Add toy problem README with problem details

gdplib/ ex1_linan_2023/ ex1_linan_2023.py

@@ -0,0 +1,263 @@
+"""
+ex1_linan_2023.py: Toy problem from Liñán and Ricardez-Sandoval (2023) [1]
+
+TThe ex1_linan.py file is a simple optimization problem that involves two Boolean variables, two continuous variables, and a nonlinear objective function.
+The problem is formulated as a Generalized Disjunctive Programming (GDP) model. 
+The Boolean variables are associated with disjuncts that define the feasible regions of the continuous variables. 
+The problem includes logical constraints that ensure that only one Boolean variable is true at a time.
+Additionally, there are two disjunctions, one for each Boolean variable, where only one disjunct in each disjunction must be true. 
+A specific logical constraint also enforces that Y1[3] must be false, making this particular disjunct infeasible.
+The objective function is -0.9995999999999999 when the continuous variables are alpha = 0 (Y1[2]=True) and beta=-0.7 (Y2[3]=True).
+
+References
+----------
+[1] Liñán, D. A., & Ricardez-Sandoval, L. A. (2023). A Benders decomposition framework for the optimization of disjunctive superstructures with ordered discrete decisions. AIChE Journal, 69(5), e18008. https://doi.org/10.1002/aic.18008
+[2] Gomez, S., & Levy, A. V. (1982). The tunnelling method for solving the constrained global optimization problem with several non-connected feasible regions. In Numerical Analysis: Proceedings of the Third IIMAS Workshop Held at Cocoyoc, Mexico, January 1981 (pp. 34-47). Springer Berlin Heidelberg. https://doi.org/10.1007/BFb0092958
+"""
+
+import pyomo.environ as pyo
+from pyomo.gdp import Disjunct, Disjunction
+
+
+def build_model():
+    """
+    Build the toy problem model
+
+    Returns
+    -------
+    Pyomo.ConcreteModel
+        Toy problem model
+    """
+
+    # Build Model
+    m = pyo.ConcreteModel()
+
+    # Sets
+    m.set1 = pyo.RangeSet(1, 5, doc="set of first group of Boolean variables")
+    m.set2 = pyo.RangeSet(1, 5, doc="set of second group of Boolean variables")
+
+    m.sub1 = pyo.Set(initialize=[3], within=m.set1)
+
+    # Variables
+    m.Y1 = pyo.BooleanVar(m.set1, doc="Boolean variable associated to set 1")
+    m.Y2 = pyo.BooleanVar(m.set2, doc="Boolean variable associated to set 2")
+
+    m.alpha = pyo.Var(
+        within=pyo.Reals, bounds=(-0.1, 0.4), doc="continuous variable alpha"
+    )
+    m.beta = pyo.Var(
+        within=pyo.Reals, bounds=(-0.9, -0.5), doc="continuous variable beta"
+    )
+
+    # Objective Function
+    def obj_fun(m):
+        """
+        Objective function
+
+        Parameters
+        ----------
+        m : Pyomo.ConcreteModel
+            Toy problem model
+
+        Returns
+        -------
+        Pyomo.Objective
+            Build the objective function of the toy problem
+        """
+        return (
+            4 * (pow(m.alpha, 2))
+            - 2.1 * (pow(m.alpha, 4))
+            + (1 / 3) * (pow(m.alpha, 6))
+            + m.alpha * m.beta
+            - 4 * (pow(m.beta, 2))
+            + 4 * (pow(m.beta, 4))
+        )
+
+    m.obj = pyo.Objective(rule=obj_fun, sense=pyo.minimize, doc="Objective function")
+
+    # First Disjunction
+    def build_disjuncts1(m, set1):  # Disjuncts for first Boolean variable
+        """
+        Build disjuncts for the first Boolean variable
+
+        Parameters
+        ----------
+        m : Pyomo.ConcreteModel
+            Toy problem model
+        set1 : RangeSet
+            Set of first group of Boolean variables
+        """
+
+        def constraint1(m):
+            """_summary_
+
+            Parameters
+            ----------
+            m : Pyomo.ConcreteModel
+                Toy problem model
+
+            Returns
+            -------
+            Pyomo.Constraint
+                Constraint that defines the value of alpha for each disjunct
+            """
+            return m.model().alpha == -0.1 + 0.1 * (
+                set1 - 1
+            )  # .model() is required when writing constraints inside disjuncts
+
+        m.constraint1 = pyo.Constraint(rule=constraint1)
+
+    m.Y1_disjunct = Disjunct(
+        m.set1, rule=build_disjuncts1, doc="each disjunct is defined over set 1"
+    )
+
+    def Disjunction1(m):  # Disjunction for first Boolean variable
+        """
+        Disjunction for first Boolean variable
+
+        Parameters
+        ----------
+        m : Pyomo.ConcreteModel
+            Toy problem model
+
+        Returns
+        -------
+        Pyomo.Disjunction
+            Build the disjunction for the first Boolean variable set
+        """
+        return [m.Y1_disjunct[j] for j in m.set1]
+
+    m.Disjunction1 = Disjunction(rule=Disjunction1, xor=False)
+
+    # Associate boolean variables to disjuncts
+    for n1 in m.set1:
+        m.Y1[n1].associate_binary_var(m.Y1_disjunct[n1].indicator_var)
+
+    # Second disjunction
+    def build_disjuncts2(m, set2):  # Disjuncts for second Boolean variable
+        """
+        Build disjuncts for the second Boolean variable
+
+        Parameters
+        ----------
+        m : Pyomo.ConcreteModel
+            Toy problem model
+        set2 : RangeSet
+            Set of second group of Boolean variables
+        """
+
+        def constraint2(m):
+            """_summary_
+
+            Parameters
+            ----------
+            m : Pyomo.ConcreteModel
+                Toy problem model
+
+            Returns
+            -------
+            Pyomo.Constraint
+                Constraint that defines the value of beta for each disjunct
+            """
+            return m.model().beta == -0.9 + 0.1 * (
+                set2 - 1
+            )  # .model() is required when writing constraints inside disjuncts
+
+        m.constraint2 = pyo.Constraint(rule=constraint2)
+
+    m.Y2_disjunct = Disjunct(
+        m.set2, rule=build_disjuncts2, doc="each disjunct is defined over set 2"
+    )
+
+    def Disjunction2(m):  # Disjunction for first Boolean variable
+        """
+        Disjunction for second Boolean variable
+
+        Parameters
+        ----------
+        m : Pyomo.ConcreteModel
+            Toy problem model
+
+        Returns
+        -------
+        Pyomo.Disjunction
+            Build the disjunction for the second Boolean variable set
+        """
+        return [m.Y2_disjunct[j] for j in m.set2]
+
+    m.Disjunction2 = Disjunction(rule=Disjunction2, xor=False)
+
+    # Associate boolean variables to disjuncts
+    for n2 in m.set2:
+        m.Y2[n2].associate_binary_var(m.Y2_disjunct[n2].indicator_var)
+
+    # Logical constraints
+
+    # Constraint that allow to apply the reformulation over Y1
+    def select_one_Y1(m):
+        """
+        Logical constraint that allows to apply the reformulation over Y1
+
+        Parameters
+        ----------
+        m : Pyomo.ConcreteModel
+            Toy problem model
+
+        Returns
+        -------
+        Pyomo.LogicalConstraint
+            Logical constraint that make Y1 to be true for only one element
+        """
+        return pyo.exactly(1, m.Y1)
+
+    m.oneY1 = pyo.LogicalConstraint(rule=select_one_Y1)
+
+    # Constraint that allow to apply the reformulation over Y2
+    def select_one_Y2(m):
+        """
+        Logical constraint that allows to apply the reformulation over Y2
+
+        Parameters
+        ----------
+        m : Pyomo.ConcreteModel
+            Toy problem model
+
+        Returns
+        -------
+        Pyomo.LogicalConstraint
+            Logical constraint that make Y2 to be true for only one element
+        """
+        return pyo.exactly(1, m.Y2)
+
+    m.oneY2 = pyo.LogicalConstraint(rule=select_one_Y2)
+
+    # Constraint that define an infeasible region with respect to Boolean variables
+
+    def infeasR_rule(m):
+        """
+        Logical constraint that defines an infeasible region with respect to Boolean variables
+
+        Parameters
+        ----------
+        m : Pyomo.ConcreteModel
+            Toy problem model
+
+        Returns
+        -------
+        Pyomo.LogicalConstraint
+            Logical constraint that defines an infeasible region on Y1[3]
+        """
+        return pyo.land([pyo.lnot(m.Y1[j]) for j in m.sub1])
+
+    m.infeasR = pyo.LogicalConstraint(rule=infeasR_rule)
+
+    return m
+
+
+if __name__ == "__main__":
+    m = build_model()
+    pyo.TransformationFactory("gdp.bigm").apply_to(m)
+    solver = pyo.SolverFactory("gams")
+    solver.solve(m, solver="baron", tee=True)
+    print("Solution: alpha=", pyo.value(m.alpha), " beta=", pyo.value(m.beta))
+    print("Objective function value: ", pyo.value(m.obj))

