#! /usr/bin/env python # PuLP : Python LP Modeler # Copyright (c) 2002-2005, Jean-Sebastien Roy (js@jeannot.org) # Modifications Copyright (c) 2007- Stuart Anthony Mitchell (s.mitchell@auckland.ac.nz) # $Id: pulp.py 1791 2008-04-23 22:54:34Z smit023 $ # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the # "Software"), to deal in the Software without restriction, including # without limitation the rights to use, copy, modify, merge, publish, # distribute, sublicense, and/or sell copies of the Software, and to # permit persons to whom the Software is furnished to do so, subject to # the following conditions: # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF # MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. # IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY # CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, # TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE # SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. """ PuLP is an LP modeler written in python. PuLP can generate MPS or LP files and call GLPK[1], COIN CLP/CBC[2], CPLEX[3], and GUROBI[4] to solve linear problems. See the examples directory for examples. PuLP requires Python >= 2.5. The examples require at least a solver in your PATH or a shared library file. Documentation is found on https://www.coin-or.org/PuLP/. A comprehensive wiki can be found at https://www.coin-or.org/PuLP/ Use LpVariable() to create new variables. To create a variable 0 <= x <= 3 >>> x = LpVariable("x", 0, 3) To create a variable 0 <= y <= 1 >>> y = LpVariable("y", 0, 1) Use LpProblem() to create new problems. Create "myProblem" >>> prob = LpProblem("myProblem", LpMinimize) Combine variables to create expressions and constraints and add them to the problem. >>> prob += x + y <= 2 If you add an expression (not a constraint), it will become the objective. >>> prob += -4*x + y Choose a solver and solve the problem. ex: >>> status = prob.solve(GLPK(msg = 0)) Display the status of the solution >>> LpStatus[status] 'Optimal' You can get the value of the variables using value(). ex: >>> value(x) 2.0 Exported Classes: - LpProblem -- Container class for a Linear programming problem - LpVariable -- Variables that are added to constraints in the LP - LpConstraint -- A constraint of the general form a1x1+a2x2 ...anxn (<=, =, >=) b - LpConstraintVar -- Used to construct a column of the model in column-wise modelling Exported Functions: - value() -- Finds the value of a variable or expression - lpSum() -- given a list of the form [a1*x1, a2x2, ..., anxn] will construct a linear expression to be used as a constraint or variable - lpDot() --given two lists of the form [a1, a2, ..., an] and [ x1, x2, ..., xn] will construct a linear epression to be used as a constraint or variable Comments, bug reports, patches and suggestions are welcome. pulp-or-discuss@googlegroups.com References: [1] http://www.gnu.org/software/glpk/glpk.html [2] http://www.coin-or.org/ [3] http://www.cplex.com/ [4] http://www.gurobi.com/ """ import types import string import itertools from .constants import * from .solvers import * from collections import Iterable import logging log = logging.getLogger(__name__) try: # allow Python 2/3 compatibility maketrans = str.maketrans except AttributeError: from string import maketrans _DICT_TYPE = dict if sys.platform not in ['cli']: # iron python does not like an OrderedDict try: from odict import OrderedDict _DICT_TYPE = OrderedDict except ImportError: pass try: #python 2.7 or 3.1 from collections import OrderedDict _DICT_TYPE = OrderedDict except ImportError: pass def setConfigInformation(**keywords): """ set the data in the configuration file at the moment will only edit things in [locations] the keyword value pairs come from the keywords dictionary """ #TODO: extend if we ever add another section in the config file #read the old configuration config = ConfigParser.SafeConfigParser() config.read(config_filename) #set the new keys for (key,val) in keywords.items(): config.set("locations",key,val) #write the new configuration fp = open(config_filename,"w") config.write(fp) fp.close() # Default solver selection if PULP_CBC_CMD().available(): LpSolverDefault = PULP_CBC_CMD() elif GLPK_CMD().available(): LpSolverDefault = GLPK_CMD() elif COIN_CMD().available(): LpSolverDefault = COIN_CMD() else: LpSolverDefault = None class LpElement(object): """Base class for LpVariable and LpConstraintVar """ #to remove illegal characters from the names trans = maketrans("-+[] ->/","________") def setName(self,name): if name: self.__name = str(name).translate(self.trans) else: self.__name = None def getName(self): return self.__name name = property(fget = getName,fset = setName) def __init__(self, name): self.name = name # self.hash MUST be different for each variable # else dict() will call the comparison operators that are overloaded self.hash = id(self) self.modified = True def __hash__(self): return self.hash def __str__(self): return self.name def __repr__(self): return self.name def __neg__(self): return - LpAffineExpression(self) def __pos__(self): return self def __bool__(self): return 1 def __add__(self, other): return LpAffineExpression(self) + other def __radd__(self, other): return LpAffineExpression(self) + other def __sub__(self, other): return LpAffineExpression(self) - other def __rsub__(self, other): return other - LpAffineExpression(self) def __mul__(self, other): return LpAffineExpression(self) * other def __rmul__(self, other): return LpAffineExpression(self) * other def __div__(self, other): return LpAffineExpression(self)/other def __rdiv__(self, other): raise TypeError("Expressions cannot be divided by a variable") def __le__(self, other): return LpAffineExpression(self) <= other def __ge__(self, other): return LpAffineExpression(self) >= other def __eq__(self, other): return LpAffineExpression(self) == other def __ne__(self, other): if isinstance(other, LpVariable): return self.name is not other.name elif isinstance(other, LpAffineExpression): if other.isAtomic(): return self is not other.atom() else: return 1 else: return 1 class LpVariable(LpElement): """ This class models an LP Variable with the specified associated parameters :param name: The name of the variable used in the output .lp file :param lowbound: The lower bound on this variable's range. Default is negative infinity :param upBound: The upper bound on this variable's range. Default is positive infinity :param cat: The category this variable is in, Integer, Binary or Continuous(default) :param e: Used for column based modelling: relates to the variable's existence in the objective function and constraints """ def __init__(self, name, lowBound = None, upBound = None, cat = LpContinuous, e = None): LpElement.