class Model:
def __init__(self, name: str = "",
sense: str = MINIMIZE,
solver_name: str = ''):
# initializing variables with default values
self.name: str = name
self.sense: str = sense
self.solver_name: str = solver_name
self.solver: Solver = None
# list of constraints and variables
self.constrs: List[Constr] = []
self.vars: List[Var] = []
if solver_name.upper() == GUROBI:
from mip.gurobi import SolverGurobi
self.solver = SolverGurobi(self, name, sense)
elif solver_name.upper() == CBC:
from mip.cbc import SolverCbc
self.solver = SolverCbc(self, name, sense)
else:
# search for the best solver available
if gurobi.has_gurobi:
from mip.gurobi import SolverGurobi
self.solver = SolverGurobi(self, name, sense)
elif cbc.has_cbc:
from mip.cbc import SolverCbc
self.solver = SolverCbc(self, name, sense)
def __del__(self):
if self.solver:
del self.solver
def __iadd__(self, other) -> 'Model':
if isinstance(other, LinExpr):
if len(other.sense) == 0:
# adding objective function components
self.set_objective(other)
else:
# adding constraint
self.add_constr(other)
elif isinstance(other, tuple):
if isinstance(other[0], LinExpr) and isinstance(other[1], str):
if len(other[0].sense) == 0:
self.set_objective(other[0])
else:
self.add_constr(other[0], other[1])
return self
def add_var(self, name: str = "",
lb: float = 0.0,
ub: float = INF,
obj: float = 0.0,
type: str = CONTINUOUS,
column: "Column" = None) -> "Var":
if len(name.strip()) == 0:
nc = self.solver.num_cols()
name = 'C{:011d}'.format(nc)
idx = self.solver.add_var(obj, lb, ub, type, column, name)
self.vars.append(Var(self, idx, name))
return self.vars[-1]
def add_constr(self, lin_expr: "LinExpr", name: str = "") -> Constr:
if isinstance(lin_expr, bool):
return None # empty constraint
idx = self.solver.add_constr(lin_expr, name)
self.constrs.append(Constr(self, idx, name))
return self.constrs[-1]
def copy(self, solver_name: str = None) -> "Model":
if not solver_name:
solver_name = self.solver_name
copy: Model = Model(self.name, self.sense, solver_name)
# adding variables
for v in self.vars:
copy.add_var(name=v.name, lb=v.lb, ub=v.ub, obj=v.obj, type=v.type)
# adding constraints
for c in self.constrs:
expr = c.expr # todo: make copy of constraint's lin_expr
copy.add_constr(lin_expr=expr, name=c.name)
# setting objective function's constant
copy.set_objective_const(self.get_objective_const())
return copy
def get_objective(self) -> LinExpr:
return self.solver.get_objective()
def get_objective_const(self) -> float:
return self.solver.get_objective_const()
def optimize(self,
maxSeconds=inf,
maxNodes=inf,
maxSolutions=inf
) -> int:
if maxSeconds != inf or maxNodes != inf or maxSolutions != inf:
self.solver.set_processing_limits(maxSeconds, maxNodes, maxSolutions)
self.solver.optimize()
def get_objective_value(self) -> float:
return self.solver.get_objective_value()
def set_start(self, variables: List["Var"], values: List[float]):
self.solver.set_start(variables, values)
def set_objective(self, expr, sense: str = "") -> None:
if isinstance(expr, int) or isinstance(expr, float):
self.solver.set_objective(LinExpr([], [], expr))
elif isinstance(expr, Var):
self.solver.set_objective(LinExpr([expr], [1]))
elif isinstance(expr, LinExpr):
self.solver.set_objective(expr, sense)
def set_objective_const(self, const: float) -> None:
return self.solver.set_objective_const(const)
def write(self, path: str) -> None:
self.solver.write(path)
def read(self, path: str) -> None:
self.solver.read(path)
nCols = self.solver.num_cols()
nRows = self.solver.num_rows()
for i in range(nCols):
self.vars.append(Var(self, i, self.solver.var_get_name(i)))
for i in range(nRows):
self.constrs.append(Constr(self, i, self.solver.constr_get_name(i)))
@property
def num_cols(self) -> int:
return len(self.vars)
@property
def num_rows(self) -> int:
return len(self.constrs)
class Model:
""" Mixed Integer Programming Model
This is the main class, providing methods for building, optimizing,
querying optimization results and reoptimizing Mixed-Integer Programming
Models.
To check how models are created please see the examples included.
