decogo.pyomo_problem.subproblem

This module implements and manages all sub-problems of Pyomo models

Classes

PyomoLineSearchSubProblem(block_model, block_id)	This class defines line search sub-problem between exterior point \(x_k^{ext}\) and interior point \(x_k^{int}\)
PyomoMinlpSubProblem(block_model, block_id)	A class for defining the following sub-problem
PyomoProjectionSubProblem(block_model, block_id)	A class for defining a projection sub-problem
PyomoResourceProjectionSubProblem(...)	A class for defining a projection sub-problem
PyomoSubProblemBase(block_model, block_id)	A base class for construction of Pyomo model.
PyomoSubProblems(block_model, block_id)	A container class for managing all sub-problems

class decogo.pyomo_problem.subproblem.PyomoSubProblemBase(block_model, block_id)

A base class for construction of Pyomo model. Here are implemented methods for creating local linear and nonlinear constraints

Parameters:

• block_model (PyomoBlockModel) – Block model

• block_id (int) – Block identifier

__init__(block_model, block_id)

Constructor method

solve(solver_name, start_point=None, solver_options=None)

Base method for calling the external solver to solve the model

Parameters:

• solver_name (str) – External solver name

• start_point (ndaray or None) – Starting point for the solver, defaults to None

• solver_options (list) – Options for external solver, defaults to None

Returns:

Solution point, primal bound, dual bound, flag if the primal bound is feasible

Return type:

tuple

add_linear_constraint()

Adds new linear constraint

set_nlp()

Relaxes integer varaibles to continious

unset_nlp()

Sets to integer type for the variables which are integer in the original formulation

update_var_lower_bound(index)

Updates the lower bound of the variable. The value is taken form the BlockModel

Parameters:

index (tuple) – Index (block_id, index)

update_var_upper_bound(index)

Updates the upper bound of the variable. The value is taken form the BlockModel

Parameters:

index (tuple) – Index (block_id, index)

fix_integers(x)

Fixes integer variables with given value

Parameters:

x (ndarray) – Given array

unfix_integers()

Unfixes all integer variables

add_objective()

Sets default objective function, i.e. \(c_k^Tx_k\), where \(c_k\) - partial objective from the original model

set_objective(direction)

Sets the objective function with given direction vector

Parameters:

direction (ndarray) – Given vector

class decogo.pyomo_problem.subproblem.PyomoMinlpSubProblem(block_model, block_id)

A class for defining the following sub-problem

\[\begin{equation} \begin{split} \min \ &d_k^Ty_k, \newline &y_k \in X_k, d_k \in \mathbb{R}^{n_k} \end{split} \end{equation}\]

Parameters:

• block_model (PyomoBlockModel) – Block model

• block_id (int) – Block identifier

__init__(block_model, block_id)

Constructor method

class decogo.pyomo_problem.subproblem.PyomoProjectionSubProblem(block_model, block_id)

A class for defining a projection sub-problem

\[\begin{equation} \begin{split} \min \ &||y_k-x_k||^2,\newline &y_k \in G_k, x_k \text{ is fixed} \end{split} \end{equation}\]

Parameters:

• block_model (PyomoBlockModel) – Block model

• block_id (int) – Block identifier

__init__(block_model, block_id)

Constructor method

obj_rule()

Defines the objective function

Returns:

Objective expression

Return type:

Expression

set_projection_point(point_to_project)

Sets projection point, i.e. \(x_k\)

Parameters:

point_to_project (ndarray) – Projection point

class decogo.pyomo_problem.subproblem.PyomoResourceProjectionSubProblem(block_model, block_id)

A class for defining a projection sub-problem

\[\begin{equation} \begin{split} \min \ &||A_kx_k - w_k||^2,\newline &y_k \in G_k, w_k \text{ is fixed} \end{split} \end{equation}\]

Parameters:

• block_model (PyomoBlockModel) – Block model

• block_id (int) – Block identifier

__init__(block_model, block_id)

Constructor method

obj_rule()

Defines the objective function

Returns:

Objective expression

Return type:

Expression

set_projection_point(point_to_project)

Sets projection point, i.e. \(w_k\)

