SharedlinProg.sageOpen in CoCalc
Authors: Ariane Masuda, Johann Thiel
Views : 33
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##########################################
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# Linear Programming Scripts
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##########################################
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#
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# Johann Thiel
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# ver 12.18.18
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# Functions to solve linear
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# programming problems.
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#
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# Necessary modules
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from sage.numerical.backends.generic_backend import get_solver
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import sage.numerical.backends.glpk_backend as backend
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from tabulate import tabulate
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##########################################
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##########################################
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# Generic linear programming solver that
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# produces a sensitivity report
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##########################################
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# var = list of variable names
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# con = list of constraint names
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# ob = list of coefficients of objective
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# functions
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# M = matrix of constraint coefficients
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# inq = list of inequality direction
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# 1 for '<=', -1 for '>=' and
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# 0 for '='.
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# bnd = list of constraint bounds
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# mx = Boolean to determine if the
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# problem is a maximization (True)
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# or minimization (False) problem.
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# Default is set to maximization.
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##########################################
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def lp(var, con, ob, M, inq, bnd, mx=True):
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# loads the solver
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q = get_solver(solver = 'GLPK')
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# sets solver to min, max otherwise
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if not mx:
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q.set_sense(-1)
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# adds all variables
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for v in va:
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q.add_variable(name=v)
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# adds all constraints
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for i in range(len(M)):
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if inq[i] == 1:
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q.add_linear_constraint(list(zip(range(len(M[0])), M[i])), None, bnd[i], con[i])
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elif inq[i] == -1:
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q.add_linear_constraint(list(zip(range(len(M[0])), M[i])), bnd[i], None, con[i])
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else:
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q.add_linear_constraint(list(zip(range(len(M[0])), M[i])), bnd[i], bnd[i], con[i])
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# sets objective
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q.set_objective(ob)
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q.solver_parameter(backend.glp_simplex_or_intopt, backend.glp_simplex_only)
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# solves the problem
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q.solve()
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# produces sensitivity report
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q.print_ranges()
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##########################################
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##########################################
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# Generic linear programming solver for
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# integer programming problems (produces
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# no sensitivity report)
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##########################################
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# var = list of variable names
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# con = list of constraint names
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# ob = list of coefficients of objective
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# functions
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# M = matrix of constraint coefficients
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# inq = list of inequality direction
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# 1 for '<=', -1 for '>=' and
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# 0 for '='.
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# bnd = list of constraint bounds
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# mx = Boolean to determine if the
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# problem is a maximization (True)
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# or minimization (False) problem.
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# Default is set to maximization.
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##########################################
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def lpInt(var, con, ob, M, inq, bnd, mx=True):
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# loads the solver
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q = get_solver(solver = 'GLPK')
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# sets solver to min, max otherwise
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if not mx:
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q.set_sense(-1)
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# adds all variables
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for v in var:
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q.add_variable(integer=True, name=v)
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# adds all constraints
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for i in range(len(M)):
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if inq[i] == 1:
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q.add_linear_constraint(list(zip(range(len(M[0])), M[i])), None, bnd[i], con[i])
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elif inq[i] == -1:
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q.add_linear_constraint(list(zip(range(len(M[0])), M[i])), bnd[i], None, con[i])
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else:
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q.add_linear_constraint(list(zip(range(len(M[0])), M[i])), bnd[i], bnd[i], con[i])
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# sets objective
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q.set_objective(ob)
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q.solver_parameter(backend.glp_simplex_then_intopt)
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# solves the problem
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q.solve()
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# The following lines all produce an output report
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if mx:
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st = ' (max) '
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else:
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st = ' (min) '
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sol = [q.get_variable_value(i) for i in range(q.ncols())]
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print 'Optimal'+st+'value: ', q.get_objective_value()
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print ''
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results = [[a,b] for a,b in zip(var,sol)]
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print tabulate(results, headers=['Variable', 'Value'])
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print ''
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slack = [[q.row_name(j), round(max(0,abs(bnd[j]-sum([a*b for a,b in zip(sol,M[j])]))),3)] for j in range(q.nrows())]
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print tabulate(slack, headers=['Constraint', 'Slack'])
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##########################################
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##########################################
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# Generic linear programming solver for
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# binary integer programming problems
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# (produces no sensitivity report)
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##########################################
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#
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# var = list of variable names
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# con = list of constraint names
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# ob = list of coefficients of objective
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# functions
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# M = matrix of constraint coefficients
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# inq = list of inequality direction
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# 1 for '<=', -1 for '>=' and
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# 0 for '='.
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# bnd = list of constraint bounds
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# mx = Boolean to determine if the
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# problem is a maximization (True)
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# or minimization (False) problem.
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# Default is set to maximization.
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##########################################
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def lpBin(var, con, ob, M, inq, bnd, mx=True):
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# loads the solver
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q = get_solver(solver = 'GLPK')
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# sets solver to min, max otherwise
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if not mx:
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q.set_sense(-1)
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# adds all variables
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for v in var:
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q.add_variable(binary=True, name=v)
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# adds all constraints
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for i in range(len(M)):
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if inq[i] == 1:
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q.add_linear_constraint(list(zip(range(len(M[0])), M[i])), None, bnd[i], con[i])
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elif inq[i] == -1:
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q.add_linear_constraint(list(zip(range(len(M[0])), M[i])), bnd[i], None, con[i])
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else:
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q.add_linear_constraint(list(zip(range(len(M[0])), M[i])), bnd[i], bnd[i], con[i])
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# sets objective
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q.set_objective(ob)
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q.solver_parameter(backend.glp_simplex_then_intopt)
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# solves the problem
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q.solve()
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# The following lines all produce an output report
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if mx:
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st = ' (max) '
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else:
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st = ' (min) '
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sol = [q.get_variable_value(i) for i in range(q.ncols())]
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print 'Optimal'+st+'value: ', q.get_objective_value()
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print ''
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results = [[a,b] for a,b in zip(va,sol)]
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print tabulate(results, headers=['Variable', 'Value'])
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print ''
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slack = [[q.row_name(j), round(max(0,abs(bnd[j]-sum([a*b for a,b in zip(sol,M[j])]))),3)] for j in range(q.nrows())]
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print tabulate(slack, headers=['Constraint', 'Slack'])
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##########################################