"""
def __init__(self, name: str = "",
sense: str = MINIMIZE,
solver_name: str = ""):
"""Model constructor
Creates a Mixed-Integer Linear Programming Model. The default model
optimization direction is Minimization. To store and optimize the model
the MIP package automatically searches and connects in runtime to the
dynamic library of some MIP solver installed on your computer, nowadays
gurobi and cbc are supported. This solver is automatically selected,
but you can force the selection of a specific solver with the parameter
solver_name.
Args:
name (str): model name
sense (str): MINIMIZATION ("MIN") or MAXIMIZATION ("MAX")
solver_name: gurobi or cbc, searches for which
solver is available if not informed
"""
# initializing variables with default values
self.name = name
self.solver_name = solver_name
self.solver = None
if "solver_name" in environ:
solver_name = environ["solver_name"]
if "solver_name".upper() in environ:
solver_name = environ["solver_name".upper()]
self.__mipStart = []
# list of constraints and variables
self.constrs = []
self.constrs_by_name = {}
self.vars = []
self.vars_by_name = {}
self.cut_generators = []
if solver_name.upper() == GUROBI:
from mip.gurobi import SolverGurobi
self.solver = SolverGurobi(self, name, sense)
elif solver_name.upper() == CBC:
from mip.cbc import SolverCbc
self.solver = SolverCbc(self, name, sense)
else:
# checking which solvers are available
from mip import gurobi
if gurobi.has_gurobi:
from mip.gurobi import SolverGurobi
self.solver = SolverGurobi(self, name, sense)
self.solver_name = GUROBI
else:
from mip import cbc
from mip.cbc import SolverCbc
self.solver = SolverCbc(self, name, sense)
self.solver_name = CBC
self.sense = sense
def __del__(self):
if self.solver:
del self.solver
def __iadd__(self, other) -> "Model":
if isinstance(other, LinExpr):
if len(other.sense) == 0:
# adding objective function components
self.objective = other
else:
# adding constraint
self.add_constr(other)
elif isinstance(other, tuple):
if isinstance(other[0], LinExpr) and isinstance(other[1], str):
if len(other[0].sense) == 0:
self.objective = other[0]
else:
self.add_constr(other[0], other[1])
return self
def add_var(self, name: str = "",
lb: float = 0.0,
ub: float = INF,
obj: float = 0.0,
var_type: str = CONTINUOUS,
column: "Column" = None) -> "Var":
""" Creates a new variable
Adds a new variable to the model.
Args:
name (str): variable name (optional)
lb (float): variable lower bound, default 0.0
ub (float): variable upper bound, default infinity
obj (float): coefficient of this variable in the objective function, default 0
var_type (str): CONTINUOUS ("C"), BINARY ("B") or INTEGER ("I")
column (Column): constraints where this variable will appear, necessary \
only when constraints are already created in the model and a new \
variable will be created.
Examples:
To add a variable x which is continuous and greater or equal to zero to model m::
x = m.add_var()
The following code creates a vector of binary variables x[0], ..., x[n-1] to model m::
x = [m.add_var(type=BINARY) for i in range(n)]
"""
if var_type == BINARY:
lb = 0.0
ub = 1.0
if len(name.strip()) == 0:
nc = self.solver.num_cols()
name = "C{:011d}".format(nc)
idx = self.solver.add_var(obj, lb, ub, var_type, column, name)
self.vars.append(Var(self, idx, name))
self.vars_by_name[name] = self.vars[-1]
return self.vars[-1]
def add_constr(self, lin_expr: "LinExpr", name: str = "") -> Constr:
""" Creates a new constraint (row)
Adds a new constraint to the model
Args:
lin_expr (LinExpr): linear expression
name (str): optional constraint name, used when saving model to\
lp or mps files
Examples:
The following code adds the constraint :math:`x_1 + x_2 \leq 1`
(x1 and x2 should be created first using
:func:`add_var<mip.model.Model.add_var>`)::
m += x1 + x2 <= 1
Which is equivalent to::
m.add_constr( x1 + x2 <= 1 )
Summation expressions can be used also, to add the constraint \
:math:`\displaystyle \sum_{i=0}^{n-1} x_i = y` and name this \
constraint cons1::
m += xsum(x[i] for i in range(n)) == y, "cons1"
"""
if isinstance(lin_expr, bool):
return None # empty constraint
idx = self.solver.add_constr(lin_expr, name)
self.constrs.append(Constr(self, idx, name))
self.constrs_by_name[name] = self.constrs[-1]
return self.constrs[-1]
def copy(self, solver_name: str = None) -> "Model":
""" Creates a copy of the current model
Args:
solver_name(str): solver name (optional)
Returns:
Model: clone of current model
"""
if not solver_name:
solver_name = self.solver_name
copy = Model(self.name, self.sense, solver_name)
# adding variables
for v in self.vars:
copy.add_var(name=v.name, lb=v.lb, ub=v.ub, obj=v.obj, var_type=v.var_type)
# adding constraints
for c in self.constrs:
expr = c.expr # todo: make copy of constraint"s lin_expr
copy.add_constr(lin_expr=expr, name=c.name)
# setting objective function"s constant
copy.objective_const = self.get_objective_const()
return copy
def get_constr_by_name(self, name: str) -> "Constr":
""" Queries a constraint per name
Args:
name(str): constraint name
Returns:
Constr: constraint
"""
return self.constrs_by_name.get(name, None)
@property
def objective_bound(self) -> float:
return self.solver.get_objective_bound()
@property
def objective(self) -> LinExpr:
"""LinExpr: Objective function of the problem
The objective function of the problem as a linear expression.
