A few more GDP examples

examples/gdp/circles/circles.py

@@ -0,0 +1,257 @@
+"""
+The "circles" GDP example problem originating in Lee and Grossman (2000). The 
+goal is to choose a point to minimize a convex quadratic function over a set of 
+disjoint hyperspheres.
+"""
+
+from __future__ import division
+
+from pyomo.environ import (
+    ConcreteModel,
+    Objective,
+    Param,
+    RangeSet,
+    Var,
+    Constraint,
+    value,
+)
+
+# Circles2D3 is the original example described in the papers. Ruiz and Grossman
+# (2012) discuss two more example instances, Circles2D36 and Circles3D36, but I
+# couldn't find data for them, so I made a couple.
+# format: dimension, circle_centers, circle_rvals, circle_penalties, reference_point, upper_bound
+circles_model_examples = {
+    "Circles2D3": {
+        'dimension': 2,
+        # written as {(circle number, coordinate index): value}, for example below
+        # means {circle 1: (0, 0), circle 2: (4, 1), circle 3: (2, 4)},
+        'circle_centers': {
+            (1, 1): 0,
+            (1, 2): 0,
+            (2, 1): 4,
+            (2, 2): 1,
+            (3, 1): 2,
+            (3, 2): 4,
+        },
+        'circle_rvals': {1: 1, 2: 1, 3: 1},
+        'circle_penalties': {1: 2, 2: 1, 3: 3},
+        'reference_point': {1: 3, 2: 2},
+        'upper_bound': 8,
+    },
+    # Here the solver has a local minimum to avoid by not choosing the closest point
+    "Circles2D3_modified": {
+        'dimension': 2,
+        'circle_centers': {
+            (1, 1): 0,
+            (1, 2): 0,
+            (2, 1): 4,
+            (2, 2): 1,
+            (3, 1): 2,
+            (3, 2): 4,
+        },
+        'circle_rvals': {1: 1, 2: 1, 3: 1},
+        'circle_penalties': {1: 2, 2: 3, 3: 1},
+        'reference_point': {1: 3, 2: 2},
+        'upper_bound': 8,
+    },
+    # Here's a 3D model.
+    "Circles3D4": {
+        'dimension': 3,
+        'circle_centers': {
+            (1, 1): 0,
+            (1, 2): 0,
+            (1, 3): 0,
+            (2, 1): 2,
+            (2, 2): 0,
+            (2, 3): 1,
+            (3, 1): 3,
+            (3, 2): 3,
+            (3, 3): 3,
+            (4, 1): 1,
+            (4, 2): 6,
+            (4, 3): 1,
+        },
+        'circle_rvals': {1: 1, 2: 1, 3: 1, 4: 1},
+        'circle_penalties': {1: 1, 2: 3, 3: 2, 4: 1},
+        'reference_point': {1: 2, 2: 2, 3: 1},
+        'upper_bound': 10,
+    },
+}
+
+
+def build_model(data):
+    """Build a model. By default you get Circles2D3, a small instance."""
+
+    # Ensure good data was passed
+    assert len(data) == 6, "Error processing data"
+
+    dimension = data['dimension']
+    circle_centers = data['circle_centers']
+    circle_rvals = data['circle_rvals']
+    circle_penalties = data['circle_penalties']
+    reference_point = data['reference_point']
+    upper_bound = data['upper_bound']
+
+    assert len(circle_rvals) == len(circle_penalties), "Error processing data"
+    assert len(circle_centers) == len(circle_rvals) * dimension, "Error processing data"
+    assert len(reference_point) == dimension, "Error processing data"
+
+    m = ConcreteModel()
+
+    m.circles = RangeSet(len(circle_rvals), doc=f"{len(circle_rvals)} circles")
+    m.idx = RangeSet(dimension, doc="n-dimensional indexing set for coordinates")
+
+    m.circ_centers = Param(
+        m.circles, m.idx, initialize=circle_centers, doc="Center points of the circles"
+    )
+    m.circ_rvals = Param(
+        m.circles, initialize=circle_rvals, doc="Squared radii of circles"
+    )
+    m.ref_point = Param(
+        m.idx,
+        initialize=reference_point,
+        doc="Reference point for distance calculations",
+    )
+    m.circ_penalties = Param(
+        m.circles, initialize=circle_penalties, doc="Penalty for being in each circle"
+    )
+
+    # Choose a point to minimize objective
+    m.point = Var(
+        m.idx,
+        bounds=(0, upper_bound),
+        doc="Chosen point at which we evaluate objective function",
+    )
+
