Optiscope Plotting Examples¶

This notebook demonstrates the various plotting capabilities of the optiscope library, including:

1. Pareto Front (2D/3D)
2. Parallel Coordinates
3. Scatter Matrix (SPLOM)
4. Correlation Heatmap
5. Time Series
6. Optimization History
7. Multi-Result Comparison

In [1]:

import numpy as np
import pandas as pd

from optiscope import (
    Constraint,
    DesignVariable,
    Objective,
    OptimizationResult,
    ProblemMetadata,
)
from optiscope.analysis import (
    check_feasibility,
    detect_knee_points,
    identify_pareto_front,
)
from optiscope.core import OptimizationDirection
from optiscope.core.data_types import ConstraintType
from optiscope.plotting import (
    plot_correlation_heatmap,
    plot_parallel_coordinates,
    plot_pareto_front_2d,
    plot_pareto_front_3d,
    plot_scatter_matrix,
)
from optiscope.plotting.time_series import (
    plot_optimization_history,
    plot_time_series,
)

import numpy as np import pandas as pd from optiscope import ( Constraint, DesignVariable, Objective, OptimizationResult, ProblemMetadata, ) from optiscope.analysis import ( check_feasibility, detect_knee_points, identify_pareto_front, ) from optiscope.core import OptimizationDirection from optiscope.core.data_types import ConstraintType from optiscope.plotting import ( plot_correlation_heatmap, plot_parallel_coordinates, plot_pareto_front_2d, plot_pareto_front_3d, plot_scatter_matrix, ) from optiscope.plotting.time_series import ( plot_optimization_history, plot_time_series, )

In [2]:

import plotly.io as pio

pio.renderers.default = "sphinx_gallery"

import plotly.io as pio pio.renderers.default = "sphinx_gallery"

Data Generation¶

We generate a synthetic multi-objective optimization problem with 4 design variables and 3 objectives.

In [3]:

def generate_test_problem(n_points: int = 200, seed: int = 42):
    """Generate synthetic multi-objective optimization problem."""
    np.random.seed(seed)

    def objective_function(x1, x2, x3, x4, n_points):
        """ZDT-like objective function with 3 objectives."""
        f1 = x1
        g = 1 + 9 * (x2 + x3 + x4) / 3
        h1 = 1 - np.sqrt(f1 / g)
        h2 = 1 - (f1 / g) ** 2
        f2 = g * h1
        f3 = g * h2

        # Add some noise
        f2 += np.random.normal(0, 0.1, n_points)
        f3 += np.random.normal(0, 0.1, n_points)

        return f1, f2, f3

    def constraint_functions(x1, x2, x3, x4):
        """Define constraints."""
        g1 = x1 + x2 - 12  # inequality constraint: g1 <= 0
        g2 = x3 - x4 - 5  # inequality constraint: g2 <= 0
        h1 = x3 - x4  # equality constraint: h1 = 0
        return g1, g2, h1

    def observable_functions(x1, x2, x3, x4, f1, f2):
        """Define observables."""
        total_mass = x1 + x2 + x3 + x4
        efficiency = f1 / (f2 + 1e-6)
        cost = 100 * x1 + 50 * x2 + 75 * x3 + 60 * x4
        return total_mass, efficiency, cost

    # Design variables
    x1 = np.random.uniform(0, 10, n_points)
    x2 = np.random.uniform(0, 10, n_points)
    x3 = np.random.uniform(0, 10, n_points)
    x4 = np.random.uniform(0, 10, n_points)

    # Solve problem by random sampling
    f1, f2, f3 = objective_function(x1, x2, x3, x4, n_points)
    g1, g2, h1 = constraint_functions(x1, x2, x3, x4)
    total_mass, efficiency, cost = observable_functions(x1, x2, x3, x4, f1, f2)

    iterations = np.arange(n_points)

    # Create result
    result = OptimizationResult(
        problem_metadata=ProblemMetadata(
            name="3-Objective Test Problem",
            description="Synthetic multi-objective optimization test problem",
            solver="Random Sampling",
            n_design_variables=4,
            n_objectives=2,
            n_inequality_constraints=2,
            n_equality_constraints=1,
            n_evaluations=n_points,
            solver_version="1.0",
            computation_time=None,
        ),
        design_variables=pd.DataFrame(
            {
                "x1_width": x1,
                "x2_height": x2,
                "x3_depth": x3,
                "x4_thickness": x4,
                "iteration": iterations,
            }
        ),
        objectives=pd.DataFrame({"f1_cost": f1, "f2_weight": f2, "f3_volume": f3}),
        inequality_constraints=pd.DataFrame(
            {"g1_size_constraint": g1, "g2_dimensional_constraint": g2}
        ),
        equality_constraints=pd.DataFrame({"h1_balance": h1}),
        observables=pd.DataFrame(
            {"total_mass": total_mass, "efficiency": efficiency, "cost": cost}
        ),
    )

