#  ___________________________________________________________________________
#
#  Pyomo: Python Optimization Modeling Objects
#  Copyright 2017 National Technology and Engineering Solutions of Sandia, LLC
#  Under the terms of Contract DE-NA0003525 with National Technology and 
#  Engineering Solutions of Sandia, LLC, the U.S. Government retains certain 
#  rights in this software.
#  This software is distributed under the 3-clause BSD License.
#  ___________________________________________________________________________

"""Re-implementation of example 1 of Quesada and Grossmann.

Re-implementation of Quesada example 2 MINLP test problem in Pyomo
Author: David Bernal <https://github.com/bernalde>.

The expected optimal solution value is -5.512.

Ref:
    Quesada, Ignacio, and Ignacio E. Grossmann.
    "An LP/NLP based branch and bound algorithm
    for convex MINLP optimization problems."
    Computers & chemical engineering 16.10-11 (1992): 937-947.

    Problem type:    convex MINLP
            size:    1  binary variable
                     2  continuous variables
                     4  constraints


"""
from __future__ import division

from pyomo.environ import (Binary, ConcreteModel, Constraint, Reals,
                           Objective, RangeSet, Var, minimize, log)


class SimpleMINLP(ConcreteModel):

    def __init__(self, *args, **kwargs):
        """Create the problem."""
        kwargs.setdefault('name', 'DuranEx1')
        super(SimpleMINLP, self).__init__(*args, **kwargs)
        m = self

        """Set declarations"""
        I = m.I = RangeSet(1, 2, doc="continuous variables")
        J = m.J = RangeSet(1, 1, doc="discrete variables")

        # initial point information for discrete variables
        initY = {1: 1}
        # initial point information for continuous variables
        initX = {1: 0, 2: 0}

        """Variable declarations"""
        # DISCRETE VARIABLES
        Y = m.Y = Var(J, domain=Binary, initialize=initY)
        # CONTINUOUS VARIABLES
        X = m.X = Var(I, domain=Reals, initialize=initX, bounds=(-1, 50))

        """Constraint definitions"""
        # CONSTRAINTS
        m.const1 = Constraint(expr=-X[2] + 5*log(X[1] + 1) + 3*Y[1] >= 0)
        m.const2 = Constraint(expr=-X[2] + X[1]**2 - Y[1] <= 1)
        m.const3 = Constraint(expr=X[1] + X[2] +20*Y[1] <= 24)
        m.const4 = Constraint(expr=2*X[2] + 3*X[1] <= 10)

        """Cost (objective) function definition"""
        m.cost = Objective(expr=10*X[1]**2 - X[2] + 5*(Y[1] - 1),
         sense=minimize)