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"""Gurobi solver interface for LP and MILP"""
from random import randint
from scipy import sparse
from numpy import nan, inf, isinf, sum, array
import gurobipy as gp
from gurobipy import GRB as grb
from straindesign.names import *
from typing import Tuple, List
import logging
gstatus = gp.StatusConstClass
[docs]class Gurobi_MILP_LP(gp.Model):
"""Gurobi interface for MILP and LP
This class is a wrapper for the Gurobi-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 Gurobi interface provides support for indicator constraints as well as for
the populate function.
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:
gurobi = Gurobi_MILP_LP(c, A_ineq, b_ineq, A_eq, b_eq, lb, ub, vtype, indic_constr)
Args:
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
(see reference manual or docstring).
Returns:
(Gurobi_MILP_LP):
A Gurobi MILP/LP interface class.
"""
def __init__(self, c, A_ineq, b_ineq, A_eq, b_eq, lb, ub, vtype, indic_constr):
super().__init__()
try:
numvars = A_ineq.shape[1]
except:
numvars = A_eq.shape[1]
# prepare coefficient matrix
if isinstance(A_eq, list):
if not A_eq:
A_eq = sparse.csr_matrix((0, numvars))
if isinstance(A_ineq, list):
if not A_ineq:
A_ineq = sparse.csr_matrix((0, numvars))
for i, v in enumerate(b_ineq):
if isinf(v):
b_ineq[i] = grb.INFINITY
# concatenate right hand sides
# construct Gurobi problem. Add variables and linear constraints
x = self.addMVar(len(c), obj=c, lb=lb, ub=ub, vtype=[k for k in vtype])
self.setObjective(array(c) @ x, grb.MINIMIZE)
if A_ineq.shape[0]:
self.addConstr(A_ineq @ x <= array(b_ineq))
if A_eq.shape[0]:
self.addConstr(A_eq @ x == array(b_eq))
# add indicator constraints
if not indic_constr == None:
for i in range(len(indic_constr.sense)):
self.addGenConstrIndicator(x[indic_constr.binv[i]],
bool(indic_constr.indicval[i]),
sum([indic_constr.A[i,j] * x[j] \
for j in range(len(c)) if not indic_constr.A[i,j] == 0.0]),
'=' if indic_constr.sense[i] =='E' else '<',
indic_constr.b[i])
# set parameters
self.params.OutputFlag = 0
self.params.OptimalityTol = 1e-9
self.params.FeasibilityTol = 1e-9
if 'B' in vtype or 'I' in vtype:
seed = randint(0, grb.MAXINT)
# logging.info(' MILP Seed: '+str(seed))
self.params.Seed = seed
self.params.IntFeasTol = 1e-9 # (0 is not allowed by Gurobi)
# yield only optimal solutions in pool
self.params.PoolGap = 0.0
self.params.PoolGapAbs = 0.0
[docs] def solve(self) -> Tuple[List, float, float]:
"""Solve the MILP or LP
Example:
sol_x, optim, status = gurobi.solve()
Returns:
(Tuple[List, float, float])
solution_vector, optimal_value, optimization_status
"""
try:
self.optimize() # call parent solve function (that was overwritten in this class)
status = self.Status
if status in [gstatus.OPTIMAL, gstatus.SOLUTION_LIMIT, gstatus.SUBOPTIMAL, gstatus.USER_OBJ_LIMIT]: # solution
min_cx = self.ObjVal
status = OPTIMAL
elif status == gstatus.TIME_LIMIT and not hasattr(self._Model__vars[0], 'X'): # timeout without solution
x = [nan] * self.NumVars
min_cx = nan
status = TIME_LIMIT
return x, min_cx, status
elif status == gstatus.TIME_LIMIT and hasattr(self._Model__vars[0], 'X'):
min_cx = self.ObjVal
status = TIME_LIMIT_W_SOL
elif status in [gstatus.INF_OR_UNBD, gstatus.UNBOUNDED, gstatus.INFEASIBLE]:
# solve problem again without objective to verify that problem is feasible
self.params.DualReductions = 0
self.optimize()
self.params.DualReductions = 1
if self.Status == gstatus.INFEASIBLE:
x = [nan] * self.NumVars
min_cx = nan
status = INFEASIBLE
return x, min_cx, status
else:
x = [nan] * self.NumVars
min_cx = -inf
status = UNBOUNDED
return x, min_cx, status
else:
raise Exception('Status code ' + str(status) + " not yet handeld.")
x = self.getSolution()
return x, min_cx, status
except gp.GurobiError as e:
logging.error('Error code ' + str(e.errno) + ": " + str(e))
min_cx = nan
x = [nan] * self.NumVars
return x, min_cx, ERROR
[docs] def slim_solve(self) -> float:
"""Solve the MILP or LP, but return only the optimal value
Example:
optim = gurobi.slim_solve()
Returns:
(float)
Optimum value of the objective function.