Parameters:

point_to_project (ndarray) – Projection point

class decogo.pyomo_problem.subproblem.PyomoLineSearchSubProblem(block_model, block_id)

This class defines line search sub-problem between exterior point \(x_k^{ext}\) and interior point \(x_k^{int}\)

\[\begin{equation} \begin{split} \max \ & \alpha, \newline &y_k = \alpha x_k^{ext} + (1 - \alpha) x_k^{int}, \newline &y_k \in X_k \end{split} \end{equation}\]

Parameters:

• block_model (PyomoBlockModel) – Block model

• block_id (int) – Block identifier

__init__(block_model, block_id)

Constructor method

set_interior_exterior_points(exterior_point, interior_point)

Sets values of two endpoints

Parameters:

• exterior_point (ndarray) – Exterior point

• interior_point (ndarray) – Interior point

solve(solver_name, start_point=None, solver_options=None)

Solves the subproblem and gets value of \(\alpha\). For more info, see base method SubProblemBase.solve()

class decogo.pyomo_problem.subproblem.PyomoSubProblems(block_model, block_id)

A container class for managing all sub-problems

Parameters:

• minlp_sub_problem (PyomoMinlpSubProblem) – Sub-probem with linear objective

• proj_sub_problem (PyomoProjectionSubProblem) – Pure projection sub-problem

• resource_constrained_sub_problem (PyomoResourceConstrainedSubProblem) – Resource constrained sub-problem for checking the feasibility of the resources

• line_search_sub_problem (PyomoLineSearchSubProblem) – Line search sub-problem

• block_model (PyomoBlockModel) – Block model

• block_id (int) – Block identifier

__init__(block_model, block_id)

Constructor method

minlp_solve(solver_name, solver_options=None, start_point=None, direction=None, cell=None)

Solves MinlpSubProblem

Parameters:

• solver_name (str) – External solver name

• solver_options (list or None) – External solver options, defaults to None

• start_point (ndarray or None) – Staring point for the solver, defaults to None

• direction (ndarray or None) – Direction for the objective, defaults to None

• cell (Cell or None) – Cell, defaults to None

Returns:

Solution point, primal and dual bound

Return type:

tuple

fixed_minlp_solve(solver_name, start_point, solver_options=None, direction=None, cell=None)

Solves MinlpSubProblem with fixed integer variables

Parameters:

• solver_name (str) – External solver name

• start_point (ndarray or None) – Staring point for the solver, and point which is used for fixing the integers

• solver_options (list or None) – External solver options, defaults to None

• direction (ndarray or None) – Direction for the objective, defaults to None

• cell (Cell or None) – Cell, defaults to None

Returns:

Solution point, primal and dual bound

Return type:

tuple

nlp_proj_solve(solver_name, point_to_project, start_point=None)

Solves ProjSubProblem

Parameters:

• solver_name (str) – External solver name

• point_to_project (ndarray) – Projection point

• start_point (ndarray or None) – Staring point for the solver, defaults to None

Returns:

Solution point, primal bound and flag indicating the feasibility of primal solution

Return type:

tuple

resource_proj_solve(solver_name, point_to_project, solver_options=None, start_point=None)

Solves ResourceProjSubProblem

Parameters:

• solver_name (str) – External solver name

• point_to_project (ndarray) – Projection point

• start_point (ndarray or None) – Staring point for the solver, defaults to None

Returns:

Solution point, primal bound and flag indicating the feasibility of primal solution

Return type:

tuple

solve_line_search_subproblem(solver_name, exterior_point, interior_point)

Solves LineSearchSubProblem

Parameters:

• solver_name (str) – External solver name

• exterior_point (ndarray) – Exterior point

• interior_point (ndarray) – Interior point

Returns:

value of parameter \(\alpha\) and solution point

Return type:

tuple

add_linear_constraint()

Adds linear constraints to sub-problems

update_var_lower_bound(index)

Updates the lower bound of variable by index

Parameters:

index (tuple) – Index of the variable (block_id, index)

update_var_upper_bound(index)

Updates the upper bound of variable by index

Parameters:

index (tuple) – Index of the variable (block_id, index)