Examples:
The following code adds all x variables x[0], ..., x[n-1], to
the objective function of model m with weight w::
m.objective = xsum(w*x[i] for i in range(n))
A simpler way to define the objective function is the use of the
model operator += ::
m += xsum(w*x[i] for i in range(n))
Note that the only difference of adding a constraint is the lack of
a sense and a rhs.
"""
return self.solver.get_objective()
@objective.setter
def objective(self, expr):
if isinstance(expr, int) or isinstance(expr, float):
self.solver.set_objective(LinExpr([], [], expr))
elif isinstance(expr, Var):
self.solver.set_objective(LinExpr([expr], [1]))
elif isinstance(expr, LinExpr):
self.solver.set_objective(expr)
@property
def sense(self) -> str:
""" The optimization sense
Returns:
str: the objective function sense, MINIMIZE (default) or (MAXIMIZE)
"""
return self.solver.get_objective_sense()
@sense.setter
def sense(self, sense: str):
self.solver.set_objective_sense(sense)
@property
def objective_const(self) -> float:
""" Returns the current constant part of the objective function
float: the constant part in the objective function
"""
return self.solver.get_objective_const()
@objective_const.setter
def objective_const(self, const: float) -> None:
self.solver.set_objective_const(const)
@property
def objective_value(self) -> float:
""" Objective function value
Returns:
float: returns the objective function value of the solution found.
"""
return self.solver.get_objective_value()
@property
def num_solutions(self) -> int:
""" Number of solutions found during the MIP search
Returns:
int: number of solutions stored in the solution pool
"""
return self.solver.get_num_solutions()
@property
def objective_values(self) -> List[float]:
""" List of costs of all solutions in the solution pool
Returns:
List[float]: costs of all solutions stored in the solution pool
as an array from 0 (the best solution) to num_solutions-1.
"""
return [float(self.solver.get_objective_value_i(i))\
for i in range(self.num_solutions)]
def get_var_by_name(self, name) -> "Var":
""" Searchers a variable by its name
Returns:
Var: a reference to a variable
"""
return self.vars_by_name.get(name, None)
def relax(self):
""" Relax integrality constraints of variables
Changes the type of all integer and binary variables to
continuous. Bounds are preserved.
"""
self.solver.relax()
for v in self.vars:
if v.var_type == BINARY or v.var_type == INTEGER:
v.var_type = CONTINUOUS
def add_cut_generator(self, cuts_generator: "CutsGenerator") -> None:
""" Adds a cut generator
Cut generators are called whenever a solution where one or more
integer variables appear with continuous values. A cut generator will
try to produce one or more inequalities to remove this fractional point.
Args:
cuts_generator : CutsGenerator
"""
self.cut_generators.append(cuts_generator)
@property
def emphasis(self) -> int:
"""int: defines the main objective of the search, if set to 1 (FEASIBILITY) then
the search process will focus on try to find quickly feasible solutions and
improving them; if set to 2 (OPTIMALITY) then the search process will try to
find a provable optimal solution, procedures to further improve the lower bounds will
be activated in this setting, this may increase the time to produce the first
feasible solutions but will probably pay off in longer runs; the default option
if 0, where a balance between optimality and feasibility is sought.
"""
return self.solver.get_emphasis()
@emphasis.setter
def emphasis(self, emph: int):
self.solver.set_emphasis(emph)
def optimize(self,
branch_selector: "BranchSelector" = None,
incumbent_updater: "IncumbentUpdater" = None,
lazy_constrs_generator: "LazyConstrsGenerator" = None,
max_seconds: float = inf,
max_nodes: int = inf,
max_solutions: int = inf) -> int:
""" Optimizes current model
Optimizes current model, optionally specifying processing limits.