"""
try:
self.optimize() # call parent solve function (that was overwritten in this class)
status = self.Status
if status in [gstatus.OPTIMAL, gstatus.SOLUTION_LIMIT, gstatus.SUBOPTIMAL,
gstatus.USER_OBJ_LIMIT]: # solution integer optimal (tolerance)
opt = self.ObjVal
elif status in [gstatus.INF_OR_UNBD, gstatus.UNBOUNDED]:
opt = -inf
elif status in [gstatus.INFEASIBLE, gstatus.TIME_LIMIT]:
opt = nan
else:
raise Exception('Status code ' + str(status) + " not yet handeld.")
return opt
except gp.GurobiError as e:
logging.error('Error code ' + str(e.errno) + ": " + str(e))
return nan
[docs] def populate(self, n) -> Tuple[List, float, float]:
"""Generate a solution pool for MILPs
Example:
sols_x, optim, status = cplex.populate()
Returns:
(Tuple[List of lists, float, float])
solution_vectors, optimal_value, optimization_status
"""
try:
if isinf(n):
self.params.PoolSolutions = grb.MAXINT
else:
self.params.PoolSolutions = n
self.params.PoolSearchMode = 2
self.optimize() # call parent solve function (that was overwritten in this class)
self.params.PoolSearchMode = 0
status = self.Status
if status in [2, 10, 13, 15]: # solution integer optimal
min_cx = self.ObjVal
status = OPTIMAL
elif status == 9 and not hasattr(self._Model__vars[0], 'X'): # timeout without solution
x = [nan] * len(self._Model__vars)
min_cx = nan
status = TIME_LIMIT
return x, min_cx, status
elif status == 3: # infeasible
x = [nan] * len(self._Model__vars)
min_cx = nan
status = INFEASIBLE
return x, min_cx, status
elif status == 9 and hasattr(self._Model__vars[0], 'X'): # timeout with solution
min_cx = self.ObjVal
status = TIME_LIMIT_W_SOL
elif status in [4, 5]: # solution unbounded
min_cx = -inf
x = [nan] * len(self._Model__vars)
status = UNBOUNDED
return x, min_cx, status
else:
raise Exception('Status code ' + str(status) + " not yet handeld.")
x = self.getSolutions()
return x, min_cx, status
except gp.GurobiError as e:
self.params.PoolSearchMode = 0
logging.error('Error code ' + str(e.errno) + ": " + str(e))
min_cx = nan
x = [nan] * len(self._Model__vars)
return x, min_cx, ERROR
[docs] def set_objective(self, c):
"""Set the objective function with a vector"""
for i in range(len(self._Model__vars)):
self._Model__vars[i].Obj = c[i]
self.update()
[docs] def set_objective_idx(self, C):
"""Set the objective function with index-value pairs
e.g.: C=[[1, 1.0], [4,-0.2]]"""
for c in C:
self._Model__vars[c[0]].Obj = c[1]
self.update()
[docs] def set_ub(self, ub):
"""Set the upper bounds to a given vector"""
for i in range(len(ub)):
self._Model__vars[ub[i][0]].ub = ub[i][1]
self.update()
[docs] def set_time_limit(self, t):
"""Set the computation time limit (in seconds)"""
self.params.TimeLimit = t
self.update()
[docs] def add_ineq_constraints(self, 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.
Args:
A_ineq (sparse.csr_matrix):
The coefficient matrix
b_ineq (list of float):
The right hand side vector
"""
vars = self._Model__vars
for i in range(A_ineq.shape[0]):
self.addConstr(sum([A_ineq[i, j] * vars[j] for j in range(len(vars)) if not A_ineq[i, j] == 0.0]) <= b_ineq[i])
self.update()
[docs] def add_eq_constraints(self, 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.
Args:
A_eq (sparse.csr_matrix):
The coefficient matrix
b_eq (list of float):
The right hand side vector
"""
vars = self._Model__vars
for i in range(A_eq.shape[0]):
self.addConstr(sum([A_eq[i, j] * vars[j] for j in range(len(vars)) if not A_eq[i, j] == 0.0]) == b_eq[i])
self.update()
[docs] def set_ineq_constraint(self, 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
Args:
idx (int):
Index of the constraint
a_ineq (list of float):
The coefficient vector
b_ineq (float):
The right hand side value
"""
constr = self._Model__constrs[idx]
[self.chgCoeff(constr, x, val) for x, val in zip(self._Model__vars, a_ineq)]
if isinf(b_ineq):
constr.rhs = grb.INFINITY
else:
constr.rhs = b_ineq
self.update()
[docs] def getSolution(self) -> list:
"""Retrieve solution from Gurobi backend"""
return [x.X for x in self._Model__vars]
[docs] def getSolutions(self) -> list:
"""Retrieve solution pool from Gurobi backend"""
nSols = self.SolCount
x = []
for i in range(nSols):
self.setParam(grb.Param.SolutionNumber, i)
if self.PoolObjVal == self.ObjVal:
x += [[x.Xn for x in self._Model__vars]]
return x