__init__(self,name) self.lowBound = lowBound self.upBound = upBound self.cat = cat self.varValue = None self.dj = None self.init = 0 #code to add a variable to constraints for column based # modelling if cat == LpBinary: self.lowBound = 0 self.upBound = 1 self.cat = LpInteger if e: self.add_expression(e) def add_expression(self,e): self.expression = e self.addVariableToConstraints(e) def matrix(self, name, indexs, lowBound = None, upBound = None, cat = LpContinuous, indexStart = []): if not isinstance(indexs, tuple): indexs = (indexs,) if "%" not in name: name += "_%s" * len(indexs) index = indexs[0] indexs = indexs[1:] if len(indexs) == 0: return [LpVariable(name % tuple(indexStart + [i]), lowBound, upBound, cat) for i in index] else: return [LpVariable.matrix(name, indexs, lowBound, upBound, cat, indexStart + [i]) for i in index] matrix = classmethod(matrix) def dicts(self, name, indexs, lowBound = None, upBound = None, cat = LpContinuous, indexStart = []): """ Creates a dictionary of LP variables This function creates a dictionary of LP Variables with the specified associated parameters. :param name: The prefix to the name of each LP variable created :param indexs: A list of strings of the keys to the dictionary of LP variables, and the main part of the variable name itself :param lowbound: The lower bound on these variables' range. Default is negative infinity :param upBound: The upper bound on these variables' range. Default is positive infinity :param cat: The category these variables are in, Integer or Continuous(default) :return: A dictionary of LP Variables """ if not isinstance(indexs, tuple): indexs = (indexs,) if "%" not in name: name += "_%s" * len(indexs) index = indexs[0] indexs = indexs[1:] d = {} if len(indexs) == 0: for i in index: d[i] = LpVariable(name % tuple(indexStart + [str(i)]), lowBound, upBound, cat) else: for i in index: d[i] = LpVariable.dicts(name, indexs, lowBound, upBound, cat, indexStart + [i]) return d dicts = classmethod(dicts) def dict(self, name, indexs, lowBound = None, upBound = None, cat = LpContinuous): if not isinstance(indexs, tuple): indexs = (indexs,) if "%" not in name: name += "_%s" * len(indexs) lists = indexs if len(indexs)>1: # Cartesian product res = [] while len(lists): first = lists[-1] nres = [] if res: if first: for f in first: nres.extend([[f]+r for r in res]) else: nres = res res = nres else: res = [[f] for f in first] lists = lists[:-1] index = [tuple(r) for r in res] elif len(indexs) == 1: index = indexs[0] else: return {} d = {} for i in index: d[i] = self(name % i, lowBound, upBound, cat) return d dict = classmethod(dict) def getLb(self): return self.lowBound def getUb(self): return self.upBound def bounds(self, low, up): self.lowBound = low self.upBound = up self.modified = True def positive(self): self.bounds(0, None) def value(self): return self.varValue def round(self, epsInt = 1e-5, eps = 1e-7): if self.varValue is not None: if self.upBound != None and self.varValue > self.upBound and self.varValue <= self.upBound + eps: self.varValue = self.upBound elif self.lowBound != None and self.varValue < self.lowBound and self.varValue >= self.lowBound - eps: self.varValue = self.lowBound if self.cat == LpInteger and abs(round(self.varValue) - self.varValue) <= epsInt: self.varValue = round(self.varValue) def roundedValue(self, eps = 1e-5): if self.cat == LpInteger and self.varValue != None \ and abs(self.varValue - round(self.varValue)) <= eps: return round(self.varValue) else: return self.varValue def valueOrDefault(self): if self.varValue != None: return self.varValue elif self.lowBound != None: if self.upBound != None: if 0 >= self.lowBound and 0 <= self.upBound: return 0 else: if self.lowBound >= 0: return self.lowBound else: return self.upBound else: if 0 >= self.lowBound: return 0 else: return self.lowBound elif self.upBound != None: if 0 <= self.upBound: return 0 else: return self.upBound else: return 0 def valid(self, eps): if self.varValue == None: return False if self.upBound != None and self.varValue > self.upBound + eps: return False if self.lowBound != None and self.varValue < self.lowBound - eps: return False if self.cat == LpInteger and abs(round(self.varValue) - self.varValue) > eps: return False return True def infeasibilityGap(self, mip = 1): if self.varValue == None: raise ValueError("variable value is None") if self.upBound != None and self.varValue > self.upBound: return self.varValue - self.upBound if self.lowBound != None and self.varValue < self.lowBound: return self.varValue - self.lowBound if mip and self.cat == LpInteger and round(self.varValue) - self.varValue != 0: return round(self.varValue) - self.varValue return 0 def isBinary(self): return self.cat == LpInteger and self.lowBound == 0 and self.upBound == 1 def isInteger(self): return self.cat == LpInteger def isFree(self): return self.lowBound == None and self.upBound == None def isConstant(self): return self.lowBound != None and self.upBound == self.lowBound def isPositive(self): return self.lowBound == 0 and self.upBound == None def asCplexLpVariable(self): if self.isFree(): return self.name + " free" if self.isConstant(): return self.name + " = %.12g" % self.lowBound if self.lowBound == None: s= "-inf <= " # Note: XPRESS and CPLEX do not interpret integer variables without # explicit bounds elif (self.lowBound == 0 and self.cat == LpContinuous): s = "" else: s= "%.12g <= " % self.lowBound s += self.name if self.upBound != None: s+= " <= %.12g" % self.upBound return s def asCplexLpAffineExpression(self, name, constant = 1): return LpAffineExpression(self).asCplexLpAffineExpression(name, constant) def __ne__(self, other): if isinstance(other, LpElement): return self.name is not other.name elif isinstance(other, LpAffineExpression): if other.isAtomic(): return self is not other.atom() else: return 1 else: return 1 def addVariableToConstraints(self,e): """adds a variable to the constraints indicated by the LpConstraintVars in e """ for constraint, coeff in e.items(): constraint.addVariable(self,coeff) def setInitialValue(self,val): """sets the initial value of the Variable to val may of may not be supported by the solver """ raise NotImplementedError class LpAffineExpression(_DICT_TYPE): """ A linear combination of :class:`LpVariables`. Can be initialised with the following: #. e = None: an empty Expression #. e = dict: gives an expression with the values being the coefficients of the keys (order of terms is undetermined) #. e = list or generator of 2-tuples: equivalent to dict.items() #. e = LpElement: an expression of length 1 with the coefficient 1 #. e = other: the constant is initialised as e Examples: >>> f=LpAffineExpression(LpElement('x')) >>> f 1*x + 0 >>> x_name = ['x_0', 'x_1', 'x_2'] >>> x = [LpVariable(x_name[i], lowBound = 0, upBound = 10) for i in range(3) ] >>> c = LpAffineExpression([ (x[0],1), (x[1],-3), (x[2],4)]) >>> c 1*x_0 + -3*x_1 + 4*x_2 + 0 """ #to remove illegal characters from the names trans = maketrans("-+[] ","_____") def setName(self,name): if name: self.__name = str(name).translate(self.trans) else: self.__name = None def getName(self): return self.__name name = property(fget=getName, fset=setName) def __init__(self, e = None, constant = 0, name = None): self.name = name #TODO remove isinstance usage if e is None: e = {} if isinstance(e, LpAffineExpression): # Will not copy the name self.constant = e.constant super(LpAffineExpression, self).__init__(list(e.items())) elif isinstance(e, dict): self.constant = constant super(LpAffineExpression, self).__init__(list(e.items())) elif isinstance(e, Iterable): self.constant = constant super(LpAffineExpression, self).__init__(e) elif isinstance(e,LpElement): self.constant = 0 super(LpAffineExpression, self).__init__( [(e, 1)]) else: self.constant = e super(LpAffineExpression, self).