+    # Let's set up the "active penalty" this way
+    m.active_penalty = Var(
+        bounds=(0, max(m.circ_penalties[i] for i in m.circles)),
+        doc="Penalty for being in the current circle",
+    )
+
+    # Disjunction: we must be in at least one circle (in fact exactly one since they are disjoint)
+    @m.Disjunct(m.circles)
+    def circle_disjunct(d, circ):
+        m = d.model()
+        d.inside_circle = Constraint(
+            expr=sum((m.point[i] - m.circ_centers[circ, i]) ** 2 for i in m.idx)
+            <= m.circ_rvals[circ]
+        )
+        d.penalty = Constraint(expr=m.active_penalty == m.circ_penalties[circ])
+
+    @m.Disjunction()
+    def circle_disjunction(m):
+        return [m.circle_disjunct[i] for i in m.circles]
+
+    # Objective function is Euclidean distance from reference point, plus a penalty depending on which circle we are in
+    m.cost = Objective(
+        expr=sum((m.point[i] - m.ref_point[i]) ** 2 for i in m.idx) + m.active_penalty,
+        doc="Distance from reference point plus penalty",
+    )
+
+    return m
+
+
+def draw_model(m, title=None):
+    """Draw a model using matplotlib to illustrate what's going on. Pass 'title' arg to give chart a title"""
+
+    if len(m.idx) != 2:
+        print(
+            f"Unable to draw: this drawing code only supports 2D models, but a {len(m.idx)}-dimensional model was passed."
+        )
+        return
+
+    # matplotlib setup
+    import matplotlib as mpl
+    import matplotlib.pyplot as plt
+
+    fig, ax = plt.subplots(1, 1, figsize=(10, 10))
+    ax.set_xlabel("x")
+    ax.set_ylabel("y")
+
+    ax.set_xlim([0, 10])
+    ax.set_ylim([0, 10])
+
+    if title is not None:
+        plt.title(title)
+
+    for c in m.circles:
+        x = m.circ_centers[c, 1]
+        y = m.circ_centers[c, 2]
+        # remember, we are keeping around the *squared* radii for some reason
+        r = m.circ_rvals[c] ** 0.5
+        penalty = m.circ_penalties[c]
+        print(f"drawing circle {c}: x={x}, y={y}, r={r}, penalty={penalty}")
+
+        ax.add_patch(
+            mpl.patches.Circle(
+                (x, y), radius=r, facecolor="#0d98e6", edgecolor="#000000"
+            )
+        )
+        # the alignment appears to work by magic
+        ax.text(
+            x,
+            y + r + 0.3,
+            f"Circle {c}: penalty {penalty}",
+            horizontalalignment="center",
+        )
+
+    # now the reference point
+    ax.add_patch(
+        mpl.patches.Circle(
+            (m.ref_point[1], m.ref_point[2]),
+            radius=0.05,
+            facecolor="#902222",
+            edgecolor="#902222",
+        )
+    )
+    ax.text(
+        m.ref_point[1],
+        m.ref_point[2] + 0.15,
+        "Reference Point",
+        horizontalalignment="center",
+    )
+
+    # and the chosen point
+    ax.add_patch(
+        mpl.patches.Circle(
+            (value(m.point[1]), value(m.point[2])),
+            radius=0.05,
+            facecolor="#11BB11",
+            edgecolor="#11BB11",
+        )
+    )
+    ax.text(
+        value(m.point[1]),
+        value(m.point[2]) + 0.15,
+        "Chosen Point",
+        horizontalalignment="center",
+    )
+
+    plt.show()
+
+
+if __name__ == "__main__":
+    from pyomo.environ import SolverFactory
+    from pyomo.core.base import TransformationFactory
+
+    # Set up a solver, for example scip and bigm works
+    solver = SolverFactory("scip")
+    transformer = TransformationFactory("gdp.bigm")
+
+    for key in circles_model_examples:
+        model = build_model(circles_model_examples[key])
+        print(f"Solving model {key}")
+        transformer.apply_to(model)
+        solver.solve(model)
+        pt_string = (
+            "("
+            + "".join(
+                str(value(model.point[i])) + (", " if i != len(model.idx) else "")
+                for i in model.idx
+            )
+            + ")"
+        )
+        print(f"Optimal value found: {model.cost()} with chosen point {pt_string}")
+        draw_model(model, title=key)
+        print()