To optimize model m within a processing time limit of 300 seconds::
m.optimize(max_seconds=300)
Args:
branch_selector (BranchSelector): Callback to select branch (an object of a class inheriting from BranchSelector must be passed)
cuts_generator (CutsGenerator): Callback to generate cuts (an object of a class inheriting from CutsGenerator must be passed)
incumbent_updater (IncumbentUpdater): Callback to update incumbent solution (an object of a class inheriting from IncumbentUpdater must be passed)
lazy_constrs_generator (LazyConstrsGenerator): Callback to include lazy generated constraints (an object of a class inheriting from LazyConstrsGenerator must be passed)
max_seconds (float): Maximum runtime in seconds (default: inf)
max_nodes (float): Maximum number of nodes (default: inf)
max_solutions (float): Maximum number of solutions (default: inf)
Returns:
int: optimization status, which can be OPTIMAL(0), ERROR(-1), INFEASIBLE(1), UNBOUNDED(2). When optimizing problems
with integer variables some additional cases may happen, FEASIBLE(3) for the case when a feasible solution was found
but optimality was not proved, INT_INFEASIBLE(4) for the case when the lp relaxation is feasible but no feasible integer
solution exists and NO_SOLUTION_FOUND(5) for the case when an integer solution was not found in the optimization.
"""
self.solver.set_callbacks(branch_selector, incumbent_updater, lazy_constrs_generator)
self.solver.set_processing_limits(max_seconds, max_nodes, max_solutions)
return self.solver.optimize()
def read(self, path: str) -> None:
""" Reads a MIP model
Reads a MIP model in .lp or .mps file format.
Args:
path(str): file name
"""
self.solver.read(path)
n_cols = self.solver.num_cols()
n_rows = self.solver.num_rows()
for i in range(n_cols):
self.vars.append(Var(self, i, self.solver.var_get_name(i)))
self.vars_by_name[self.vars[-1].name] = self.vars[-1]
for i in range(n_rows):
self.constrs.append(Constr(self, i, self.solver.constr_get_name(i)))
self.constrs_by_name[self.constrs[-1].name] = self.constrs[-1]
self.sense = self.solver.get_objective_sense()
@property
def start(self) -> List[Tuple["Var", float]]:
""" Enter an initial feasible solution
Enters an initial feasible solution. Only the main binary/integer decision variables.
Auxiliary or continuous variables are automatically computed.
Args:
start_sol: list of tuples Var,float indicating non-zero variables
and their values in the initial feasible solution
"""
return self.__mipStart
@start.setter
def start(self, start_sol: List[Tuple["Var", float]]):
self.__mipStart = start_sol
self.solver.set_start(start_sol)
def write(self, path: str) -> None:
""" Saves the the MIP model
Args:
path(str): file name
Saves the the MIP model, use the extension ".lp" or ".mps" in the file
name to specify the file format.
"""
self.solver.write(path)
@property
def num_cols(self) -> int:
return len(self.vars)
@property
def num_rows(self) -> int:
return len(self.constrs)
@property
def cutoff(self) -> float:
"""float: upper limit for the solution cost, solutions with cost > cutoff
will be removed from the search space, a small cutoff value may significantly
speedup the search, but if cutoff is set to a value too low
the model will become infeasible"""
return self.solver.get_cutoff()
@cutoff.setter
def cutoff(self, value: float):
self.solver.set_cutoff(value)
@property
def mip_gap_abs(self) -> float:
"""float: tolerance for the quality of the optimal solution, if a
solution with cost c and a lower bound l are available and c-l<mip_gap_abs,
the search will be concluded, see mip_gap to determine
a percentage value """
return self.solver.get_mip_gap_abs()
@mip_gap_abs.setter
def mip_gap_abs(self, value):
self.solver.set_mip_gap(value)
@property
def mip_gap(self) -> float:
"""float: percentage indicating the tolerance for the maximum percentage deviation
from the optimal solution cost, if a solution with cost c and a lower bound l
are available and (c-l)/l < mip_gap the search will be concluded."""
return self.solver.get_mip_gap()
@mip_gap.setter
def mip_gap(self, value):
self.solver.set_mip_gap(value)
@property
def max_seconds(self) -> float:
"""float: time limit in seconds for search"""
return self.solver.get_max_seconds()
@max_seconds.setter
def max_seconds(self, max_seconds: float):
self.solver.set_max_seconds(max_seconds)
@property
def max_nodes(self) -> int:
"""int: maximum number of nodes to be explored in the search tree"""
return self.solver.get_max_nodes()
@max_nodes.setter
def max_nodes(self, max_nodes: int):
self.solver.set_max_nodes(max_nodes)
@property
def max_solutions(self) -> int:
"""int: solution limit, search will be stopped when max_solutions were found"""
return self.solver.get_max_solutions()
@max_solutions.setter
def max_solutions(self, max_solutions: int):
self.solver.set_max_solutions(max_solutions)