])

```

Also supports derivative usage.

Contains 2 methods:

  • __init__(des_type, sim_type, sim_inds, bound_type='upper', bound=0)

  • __call__(x, sx)

The __init__ method inherits from the ConstraintFunction ABC.

The __call__ evaluate the slack (negative values are feasible).

__init__(des_type, sim_type, sim_inds, bound_type='upper', bound=0.0)

Constructor for SumOfSimSquaresBound class.

Parameters:

  • des_type (np.dtype) – The numpy.dtype of the design variables.

  • sim_type (np.dtype) – The numpy.dtype of the simulation outputs.

  • sim_inds (list) – The list of names (or name, index pairs for sims with more than one output) of the simulation outputs to sum over.

  • bound_type (str) – Either ‘lower’ to lower-bound or ‘upper’ to upper-bound. Defaults to ‘upper’.

  • bound (float) – The lower/upper bound for this constraint. Defaults to 0.

__call__(x, sx)

Define constraint evaluation.

Parameters:

  • x (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of a design point to evaluate.

  • sx (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of the simulation output(s) at x.

Returns:

The (negative when feasible) slack in this constraint for the input sx (x is unused).

Return type:

float

class constraints.const_lib.SumOfSimsBound(des_type, sim_type, sim_inds, bound_type='upper', bound=0.0, absolute=False)

Class for bounding the (absolute) sum of simulation outputs.

If upper bounding:

``` def const_func(x, sx):

return sum([sx[i] for all i]) - upper_bound

```

If lower bounding:

``` def const_func(x, sx):

return lower_bound - sum([sx[i] for all i])

```

If upper bounding absolute sum:

``` def const_func(x, sx):

return sum([abs(sx[i]) for all i]) - upper_bound

```

If lower bounding absolute sum:

``` def const_func(x, sx):

return lower_bound - sum([abs(sx[i]) for all i])

```

Also supports derivative usage.

Contains 2 methods:
  • ``__init__(des_type, sim_type, sim_inds,

    bound_type=’upper’, bound=0, absolute=False)``

  • __call__(x, sim)

The __init__ method inherits from the ConstraintFunction ABC.

The __call__ evaluate the slack (negative values are feasible).

__init__(des_type, sim_type, sim_inds, bound_type='upper', bound=0.0, absolute=False)

Constructor for SumOfSimsBound class.

Parameters:

  • des_type (np.dtype) – The numpy.dtype of the design variables.

  • sim_type (np.dtype) – The numpy.dtype of the simulation outputs.

  • sim_inds (list) – The list of names (or name, index pairs for sims with more than one output) of the simulation outputs to sum over.

  • bound_type (str) – Either ‘lower’ to lower-bound or ‘upper’ to upper-bound. Defaults to ‘upper’.

  • bound (float) – The lower/upper bound for this constraint. Defaults to 0.

  • absolute (bool) – True to bound absolute sum, False to bound raw sum. Defaults to False.

__call__(x, sx)

Define constraint evaluation.

Parameters:

  • x (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of a design point to evaluate.

  • sx (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of the simulation output(s) at x.

Returns:

The (negative when feasible) slack in this constraint for the input sx (x is unused).

Return type:

float

class constraints.const_lib.SingleSimBoundGradient(des_type, sim_type, sim_ind, bound_type='upper', bound=0.0)

Gradient class for SingleSimBound.

Inherits from the SingleSimBound class, but overwrites the __call__ method to return the gradients wrt x and sx, respectively.

__init__(des_type, sim_type, sim_ind, bound_type='upper', bound=0.0)

Constructor for SingleSimBound class.

Parameters:

  • des_type (np.dtype) – The numpy.dtype of the design variables.

  • sim_type (np.dtype) – The numpy.dtype of the simulation outputs.

  • sim_ind (str or tuple) – The name (or name, output index pair for simulations with more than one output field) designating the simulation output to minimize or maximize.

  • bound_type (str) – Either ‘lower’ to lower-bound or ‘upper’ to upper-bound. Defaults to ‘upper’.

  • bound (float) – The lower/upper bound for this constraint. Defaults to 0.

__call__(x, sx)

Define gradient evaluation.

Parameters:

  • x (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of a design point to evaluate.

  • sx (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of the simulation output(s) at x.

Returns:

The gradient output of the simulation at self.sim_ind given the input (x, sx) wrt x and sx, respectively.

Return type:

dict, dict

class constraints.const_lib.SumOfSimSquaresBoundGradient(des_type, sim_type, sim_inds, bound_type='upper', bound=0.0)

Gradient class for SumOfSimSquaresBound.

Inherits from the SumOfSimSquaresBound class, but overwrites the __call__ method to return the gradients wrt x and sx, respectively.

__init__(des_type, sim_type, sim_inds, bound_type='upper', bound=0.0)

Constructor for SumOfSimSquaresBound class.

Parameters:

  • des_type (np.dtype) – The numpy.dtype of the design variables.

  • sim_type (np.dtype) – The numpy.dtype of the simulation outputs.

  • sim_inds (list) – The list of names (or name, index pairs for sims with more than one output) of the simulation outputs to sum over.

  • bound_type (str) – Either ‘lower’ to lower-bound or ‘upper’ to upper-bound. Defaults to ‘upper’.

  • bound (float) – The lower/upper bound for this constraint. Defaults to 0.

__call__(x, sx)

Define gradient evaluation.

Parameters:

  • x (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of a design point to evaluate.

  • sx (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of the simulation output(s) at x.

Returns:

The gradient of the sum of squared simulation outputs given the input (x, sx) wrt x and sx, respectively.

Return type:

dict, dict

class constraints.const_lib.SumOfSimsBoundGradient(des_type, sim_type, sim_inds, bound_type='upper', bound=0.0, absolute=False)

Gradient class for SumOfSimsBound.

Inherits from the SumOfSimsBound class, but overwrites the __call__ method to return the gradients wrt x and sx, respectively.

__init__(des_type, sim_type, sim_inds, bound_type='upper', bound=0.0, absolute=False)

Constructor for SumOfSimsBound class.

Parameters:

  • des_type (np.dtype) – The numpy.dtype of the design variables.

  • sim_type (np.dtype) – The numpy.dtype of the simulation outputs.

  • sim_inds (list) – The list of names (or name, index pairs for sims with more than one output) of the simulation outputs to sum over.

  • bound_type (str) – Either ‘lower’ to lower-bound or ‘upper’ to upper-bound. Defaults to ‘upper’.

  • bound (float) – The lower/upper bound for this constraint. Defaults to 0.

  • absolute (bool) – True to bound absolute sum, False to bound raw sum. Defaults to False.

__call__(x, sx)

Define gradient evaluation.

Parameters:

  • x (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of a design point to evaluate.

  • sx (dict or structured array) – A Python dictionary or numpy structured array containing the names (as keys) and corresponding values of the simulation output(s) at x.

Returns:

The gradient of the sum of (absolute) simulation outputs given the input (x, sx) wrt x and sx, respectively.

Return type:

dict, dict