__init__() # Proxy functions for variables def isAtomic(self): return len(self) == 1 and self.constant == 0 and list(self.values())[0] == 1 def isNumericalConstant(self): return len(self) == 0 def atom(self): return list(self.keys())[0] # Functions on expressions def __bool__(self): return (float(self.constant) != 0.0) or (len(self) > 0) def value(self): s = self.constant for v,x in self.items(): if v.varValue is None: return None s += v.varValue * x return s def valueOrDefault(self): s = self.constant for v,x in self.items(): s += v.valueOrDefault() * x return s def addterm(self, key, value): y = self.get(key, 0) if y: y += value self[key] = y else: self[key] = value def emptyCopy(self): return LpAffineExpression() def copy(self): """Make a copy of self except the name which is reset""" # Will not copy the name return LpAffineExpression(self) def __str__(self, constant = 1): s = "" for v in self.sorted_keys(): val = self[v] if val<0: if s != "": s += " - " else: s += "-" val = -val elif s != "": s += " + " if val == 1: s += str(v) else: s += str(val) + "*" + str(v) if constant: if s == "": s = str(self.constant) else: if self.constant < 0: s += " - " + str(-self.constant) elif self.constant > 0: s += " + " + str(self.constant) elif s == "": s = "0" return s def sorted_keys(self): """ returns the list of keys sorted by name """ result = [(v.name, v) for v in self.keys()] result.sort() result = [v for _, v in result] return result def __repr__(self): l = [str(self[v]) + "*" + str(v) for v in self.sorted_keys()] l.append(str(self.constant)) s = " + ".join(l) return s @staticmethod def _count_characters(line): #counts the characters in a list of strings return sum(len(t) for t in line) def asCplexVariablesOnly(self, name): """ helper for asCplexLpAffineExpression """ result = [] line = ["%s:" % name] notFirst = 0 variables = self.sorted_keys() for v in variables: val = self[v] if val < 0: sign = " -" val = -val elif notFirst: sign = " +" else: sign = "" notFirst = 1 if val == 1: term = "%s %s" %(sign, v.name) else: term = "%s %.12g %s" % (sign, val, v.name) if self._count_characters(line) + len(term) > LpCplexLPLineSize: result += ["".join(line)] line = [term] else: line += [term] return result, line def asCplexLpAffineExpression(self, name, constant = 1): """ returns a string that represents the Affine Expression in lp format """ #refactored to use a list for speed in iron python result, line = self.asCplexVariablesOnly(name) if not self: term = " %s" % self.constant else: term = "" if constant: if self.constant < 0: term = " - %s" % (-self.constant) elif self.constant > 0: term = " + %s" % self.constant if self._count_characters(line) + len(term) > LpCplexLPLineSize: result += ["".join(line)] line = [term] else: line += [term] result += ["".join(line)] result = "%s\n" % "\n".join(result) return result def addInPlace(self, other): if other is 0: return self if other is None: return self if isinstance(other,LpElement): self.addterm(other, 1) elif isinstance(other,LpAffineExpression): self.constant += other.constant for v,x in other.items(): self.addterm(v, x) elif isinstance(other,dict): for e in other.values(): self.addInPlace(e) elif (isinstance(other,list) or isinstance(other, Iterable)): for e in other: self.addInPlace(e) else: self.constant += other return self def subInPlace(self, other): if other is 0: return self if other is None: return self if isinstance(other,LpElement): self.addterm(other, -1) elif isinstance(other,LpAffineExpression): self.constant -= other.constant for v,x in other.items(): self.addterm(v, -x) elif isinstance(other,dict): for e in other.values(): self.subInPlace(e) elif (isinstance(other,list) or isinstance(other, Iterable)): for e in other: self.subInPlace(e) else: self.constant -= other return self def __neg__(self): e = self.emptyCopy() e.constant = - self.constant for v,x in self.items(): e[v] = - x return e def __pos__(self): return self def __add__(self, other): return self.copy().addInPlace(other) def __radd__(self, other): return self.copy().addInPlace(other) def __iadd__(self, other): return self.addInPlace(other) def __sub__(self, other): return self.copy().subInPlace(other) def __rsub__(self, other): return (-self).addInPlace(other) def __isub__(self, other): return (self).subInPlace(other) def __mul__(self, other): e = self.emptyCopy() if isinstance(other,LpAffineExpression): e.constant = self.constant * other.constant if len(other): if len(self): raise TypeError("Non-constant expressions cannot be multiplied") else: c = self.constant if c != 0: for v,x in other.items(): e[v] = c * x else: c = other.constant if c != 0: for v,x in self.items(): e[v] = c * x elif isinstance(other,LpVariable): return self * LpAffineExpression(other) else: if other != 0: e.constant = self.constant * other for v,x in self.items(): e[v] = other * x return e def __rmul__(self, other): return self * other def __div__(self, other): if isinstance(other,LpAffineExpression) or isinstance(other,LpVariable): if len(other): raise TypeError("Expressions cannot be divided by a non-constant expression") other = other.constant e = self.emptyCopy() e.constant = self.constant / other for v,x in self.items(): e[v] = x / other return e def __truediv__(self, other): if isinstance(other,LpAffineExpression) or isinstance(other,LpVariable): if len(other): raise TypeError("Expressions cannot be divided by a non-constant expression") other = other.constant e = self.emptyCopy() e.constant = self.constant / other for v,x in self.items(): e[v] = x / other return e def __rdiv__(self, other): e = self.emptyCopy() if len(self): raise TypeError("Expressions cannot be divided by a non-constant expression") c = self.constant if isinstance(other,LpAffineExpression): e.constant = other.constant / c for v,x in other.items(): e[v] = x / c else: e.constant = other / c return e def __le__(self, other): return LpConstraint(self - other, LpConstraintLE) def __ge__(self, other): return LpConstraint(self - other, LpConstraintGE) def __eq__(self, other): return LpConstraint(self - other, LpConstraintEQ) class LpConstraint(LpAffineExpression): """An LP constraint""" def __init__(self, e = None, sense = LpConstraintEQ, name = None, rhs = None): """ :param e: an instance of :class:`LpAffineExpression` :param sense: one of :data:`~pulp.constants.LpConstraintEQ`, :data:`~pulp.constants.LpConstraintGE`, :data:`~pulp.constants.LpConstraintLE` (0, 1, -1 respectively) :param name: identifying string :param rhs: numerical value of constraint target """ LpAffineExpression.__init__(self, e, name = name) if rhs is not None: self.constant = - rhs self.sense = sense self.pi = None self.slack = None self.modified = True def getLb(self): if ( (self.sense == LpConstraintGE) or (self.sense == LpConstraintEQ) ): return -self.constant else: return None def getUb(self): if ( (self.sense == LpConstraintLE) or (self.sense == LpConstraintEQ) ): return -self.constant else: return None def __str__(self): s = LpAffineExpression.