gdplib/ ex1_linan_2023/README.md

@@ -0,0 +1,14 @@
+## Example 1 Problem of Liñán (2023)
+
+The Example 1 Problem of Liñán (2023) is a simple optimization problem that involves two Boolean variables, two continuous variables, and a nonlinear objective function. The problem is formulated as a Generalized Disjunctive Programming (GDP) model.
+
+The Boolean variables are associated with disjuncts that define the feasible regions of the continuous variables. The problem also includes logical constraints that ensure that only one Boolean variable is true at a time. Additionally, there are two disjunctions, one for each Boolean variable, where only one disjunct in each disjunction must be true. A specific logical constraint also enforces that `Y1[3]` must be false, making this particular disjunct infeasible.
+
+The objective function is -0.9995999999999999 when the continuous variables are alpha = 0 (`Y1[2]=True`) and beta=-0.7 (`Y2[3]=True`).
+
+The objective function originates from Problem No. 6 of Gomez's paper, and Liñán introduced logical propositions, logical disjunctions, and the following equations as constraints.
+
+### References
+
+[1] Liñán, D. A., & Ricardez-Sandoval, L. A. (2023). A Benders decomposition framework for the optimization of disjunctive superstructures with ordered discrete decisions. AIChE Journal, 69(5), e18008. https://doi.org/10.1002/aic.18008
+[2] Gomez, S., & Levy, A. V. (1982). The tunnelling method for solving the constrained global optimization problem with several non-connected feasible regions. In Numerical Analysis: Proceedings of the Third IIMAS Workshop Held at Cocoyoc, Mexico, January 1981 (pp. 34-47). Springer Berlin Heidelberg. https://doi.org/10.1007/BFb0092958