straindesign.glpk_interface

GLPK solver interface for LP and MILP

Module Contents

class straindesign.glpk_interface.GLPK_MILP_LP(c, A_ineq, b_ineq, A_eq, b_eq, lb, ub, vtype, indic_constr, M=None)

GLPK interface for MILP and LP

This class is a wrapper for the GLPK-Python API to offer bindings and namings for functions for the construction and manipulation of MILPs and LPs in an vector-matrix-based manner that are consistent with those of the other solver interfaces in the StrainDesign package. The purpose is to unify the instructions for operating with MILPs and LPs throughout StrainDesign.

The GLPK interface does not natively support indicator constraints. They are hence translated to bigM-constraints when passed to the GLPK constructor (see docstring of IndicatorConstraints). The GLPK interface does not natively support the populate function. A high level implementation emulates the behavior of populate.

Accepts a (mixed integer) linear problem in the form:

minimize(c), subject to: A_ineq * x <= b_ineq, A_eq * x = b_eq, lb <= x <= ub, forall(i) type(x_i) = vtype(i) (continous, binary, integer), indicator constraints: x(j) = [0|1] -> a_indic * x [<=|=|>=] b_indic

Please ensure that the number of variables and (in)equalities is consistent

Example

glpk = GLPK_MILP_LP(c, A_ineq, b_ineq, A_eq, b_eq, lb, ub, vtype, indic_constr, M)

Parameters:

• c (list of float) – (Default: None) The objective vector (Objective sense: minimization).

• A_ineq (sparse.csr_matrix) – (Default: None) A coefficient matrix of the static inequalities.

• b_ineq (list of float) – (Default: None) The right hand side of the static inequalities.

• A_eq (sparse.csr_matrix) – (Default: None) A coefficient matrix of the static equalities.

• b_eq (list of float) – (Default: None) The right hand side of the static equalities.

• lb (list of float) – (Default: None) The lower variable bounds.

• ub (list of float) – (Default: None) The upper variable bounds.

• vtype (str) – (Default: None) A character string that specifies the type of each variable: ‘c’ontinous, ‘b’inary or ‘i’nteger

• indic_constr (IndicatorConstraints) – (Default: None) A set of indicator constraints stored in an object of IndicatorConstraints. To make GLPK compatible with indicator constraints, they are translated into bigM-constraints (see reference manual or docstring of IndicatorConstraints).

• M (int) – (Default: None) A large value that is used in the translation of indicator constraints to bigM-constraints. If no value is provided, 1000 is used.

• Returns –

  (GLPK_MILP_LP):

  A GLPK MILP/LP interface class.

addExclusionConstraintsIneq(x)

Function to add exclusion constraint (GLPK compatibility function)

add_eq_constraints(A_eq, b_eq)

Add equality constraints to the model

Additional equality constraints have the form A_eq * x = b_eq. The number of columns in A_eq must match with the number of variables x in the problem.

Parameters:

• A_eq (sparse.csr_matrix) – The coefficient matrix

• b_eq (list of float) – The right hand side vector

add_ineq_constraints(A_ineq, b_ineq)

Add inequality constraints to the model

Additional inequality constraints have the form A_ineq * x <= b_ineq. The number of columns in A_ineq must match with the number of variables x in the problem.

Parameters:

• A_ineq (sparse.csr_matrix) – The coefficient matrix

• b_ineq (list of float) – The right hand side vector

getSolution(status) → list

Retrieve solution from GLPK backend

populate(pool_limit) → Tuple[List, float, float]

Generate a solution pool for MILPs

This is only a high-level implementation of the populate function. There is no native support in GLPK.

Example

sols_x, optim, status = glpk.populate()

Returns:

(Tuple[List of lists, float, float])

solution_vectors, optimal_value, optimization_status

set_ineq_constraint(idx, a_ineq, b_ineq)

Replace a specific inequality constraint

Replace the constraint with the index idx with the constraint a_ineq*x ~ b_ineq

Parameters:

• idx (int) – Index of the constraint

• a_ineq (list of float) – The coefficient vector

• b_ineq (float) – The right hand side value

set_objective(c)

Set the objective function with a vector

set_objective_idx(C)

Set the objective function with index-value pairs

e.g.: C=[[1, 1.0], [4,-0.2]]

set_time_limit(t)

Set the computation time limit (in seconds)

set_ub(ub)

Set the upper bounds to a given vector

slim_solve() → float

Solve the MILP or LP, but return only the optimal value

Example

optim = glpk.slim_solve()

Returns:

(float)

Optimum value of the objective function.

solve() → Tuple[List, float, float]

Solve the MILP or LP

Example

sol_x, optim, status = glpk.solve()

Returns:

(Tuple[List, float, float])

solution_vector, optimal_value, optimization_status

solve_MILP_LP() → Tuple[float, int, bool]

Trigger GLPK solution through backend