__str__(self, 0) if self.sense is not None: s += " " + LpConstraintSenses[self.sense] + " " + str(-self.constant) return s def asCplexLpConstraint(self, name): """ Returns a constraint as a string """ result, line = self.asCplexVariablesOnly(name) if not list(self.keys()): line += ["0"] c = -self.constant if c == 0: c = 0 # Supress sign term = " %s %.12g" % (LpConstraintSenses[self.sense], c) if self._count_characters(line)+len(term) > LpCplexLPLineSize: result += ["".join(line)] line = [term] else: line += [term] result += ["".join(line)] result = "%s\n" % "\n".join(result) return result def changeRHS(self, RHS): """ alters the RHS of a constraint so that it can be modified in a resolve """ self.constant = -RHS self.modified = True def __repr__(self): s = LpAffineExpression.__repr__(self) if self.sense is not None: s += " " + LpConstraintSenses[self.sense] + " 0" return s def copy(self): """Make a copy of self""" return LpConstraint(self, self.sense) def emptyCopy(self): return LpConstraint(sense = self.sense) def addInPlace(self, other): if isinstance(other,LpConstraint): if self.sense * other.sense >= 0: LpAffineExpression.addInPlace(self, other) self.sense |= other.sense else: LpAffineExpression.subInPlace(self, other) self.sense |= - other.sense elif isinstance(other,list): for e in other: self.addInPlace(e) else: LpAffineExpression.addInPlace(self, other) #raise TypeError, "Constraints and Expressions cannot be added" return self def subInPlace(self, other): if isinstance(other,LpConstraint): if self.sense * other.sense <= 0: LpAffineExpression.subInPlace(self, other) self.sense |= - other.sense else: LpAffineExpression.addInPlace(self, other) self.sense |= other.sense elif isinstance(other,list): for e in other: self.subInPlace(e) else: LpAffineExpression.subInPlace(self, other) #raise TypeError, "Constraints and Expressions cannot be added" return self def __neg__(self): c = LpAffineExpression.__neg__(self) c.sense = - c.sense return c def __add__(self, other): return self.copy().addInPlace(other) def __radd__(self, other): return self.copy().addInPlace(other) def __sub__(self, other): return self.copy().subInPlace(other) def __rsub__(self, other): return (-self).addInPlace(other) def __mul__(self, other): if isinstance(other,LpConstraint): c = LpAffineExpression.__mul__(self, other) if c.sense == 0: c.sense = other.sense elif other.sense != 0: c.sense *= other.sense return c else: return LpAffineExpression.__mul__(self, other) def __rmul__(self, other): return self * other def __div__(self, other): if isinstance(other,LpConstraint): c = LpAffineExpression.__div__(self, other) if c.sense == 0: c.sense = other.sense elif other.sense != 0: c.sense *= other.sense return c else: return LpAffineExpression.__mul__(self, other) def __rdiv__(self, other): if isinstance(other,LpConstraint): c = LpAffineExpression.__rdiv__(self, other) if c.sense == 0: c.sense = other.sense elif other.sense != 0: c.sense *= other.sense return c else: return LpAffineExpression.__mul__(self, other) def valid(self, eps = 0): val = self.value() if self.sense == LpConstraintEQ: return abs(val) <= eps else: return val * self.sense >= - eps def makeElasticSubProblem(self, *args, **kwargs): """ Builds an elastic subproblem by adding variables to a hard constraint uses FixedElasticSubProblem """ return FixedElasticSubProblem(self, *args, **kwargs) class LpFractionConstraint(LpConstraint): """ Creates a constraint that enforces a fraction requirement a/b = c """ def __init__(self, numerator, denominator = None, sense = LpConstraintEQ, RHS = 1.0, name = None, complement = None): """ creates a fraction Constraint to model constraints of the nature numerator/denominator {==, >=, <=} RHS numerator/(numerator + complement) {==, >=, <=} RHS :param numerator: the top of the fraction :param denominator: as described above :param sense: the sense of the relation of the constraint :param RHS: the target fraction value :param complement: as described above """ self.numerator = numerator if denominator is None and complement is not None: self.complement = complement self.denominator = numerator + complement elif denominator is not None and complement is None: self.denominator = denominator self.complement = denominator - numerator else: self.denominator = denominator self.complement = complement lhs = self.numerator - RHS * self.denominator LpConstraint.__init__(self, lhs, sense = sense, rhs = 0, name = name) self.RHS = RHS def findLHSValue(self): """ Determines the value of the fraction in the constraint after solution """ if abs(value(self.denominator))>= EPS: return value(self.numerator)/value(self.denominator) else: if abs(value(self.numerator))<= EPS: #zero divided by zero will return 1 return 1.0 else: raise ZeroDivisionError def makeElasticSubProblem(self, *args, **kwargs): """ Builds an elastic subproblem by adding variables and splitting the hard constraint uses FractionElasticSubProblem """ return FractionElasticSubProblem(self, *args, **kwargs) class LpConstraintVar(LpElement): """A Constraint that can be treated as a variable when constructing a LpProblem by columns """ def __init__(self, name = None ,sense = None, rhs = None, e = None): LpElement.__init__(self,name) self.constraint = LpConstraint(name = self.name, sense = sense, rhs = rhs , e = e) def addVariable(self, var, coeff): """ Adds a variable to the constraint with the activity coeff """ self.constraint.addterm(var, coeff) def value(self): return self.constraint.value() class LpProblem(object): """An LP Problem""" def __init__(self, name = "NoName", sense = LpMinimize): """ Creates an LP Problem This function creates a new LP Problem with the specified associated parameters :param name: name of the problem used in the output .lp file :param sense: of the LP problem objective. \ Either :data:`~pulp.constants.LpMinimize` (default) \ or :data:`~pulp.constants.LpMaximize`. :return: An LP Problem """ self.objective = None self.constraints = _DICT_TYPE() self.name = name self.sense = sense self.sos1 = {} self.sos2 = {} self.status = LpStatusNotSolved self.noOverlap = 1 self.solver = None self.initialValues = {} self.modifiedVariables = [] self.modifiedConstraints = [] self.resolveOK = False self._variables = [] self._variable_ids = {} #old school using dict.keys() for a set self.dummyVar = None # locals self.lastUnused = 0 def __repr__(self): string = self.name+":\n" if self.sense == 1: string += "MINIMIZE\n" else: string += "MAXIMIZE\n" string += repr(self.objective) +"\n" if self.constraints: string += "SUBJECT TO\n" for n, c in self.constraints.items(): string += c.asCplexLpConstraint(n) +"\n" string += "VARIABLES\n" for v in self.variables(): string += v.asCplexLpVariable() + " " + LpCategories[v.cat] + "\n" return string def copy(self): """Make a copy of self. Expressions are copied by reference""" lpcopy = LpProblem(name = self.name, sense = self.sense) lpcopy.objective = self.objective lpcopy.constraints = self.constraints.copy() lpcopy.sos1 = self.sos1.copy() lpcopy.sos2 = self.sos2.copy() return lpcopy def deepcopy(self): """Make a copy of self. Expressions are copied by value""" lpcopy = LpProblem(name = self.name, sense = self.sense) if self.objective is not None: lpcopy.objective = self.objective.copy() lpcopy.constraints = {} for k,v in self.constraints.items(): lpcopy.constraints[k] = v.copy() lpcopy.sos1 = self.sos1.copy() lpcopy.sos2 = self.sos2.copy() return lpcopy def normalisedNames(self): constraintsNames = {} i = 0 for k in self.constraints: constraintsNames[k] = "C%07d" % i i += 1 variablesNames = {} i = 0 for k in self.variables(): variablesNames[k.name] = "X%07d" % i i += 1 return constraintsNames, variablesNames, "OBJ" def