This would be a great addition. I taught linear programming this past 
summer, and while the current interface isn't especially difficult, I do 
think students would find this easier, at least at the beginning of the 
course.

john perry

On Wednesday, August 14, 2019 at 10:50:23 AM UTC-5, Mike wrote:
>
> I've written a user-friendly front-end to MixedIntegerLinearProgram 
> (intended for student use in a sage cell.)  If this seems to be generally 
> useful, I'd be happy to submit it to the sage code base, but I'm not sure 
> how to proceed.  This is not a patch to existing sage code, just some 
> additional code.
>
> What I've currently got appears below - I'd happily accept comments and 
> suggestions.
>
> Mike
>
> r"""
> Print the solution to a mixed integer linear program.
>
> Variables are assumed real unless specified as integer,
> and all variables are assumed to be nonnegative.
>
> EXAMPLES::
>
> var('x1 x2')
> maximize(20*x1 + 10*x2, {3*x1 + x2 <= 1300, x1 + 2*x2 <= 600, x2 <= 250})
> # Z = 9000.0, x1 = 400.0, x2 = 100.0
>
> var('s h a u')
> maximize(0.05*s + 0.08*h + 0.10*a + 0.13*u, {a <= 0.30*(h+a), 
>       s <= 300, u <= s, u <= 0.20*(h+a+u), s+h+a+u <= 2000})
> # Z = 174.4, s = 300.0, u = 300.0, h = 980.0, a = 420.0
>
> var('a b c d', domain='integer')
> maximize(5*a + 7*b + 2*c + 10*d, 
>       {2*a + 4*b + 7*c + 10*d <= 15, a <= 1, b <= 1, c <= 1, d <=1 })
> # Z = 17.0, a = 0, b = 1, c = 0, d = 1   (Note that integer variables <=1 
> are binary.)
>
> var('x y')
> minimize(x + y, {x + 2*y >= 7, 2*x + y >= 6})
> # Z = 4.33333333333, x = 1.66666666667, y = 2.66666666667
>
> var('x')
> var('y', domain='integer')
> minimize(x + y, {x + 2*y >= 7, 2*x + y >= 6})
> # Z = 4.5, x = 1.5, y = 3
>
> var('x y', domain='integer')
> minimize(x + y, {x + 2*y >= 7, 2*x + y >= 6})
> # Z = 5.0, x = 2, y = 3
>
> var('x y', domain='integer')
> maximize(x + y, {x + 2*y >= 7, 2*x + y >= 6})
> # GLPK: Objective is unbounded
>
> var('x y', domain='integer')
> maximize(x + y, {x + 2*y >= 7, 2*x + y <= 3})
> # GLPK: Problem has no feasible solution
>
>
> AUTHORS:
>
> - Michael Miller (2019-Aug-11): initial version
>
> """
>
> # 
> ****************************************************************************
> #       Copyright (C) 2019 Michael Miller
> #
> # This program is free software: you can redistribute it and/or modify
> # it under the terms of the GNU General Public License as published by
> # the Free Software Foundation, either version 2 of the License, or
> # (at your option) any later version.
> #                  https://www.gnu.org/licenses/
> # 
> ****************************************************************************
>
>
> from sage.numerical.mip import MIPSolverException
>
> def maximize(objective, constraints):
>     maxmin(objective, constraints, true)
>
> def minimize(objective, constraints):
>     maxmin(objective, constraints, false)
>
> def maxmin(objective, constraints, flag):
>
>     # Create a set of the original variables
>     variables = set(objective.variables())
>     for c in constraints:
>         variables.update(c.variables())
>     integer_variables = [v for v in variables if v.is_integer()]
>     real_variables    = [v for v in variables if not v.is_integer()]
>
>     # Create the MILP variables
>     p = MixedIntegerLinearProgram(maximization=flag)
>     MILP_integer_variables = p.new_variable(integer=True, nonnegative=True)
>     MILP_real_variables = p.new_variable(real=True, nonnegative=True)
>
>     # Substitute the MILP variables for the original variables
>     # (Inconveniently, the built-in subs fails with a TypeError)
>     def Subs(expr):
>         const = RDF(expr.subs({v:0 for v in variables})) # the constant 
> term
>         sum_integer = sum(expr.coefficient(v) * MILP_integer_variables[v] 
> for v in integer_variables)
>         sum_real = sum(expr.coefficient(v) * MILP_real_variables[v] for v 
> in real_variables)
>         return sum_real + sum_integer + const
>
>     objective = Subs(objective)
>     constraints = [c.operator()(Subs(c.lhs()), Subs(c.rhs())) for c in 
> constraints]
>
>     # Set up the MILP problem
>     p.set_objective(objective)
>     for c in constraints:
>         p.add_constraint(c)
>
>     # Solve the MILP problem and print the results
>     try:
>         Z = p.solve()
>         print "Z =", Z
>         for v in integer_variables:
>             print v, "=", int(p.get_values(MILP_integer_variables[v]))
>         for v in real_variables:
>             print v, "=", p.get_values(MILP_real_variables[v])
>         print
>     except MIPSolverException as msg:
>         if str(msg)=="GLPK: The LP (relaxation) problem has no dual 
> feasible solution":
>             print "GLPK: Objective is unbounded"
>             print
>         else:
>             print str(msg)
>             print
>
>
>
>

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