isMIP(self): for v in self.variables(): if v.cat == LpInteger: return 1 return 0 def roundSolution(self, epsInt = 1e-5, eps = 1e-7): """ Rounds the lp variables Inputs: - none Side Effects: - The lp variables are rounded """ for v in self.variables(): v.round(epsInt, eps) def unusedConstraintName(self): self.lastUnused += 1 while 1: s = "_C%d" % self.lastUnused if s not in self.constraints: break self.lastUnused += 1 return s def valid(self, eps = 0): for v in self.variables(): if not v.valid(eps): return False for c in self.constraints.values(): if not c.valid(eps): return False else: return True def infeasibilityGap(self, mip = 1): gap = 0 for v in self.variables(): gap = max(abs(v.infeasibilityGap(mip)), gap) for c in self.constraints.values(): if not c.valid(0): gap = max(abs(c.value()), gap) return gap def addVariable(self, variable): """ Adds a variable to the problem before a constraint is added @param variable: the variable to be added """ if id(variable) not in self._variable_ids: self._variables.append(variable) self._variable_ids[id(variable)] = variable def addVariables(self, variables): """ Adds variables to the problem before a constraint is added @param variables: the variables to be added """ for v in variables: self.addVariable(v) def variables(self): """ Returns a list of the problem variables Inputs: - none Returns: - A list of the problem variables """ if self.objective: self.addVariables(list(self.objective.keys())) for c in self.constraints.values(): self.addVariables(list(c.keys())) variables = self._variables #sort the varibles DSU variables = [[v.name, v] for v in variables] variables.sort() variables = [v for _, v in variables] return variables def variablesDict(self): variables = {} if self.objective: for v in self.objective: variables[v.name] = v for c in list(self.constraints.values()): for v in c: variables[v.name] = v return variables def add(self, constraint, name = None): self.addConstraint(constraint, name) def addConstraint(self, constraint, name = None): if not isinstance(constraint, LpConstraint): raise TypeError("Can only add LpConstraint objects") if name: constraint.name = name try: if constraint.name: name = constraint.name else: name = self.unusedConstraintName() except AttributeError: raise TypeError("Can only add LpConstraint objects") #removed as this test fails for empty constraints # if len(constraint) == 0: # if not constraint.valid(): # raise ValueError, "Cannot add false constraints" if name in self.constraints: if self.noOverlap: raise PulpError("overlapping constraint names: " + name) else: print("Warning: overlapping constraint names:", name) self.constraints[name] = constraint self.modifiedConstraints.append(constraint) self.addVariables(list(constraint.keys())) def setObjective(self,obj): """ Sets the input variable as the objective function. Used in Columnwise Modelling :param obj: the objective function of type :class:`LpConstraintVar` Side Effects: - The objective function is set """ if isinstance(obj, LpVariable): # allows the user to add a LpVariable as an objective obj = obj + 0.0 try: obj = obj.constraint name = obj.name except AttributeError: name = None self.objective = obj self.objective.name = name self.resolveOK = False def __iadd__(self, other): if isinstance(other, tuple): other, name = other else: name = None if other is True: return self if isinstance(other, LpConstraintVar): self.addConstraint(other.constraint) elif isinstance(other, LpConstraint): self.addConstraint(other, name) elif isinstance(other, LpAffineExpression): self.objective = other self.objective.name = name elif isinstance(other, LpVariable) or isinstance(other, (int, float)): self.objective = LpAffineExpression(other) self.objective.name = name else: raise TypeError("Can only add LpConstraintVar, LpConstraint, LpAffineExpression or True objects") return self def extend(self, other, use_objective = True): """ extends an LpProblem by adding constraints either from a dictionary a tuple or another LpProblem object. @param use_objective: determines whether the objective is imported from the other problem For dictionaries the constraints will be named with the keys For tuples an unique name will be generated For LpProblems the name of the problem will be added to the constraints name """ if isinstance(other, dict): for name in other: self.constraints[name] = other[name] elif isinstance(other, LpProblem): for v in set(other.variables()).difference(self.variables()): v.name = other.name + v.name for name,c in other.constraints.items(): c.name = other.name + name self.addConstraint(c) if use_objective: self.objective += other.objective else: for c in other: if isinstance(c,tuple): name = c[0] c = c[1] else: name = None if not name: name = c.name if not name: name = self.unusedConstraintName() self.constraints[name] = c def coefficients(self, translation = None): coefs = [] if translation == None: for c in self.constraints: cst = self.constraints[c] coefs.extend([(v.name, c, cst[v]) for v in cst]) else: for c in self.constraints: ctr = translation[c] cst = self.constraints[c] coefs.extend([(translation[v.name], ctr, cst[v]) for v in cst]) return coefs def writeMPS(self, filename, mpsSense = 0, rename = 0, mip = 1): wasNone, dummyVar = self.fixObjective() f = open(filename, "w") if mpsSense == 0: mpsSense = self.sense cobj = self.objective if mpsSense != self.sense: n = cobj.name cobj = - cobj cobj.name = n if rename: constraintsNames, variablesNames, cobj.name = self.normalisedNames() f.write("*SENSE:"+LpSenses[mpsSense]+"\n") n = self.name if rename: n = "MODEL" f.write("NAME "+n+"\n") vs = self.variables() # constraints f.write("ROWS\n") objName = cobj.name if not objName: objName = "OBJ" f.write(" N %s\n" % objName) mpsConstraintType = {LpConstraintLE:"L", LpConstraintEQ:"E", LpConstraintGE:"G"} for k,c in self.constraints.items(): if rename: k = constraintsNames[k] f.write(" "+mpsConstraintType[c.sense]+" "+k+"\n") # matrix f.write("COLUMNS\n") # Creation of a dict of dict: # coefs[nomVariable][nomContrainte] = coefficient coefs = {} for k,c in self.constraints.items(): if rename: k = constraintsNames[k] for v in c: n = v.name if rename: n = variablesNames[n] if n in coefs: coefs[n][k] = c[v] else: coefs[n] = {k:c[v]} for v in vs: if mip and v.cat == LpInteger: f.write(" MARK 'MARKER' 'INTORG'\n") n = v.name if rename: n = variablesNames[n] if n in coefs: cv = coefs[n] # Most of the work is done here for k in cv: f.write(" %-8s %-8s % .12e\n" % (n,k,cv[k])) # objective function if v in cobj: f.write(" %-8s %-8s % .12e\n" % (n,objName,cobj[v])) if mip and v.cat == LpInteger: f.write(" MARK 'MARKER' 'INTEND'\n") # right hand side f.write("RHS\n") for k,c in self.constraints.items(): c = -c.constant if rename: k = constraintsNames[k] if c == 0: c = 0 f.write(" RHS %-8s % .12e\n" % (k,c)) # bounds f.write("BOUNDS\n") for v in vs: n = v.name if rename: n = variablesNames[n] if v.lowBound != None and v.lowBound == v.upBound: f.write(" FX BND %-8s % .12e\n" % (n, v.lowBound)) elif v.lowBound == 0 and v.upBound == 1 and mip and v.cat == LpInteger: f.write(" BV BND %-8s\n" % n) else: if v.lowBound != None: # In MPS files, variables with no bounds (i.e. >= 0) # are assumed BV by COIN and CPLEX. # So we explicitly write a 0 lower bound in this case. if v.lowBound != 0 or (mip and v.cat == LpInteger and v.upBound == None): f.write(" LO BND %-8s % .12e\n" % (n, v.lowBound)) else: if v.upBound != None: f.write(" MI BND %-8s\n" % n) else: f.write(" FR BND %-8s\n" % n) if v.upBound != None: f.write(" UP BND %-8s % .12e\n" % (n, v.upBound)) f.write("ENDATA\n") f.close() self.restoreObjective(wasNone, dummyVar) # returns the variables, in writing order if rename == 0: return vs else: return vs, variablesNames, constraintsNames, cobj.name def writeLP(self, filename, writeSOS = 1, mip = 1): """ Write the given Lp problem to a .lp file. This function writes the specifications (objective function, constraints, variables) of the defined Lp problem to a file. :param filename: the name of the file to be created. Side Effects: - The file is created. """ f = open(filename, "w") f.write("\\* "+self.name+" *\\\n") if self.sense == 1: f.write("Minimize\n") else: f.write("Maximize\n") wasNone, dummyVar = self.fixObjective() objName = self.objective.name if not objName: objName = "OBJ" f.write(self.objective.asCplexLpAffineExpression(objName, constant = 0)) f.write("Subject To\n") ks = list(self.constraints.keys()) ks.sort() for k in ks: constraint = self.constraints[k] if not list(constraint.keys()): #empty constraint add the dummyVar dummyVar = self.get_dummyVar() constraint += dummyVar #set this dummyvar to zero so infeasible problems are not made feasible f.write((dummyVar == 0.0).asCplexLpConstraint("_dummy")) f.write(constraint.asCplexLpConstraint(k)) vs = self.variables() # check if any names are longer than 100 characters long_names = [v.name for v in vs if len(v.name) > 100] if long_names: raise PulpError('Variable names too long for Lp format\n' + str(long_names)) # check for repeated names repeated_names = {} for v in vs: repeated_names[v.name] = repeated_names.get(v.name, 0) + 1 repeated_names = [(key, value) for key, value in list(repeated_names.items()) if value >= 2] if repeated_names: raise PulpError('Repeated variable names in Lp format\n' + str(repeated_names)) # Bounds on non-"positive" variables # Note: XPRESS and CPLEX do not interpret integer variables without # explicit bounds if mip: vg = [v for v in vs if not (v.isPositive() and v.cat == LpContinuous) \ and not v.isBinary()] else: vg = [v for v in vs if not v.isPositive()] if vg: f.write("Bounds\n") for v in vg: f.write("%s\n" % v.asCplexLpVariable()) # Integer non-binary variables if mip: vg = [v for v in vs if v.cat == LpInteger and not v.isBinary()] if vg: f.write("Generals\n") for v in vg: f.write("%s\n" % v.name) # Binary variables vg = [v for v in vs if v.isBinary()] if vg: f.write("Binaries\n") for v in vg: f.write("%s\n" % v.name) # Special Ordered Sets if writeSOS and (self.sos1 or self.sos2): f.write("SOS\n") if self.sos1: for sos in self.sos1.values(): f.write("S1:: \n") for v,val in sos.items(): f.write(" %s: %.12g\n" % (v.name, val)) if self.sos2: for sos in self.sos2.values(): f.write("S2:: \n") for v,val in sos.items(): f.write(" %s: %.12g\n" % (v.name, val)) f.write("End\n") f.close() self.restoreObjective(wasNone, dummyVar) def assignVarsVals(self, values): variables = self.variablesDict() for name in values: if name != '__dummy': variables[name].varValue = values[name] def assignVarsDj(self,values): variables = self.variablesDict() for name in values: if name != '__dummy': variables[name].dj = values[name] def assignConsPi(self, values): for name in values: self.constraints[name].pi = values[name] def assignConsSlack(self, values, activity=False): for name in values: if activity: #reports the activitynot the slack self.constraints[name].slack = -1 * ( self.constraints[name].constant + float(values[name])) else: self.constraints[name].slack = float(values[name]) def get_dummyVar(self): if self.dummyVar is None: self.dummyVar = LpVariable("__dummy", 0, 0) return self.dummyVar def fixObjective(self): if self.objective is None: self.objective = 0 wasNone = 1 else: wasNone = 0 if not isinstance(self.objective, LpAffineExpression): self.objective = LpAffineExpression(self.objective) if self.objective.isNumericalConstant(): dummyVar = self.get_dummyVar() self.objective += dummyVar else: dummyVar = None return wasNone, dummyVar def restoreObjective(self, wasNone, dummyVar): if wasNone: self.objective = None elif not dummyVar is None: self.objective -= dummyVar def solve(self, solver = None, **kwargs): """ Solve the given Lp problem. This function changes the problem to make it suitable for solving then calls the solver.actualSolve() method to find the solution :param solver: Optional: the specific solver to be used, defaults to the default solver. Side Effects: - The attributes of the problem object are changed in :meth:`~pulp.solver.LpSolver.actualSolve()` to reflect the Lp solution """ if not(solver): solver = self.solver if not(solver): solver = LpSolverDefault wasNone, dummyVar = self.fixObjective() #time it self.solutionTime = -clock() status = solver.actualSolve(self, **kwargs) self.solutionTime += clock() self.restoreObjective(wasNone, dummyVar) self.solver = solver return status def sequentialSolve(self, objectives, absoluteTols = None, relativeTols = None, solver = None, debug = False): """ Solve the given Lp problem with several objective functions. This function sequentially changes the objective of the problem and then adds the objective function as a constraint :param objectives: the list of objectives to be used to solve the problem :param absoluteTols: the list of absolute tolerances to be applied to the constraints should be +ve for a minimise objective :param relativeTols: the list of relative tolerances applied to the constraints :param solver: the specific solver to be used, defaults to the default solver. """ #TODO Add a penalty variable to make problems elastic #TODO add the ability to accept different status values i.e. infeasible etc if not(solver): solver = self.solver if not(solver): solver = LpSolverDefault if not(absoluteTols): absoluteTols = [0] * len(objectives) if not(relativeTols): relativeTols = [1] * len(objectives) #time it self.solutionTime = -clock() statuses = [] for i,(obj,absol,rel) in enumerate(zip(objectives, absoluteTols, relativeTols)): self.setObjective(obj) status = solver.actualSolve(self) statuses.append(status) if debug: self.writeLP("%sSequence.lp"%i) if self.sense == LpMinimize: self += obj <= value(obj)*rel + absol,"%s_Sequence_Objective"%i elif self.sense == LpMaximize: self += obj >= value(obj)*rel + absol,"%s_Sequence_Objective"%i self.solutionTime += clock() self.solver = solver return statuses def resolve(self, solver = None, **kwargs): """ resolves an Problem using the same solver as previously """ if not(solver): solver = self.solver if self.resolveOK: return self.solver.actualResolve(self, **kwargs) else: return self.solve(solver = solver, **kwargs) def setSolver(self,solver = LpSolverDefault): """Sets the Solver for this problem useful if you are using resolve """ self.solver = solver def setInitial(self,values): self.initialValues = values def numVariables(self): return len(self._variable_ids) def numConstraints(self): return len(self.constraints) def getSense(self): return self.sense class FixedElasticSubProblem(LpProblem): """ Contains the subproblem generated by converting a fixed constraint :math:`\sum_{i}a_i x_i = b` into an elastic constraint. :param constraint: The LpConstraint that the elastic constraint is based on :param penalty: penalty applied for violation (+ve or -ve) of the constraints :param proportionFreeBound: the proportional bound (+ve and -ve) on constraint violation that is free from penalty :param proportionFreeBoundList: the proportional bound on \ constraint violation that is free from penalty, expressed as a list\ where [-ve, +ve] """ def __init__(self, constraint, penalty = None, proportionFreeBound = None, proportionFreeBoundList = None): subProblemName = "%s_elastic_SubProblem" % constraint.name LpProblem.__init__(self, subProblemName, LpMinimize) self.objective = LpAffineExpression() self.constraint = constraint self.constant = constraint.constant self.RHS = - constraint.constant self.objective = LpAffineExpression() self += constraint, "_Constraint" #create and add these variables but disabled self.freeVar = LpVariable("_free_bound", upBound = 0, lowBound = 0) self.upVar = LpVariable("_pos_penalty_var", upBound = 0, lowBound = 0) self.lowVar = LpVariable("_neg_penalty_var", upBound = 0, lowBound = 0) constraint.addInPlace(self.freeVar + self.lowVar + self.upVar) if proportionFreeBound: proportionFreeBoundList = [proportionFreeBound, proportionFreeBound] if proportionFreeBoundList: #add a costless variable self.freeVar.upBound = abs(constraint.constant * proportionFreeBoundList[0]) self.freeVar.lowBound = -abs(constraint.constant * proportionFreeBoundList[1]) # Note the reversal of the upbound and lowbound due to the nature of the # variable if penalty is not None: #activate these variables self.upVar.upBound = None self.lowVar.lowBound = None self.objective = penalty*self.upVar - penalty*self.lowVar def _findValue(self, attrib): """ safe way to get the value of a variable that may not exist """ var = getattr(self, attrib, 0) if var: if value(var) is not None: return value(var) else: return 0.0 else: return 0.0 def isViolated(self): """ returns true if the penalty variables are non-zero """ upVar = self._findValue("upVar") lowVar = self._findValue("lowVar") freeVar = self._findValue("freeVar") result = abs(upVar + lowVar) >= EPS if result: log.debug("isViolated %s, upVar %s, lowVar %s, freeVar %s result %s"%( self.name, upVar, lowVar, freeVar, result)) log.debug("isViolated value lhs %s constant %s"%( self.findLHSValue(), self.RHS)) return result def findDifferenceFromRHS(self): """ The amount the actual value varies from the RHS (sense: LHS - RHS) """ return self.findLHSValue() - self.RHS def findLHSValue(self): """ for elastic constraints finds the LHS value of the constraint without the free variable and or penalty variable assumes the constant is on the rhs """ upVar = self._findValue("upVar") lowVar = self._findValue("lowVar") freeVar = self._findValue("freeVar") return self.constraint.value() - self.constant - \ upVar - lowVar - freeVar def deElasticize(self): """ de-elasticize constraint """ self.upVar.upBound = 0 self.lowVar.lowBound = 0 def reElasticize(self): """ Make the Subproblem elastic again after deElasticize """ self.upVar.lowBound = 0 self.upVar.upBound = None self.lowVar.upBound = 0 self.lowVar.lowBound = None def alterName(self, name): """ Alters the name of anonymous parts of the problem """ self.name = "%s_elastic_SubProblem" % name if hasattr(self, 'freeVar'): self.freeVar.name = self.name + "_free_bound" if hasattr(self, 'upVar'): self.upVar.name = self.name + "_pos_penalty_var" if hasattr(self, 'lowVar'): self.lowVar.name = self.name + "_neg_penalty_var" class FractionElasticSubProblem(FixedElasticSubProblem): """ Contains the subproblem generated by converting a Fraction constraint numerator/(numerator+complement) = b into an elastic constraint :param name: The name of the elastic subproblem :param penalty: penalty applied for violation (+ve or -ve) of the constraints :param proportionFreeBound: the proportional bound (+ve and -ve) on constraint violation that is free from penalty :param proportionFreeBoundList: the proportional bound on constraint violation that is free from penalty, expressed as a list where [-ve, +ve] """ def __init__(self, name, numerator, RHS, sense, complement = None, denominator = None, penalty = None, proportionFreeBound = None, proportionFreeBoundList = None): subProblemName = "%s_elastic_SubProblem" % name self.numerator = numerator if denominator is None and complement is not None: self.complement = complement self.denominator = numerator + complement elif denominator is not None and complement is None: self.denominator = denominator self.complement = denominator - numerator else: raise PulpError('only one of denominator and complement must be specified') self.RHS = RHS self.lowTarget = self.upTarget = None LpProblem.__init__(self, subProblemName, LpMinimize) self.freeVar = LpVariable("_free_bound", upBound = 0, lowBound = 0) self.upVar = LpVariable("_pos_penalty_var", upBound = 0, lowBound = 0) self.lowVar = LpVariable("_neg_penalty_var", upBound = 0, lowBound = 0) if proportionFreeBound: proportionFreeBoundList = [proportionFreeBound, proportionFreeBound] if proportionFreeBoundList: upProportionFreeBound, lowProportionFreeBound = \ proportionFreeBoundList else: upProportionFreeBound, lowProportionFreeBound = (0, 0) #create an objective self += LpAffineExpression() #There are three cases if the constraint.sense is ==, <=, >= if sense in [LpConstraintEQ, LpConstraintLE]: #create a constraint the sets the upper bound of target self.upTarget = RHS + upProportionFreeBound self.upConstraint = LpFractionConstraint(self.numerator, self.complement, LpConstraintLE, self.upTarget, denominator = self.denominator) if penalty is not None: self.lowVar.lowBound = None self.objective += -1* penalty * self.lowVar self.upConstraint += self.lowVar self += self.upConstraint, '_upper_constraint' if sense in [LpConstraintEQ, LpConstraintGE]: #create a constraint the sets the lower bound of target self.lowTarget = RHS - lowProportionFreeBound self.lowConstraint = LpFractionConstraint(self.numerator, self.complement, LpConstraintGE, self.lowTarget, denominator = self.denominator) if penalty is not None: self.upVar.upBound = None self.objective += penalty * self.upVar self.lowConstraint += self.upVar self += self.lowConstraint, '_lower_constraint' def findLHSValue(self): """ for elastic constraints finds the LHS value of the constraint without the free variable and or penalty variable assumes the constant is on the rhs """ # uses code from LpFractionConstraint if abs(value(self.denominator))>= EPS: return value(self.numerator)/value(self.denominator) else: if abs(value(self.numerator))<= EPS: #zero divided by zero will return 1 return 1.0 else: raise ZeroDivisionError def isViolated(self): """ returns true if the penalty variables are non-zero """ if abs(value(self.denominator))>= EPS: if self.lowTarget is not None: if self.lowTarget > self.findLHSValue(): return True if self.upTarget is not None: if self.findLHSValue() > self.upTarget: return True else: #if the denominator is zero the constraint is satisfied return False class LpVariableDict(dict): """An LP variable generator""" def __init__(self, name, data = {}, lowBound = None, upBound = None, cat = LpContinuous): self.name = name dict.__init__(self, data) def __getitem__(self, key): if key in self: return dict.__getitem__(self, key) else: self[key] = LpVariable(self.name % key, lowBound, upBound, cat) return self[key] # Utility functions def lpSum(vector): """ Calculate the sum of a list of linear expressions :param vector: A list of linear expressions """ return LpAffineExpression().addInPlace(vector) def lpDot(v1, v2): """Calculate the dot product of two lists of linear expressions""" if not isiterable(v1) and not isiterable(v2): return v1 * v2 elif not isiterable(v1): return lpDot([v1]*len(v2),v2) elif not isiterable(v2): return lpDot(v1,[v2]*len(v1)) else: return lpSum([lpDot(e1,e2) for e1,e2 in zip(v1,v2)]) def isNumber(x): """Returns true if x is an int or a float""" return isinstance(x, (int, float)) def value(x): """Returns the value of the variable/expression x, or x if it is a number""" if isNumber(x): return x else: return x.value() def valueOrDefault(x): """Returns the value of the variable/expression x, or x if it is a number Variable without value (None) are affected a possible value (within their bounds).""" if isNumber(x): return x else: return x.valueOrDefault() def combination(orgset, k = None): """ returns an iterator that lists the combinations of orgset of length k :param orgset: the list to be iterated :param k: the cardinality of the subsets :return: an iterator of the subsets example: >>> c = combination([1,2,3,4],2) >>> for s in c: ... print(s) (1, 2) (1, 3) (1, 4) (2, 3) (2, 4) (3, 4) """ try: from itertools import combination as _it_combination return _it_combination(orgset, k) except ImportError: return __combination(orgset,k) def __combination(orgset,k): """ fall back if probstat is not installed note it is GPL so cannot be included """ if k == 1: for i in orgset: yield (i,) elif k>1: for i,x in enumerate(orgset): #iterates though to near the end for s in __combination(orgset[i+1:],k-1): yield (x,) + s def permutation(orgset, k = None): """ returns an iterator that lists the permutations of orgset of length k :param orgset: the list to be iterated :param k: the cardinality of the subsets :return: an iterator of the subsets example: >>> c = permutation([1,2,3,4],2) >>> for s in c: ... print(s) (1, 2) (1, 3) (1, 4) (2, 1) (2, 3) (2, 4) (3, 1) (3, 2) (3, 4) (4, 1) (4, 2) (4, 3) """ try: from itertools import permutation as _it_permutation return _it_permutation(orgset, k) except ImportError: return __permutation(orgset, k) def __permutation(orgset, k): """ fall back if probstat is not installed note it is GPL so cannot be included """ if k == 1: for i in orgset: yield (i,) elif k>1: for i,x in enumerate(orgset): #iterates though to near the end for s in __permutation(orgset[:i] + orgset[i+1:],k-1): yield (x,)+ s def allpermutations(orgset,k): """ returns all permutations of orgset with up to k items :param orgset: the list to be iterated :param k: the maxcardinality of the subsets :return: an iterator of the subsets example: >>> c = allpermutations([1,2,3,4],2) >>> for s in c: ... print(s) (1,) (2,) (3,) (4,) (1, 2) (1, 3) (1, 4) (2, 1) (2, 3) (2, 4) (3, 1) (3, 2) (3, 4) (4, 1) (4, 2) (4, 3) """ return itertools.chain(*[permutation(orgset,i) for i in range(1,k+1)]) def allcombinations(orgset,k): """ returns all permutations of orgset with up to k items :param orgset: the list to be iterated :param k: the maxcardinality of the subsets :return: an iterator of the subsets example: >>> c = allcombinations([1,2,3,4],2) >>> for s in c: ... print(s) (1,) (2,) (3,) (4,) (1, 2) (1, 3) (1, 4) (2, 3) (2, 4) (3, 4) """ return itertools.chain(*[combination(orgset,i) for i in range(1,k+1)]) def makeDict(headers, array, default = None): """ makes a list into a dictionary with the headings given in headings headers is a list of header lists array is a list with the data """ result, defdict = __makeDict(headers, array, default) return result def __makeDict(headers, array, default = None): #this is a recursive function so end the recursion as follows result ={} returndefaultvalue = None if len(headers) == 1: result.update(dict(zip(headers[0],array))) defaultvalue = default else: for i,h in enumerate(headers[0]): result[h],defaultvalue = __makeDict(headers[1:],array[i],default) if default != None: f = lambda :defaultvalue defresult = collections.defaultdict(f) defresult.update(result) result = defresult returndefaultvalue = collections.defaultdict(f) return result, returndefaultvalue def splitDict(Data): """ Split a dictionary with lists as the data, into smaller dictionaries :param Data: A dictionary with lists as the values :return: A tuple of dictionaries each containing the data separately, with the same dictionary keys """ # find the maximum number of items in the dictionary maxitems = max([len(values) for values in Data.values()]) output =[dict() for i in range(maxitems)] for key, values in Data.items(): for i, val in enumerate(values): output[i][key] = val return tuple(output) def read_table(data, coerce_type, transpose=False): ''' Reads in data from a simple table and forces it to be a particular type This is a helper function that allows data to be easily constained in a simple script ::return: a dictionary of with the keys being a tuple of the strings in the first row and colum of the table ::param data: the multiline string containing the table data ::param coerce_type: the type that the table data is converted to ::param transpose: reverses the data if needed Example: >>> table_data = """ ... L1 L2 L3 L4 L5 L6 ... C1 6736 42658 70414 45170 184679 111569 ... C2 217266 227190 249640 203029 153531 117487 ... C3 35936 28768 126316 2498 130317 74034 ... C4 73446 52077 108368 75011 49827 62850 ... C5 174664 177461 151589 153300 59916 135162 ... C6 186302 189099 147026 164938 149836 286307 ... """ >>> table = read_table(table_data, int) >>> table[("C1","L1")] 6736 >>> table[("C6","L5")] 149836 ''' lines = data.splitlines() headings = lines[1].split() result = {} for row in lines[2:]: items = row.split() for i, item in enumerate(items[1:]): if transpose: key = (headings[i], items[0]) else: key = (items[0], headings[i]) result[key] = coerce_type(item) return result def configSolvers(): """ Configure the path the the solvers on the command line Designed to configure the file locations of the solvers from the command line after installation """ configlist = [(cplex_dll_path,"cplexpath","CPLEX: "), (coinMP_path, "coinmppath","CoinMP dll (windows only): ")] print("Please type the full path including filename and extension \n" + "for each solver available") configdict = {} for (default, key, msg) in configlist: value = input(msg + "[" + str(default) +"]") if value: configdict[key] = value setConfigInformation(**configdict) def pulpTestAll(): from .tests import pulpTestSolver solvers = [PULP_CBC_CMD, CPLEX_DLL, CPLEX_CMD, CPLEX_PY, COIN_CMD, COINMP_DLL, GLPK_CMD, XPRESS, GUROBI, GUROBI_CMD, PYGLPK, YAPOSIB ] failed = False for s in solvers: if s().available(): try: pulpTestSolver(s) print("* Solver %s passed." % s) except Exception as e: print(e) print("* Solver", s, "failed.") failed = True else: print("Solver %s unavailable" % s) if failed: raise PulpError("Tests Failed") def pulpDoctest(): """ runs all doctests """ import doctest if __name__ != '__main__': from . import pulp doctest.testmod(pulp) else: doctest.testmod() if __name__ == '__main__': # Tests pulpTestAll() pulpDoctest()