    # Add metadata
    result.add_variable_metadata(
        DesignVariable(name="x1_width", units="cm", lower_bound=0, upper_bound=10)
    )
    result.add_variable_metadata(
        DesignVariable(name="x2_height", units="cm", lower_bound=0, upper_bound=10)
    )
    result.add_variable_metadata(
        DesignVariable(name="x3_depth", units="cm", lower_bound=0, upper_bound=10)
    )
    result.add_variable_metadata(
        DesignVariable(name="x4_thickness", units="mm", lower_bound=0, upper_bound=10)
    )
    result.add_variable_metadata(
        DesignVariable(name="iteration", units=None, lower_bound=0, upper_bound=n_points)
    )

    result.add_variable_metadata(
        Objective(name="f1_cost", units="$", direction=OptimizationDirection.MINIMIZE)
    )
    result.add_variable_metadata(
        Objective(name="f2_weight", units="kg", direction=OptimizationDirection.MINIMIZE)
    )
    result.add_variable_metadata(
        Objective(name="f3_volume", units="cm³", direction=OptimizationDirection.MINIMIZE)
    )

    result.add_variable_metadata(
        Constraint(
            name="g1_size_constraint", constraint_type=ConstraintType.INEQUALITY, reference_value=0
        )
    )
    result.add_variable_metadata(
        Constraint(
            name="g2_dimensional_constraint",
            constraint_type=ConstraintType.INEQUALITY,
            reference_value=0,
        )
    )
    result.add_variable_metadata(
        Constraint(
            name="h1_balance",
            constraint_type=ConstraintType.EQUALITY,
            reference_value=0,
            tolerance=0.5,
        )
    )

    return result


def setup_result_sets(result):
    """Create useful result sets for visualization."""
    # 1. Find feasible solutions
    feasible_mask = check_feasibility(result)
    feasible_indices = np.where(feasible_mask)[0].tolist()

    result.create_set(
        name="feasible",
        indices=feasible_indices,
        created_by="constraint_filter",
        description="Solutions satisfying all constraints",
        color="#2ecc71",
    )

    # 2. Create Pareto set
    pareto_mask = identify_pareto_front(
        result.objectives,
        directions=result.optimization_directions,
        mask=feasible_mask,
    )
    pareto_indices = np.where(pareto_mask)[0].tolist()

    pareto_set = result.create_set(
        name="pareto_front",
        indices=pareto_indices,
        created_by="smart_filter",
        description="Pareto optimal solutions",
        color="#e74c3c",
    )

    # 3. Knee points
    if pareto_set and len(pareto_set) >= 5:
        pareto_objectives = result.objectives.iloc[pareto_indices][["f1_cost", "f2_weight"]]
        knee_indices_relative = detect_knee_points(
            pareto_objectives, method="angle", n_knees=3, normalize=True
        )
        knee_indices = [pareto_indices[i] for i in knee_indices_relative]

        result.create_set(
            name="knee_points",
            indices=knee_indices,
            created_by="knee_detection",
            description="Knee points on Pareto front",
            color="#9b59b6",
        )

    return result

def generate_test_problem(n_points: int = 200, seed: int = 42): """Generate synthetic multi-objective optimization problem.""" np.random.seed(seed) def objective_function(x1, x2, x3, x4, n_points): """ZDT-like objective function with 3 objectives.""" f1 = x1 g = 1 + 9 * (x2 + x3 + x4) / 3 h1 = 1 - np.sqrt(f1 / g) h2 = 1 - (f1 / g) ** 2 f2 = g * h1 f3 = g * h2 # Add some noise f2 += np.random.normal(0, 0.1, n_points) f3 += np.random.normal(0, 0.1, n_points) return f1, f2, f3 def constraint_functions(x1, x2, x3, x4): """Define constraints.""" g1 = x1 + x2 - 12 # inequality constraint: g1 <= 0 g2 = x3 - x4 - 5 # inequality constraint: g2 <= 0 h1 = x3 - x4 # equality constraint: h1 = 0 return g1, g2, h1 def observable_functions(x1, x2, x3, x4, f1, f2): """Define observables.""" total_mass = x1 + x2 + x3 + x4 efficiency = f1 / (f2 + 1e-6) cost = 100 * x1 + 50 * x2 + 75 * x3 + 60 * x4 return total_mass, efficiency, cost # Design variables x1 = np.random.uniform(0, 10, n_points) x2 = np.random.uniform(0, 10, n_points) x3 = np.random.uniform(0, 10, n_points) x4 = np.random.uniform(0, 10, n_points) # Solve problem by random sampling f1, f2, f3 = objective_function(x1, x2, x3, x4, n_points) g1, g2, h1 = constraint_functions(x1, x2, x3, x4) total_mass, efficiency, cost = observable_functions(x1, x2, x3, x4, f1, f2) iterations = np.arange(n_points) # Create result result = OptimizationResult( problem_metadata=ProblemMetadata( name="3-Objective Test Problem", description="Synthetic multi-objective optimization test problem", solver="Random Sampling", n_design_variables=4, n_objectives=2, n_inequality_constraints=2, n_equality_constraints=1, n_evaluations=n_points, solver_version="1.0", computation_time=None, ), design_variables=pd.DataFrame( { "x1_width": x1, "x2_height": x2, "x3_depth": x3, "x4_thickness": x4, "iteration": iterations, } ), objectives=pd.DataFrame({"f1_cost": f1, "f2_weight": f2, "f3_volume": f3}), inequality_constraints=pd.DataFrame( {"g1_size_constraint": g1, "g2_dimensional_constraint": g2} ), equality_constraints=pd.DataFrame({"h1_balance": h1}), observables=pd.DataFrame( {"total_mass": total_mass, "efficiency": efficiency, "cost": cost} ), ) # Add metadata result.add_variable_metadata( DesignVariable(name="x1_width", units="cm", lower_bound=0, upper_bound=10) ) result.add_variable_metadata( DesignVariable(name="x2_height", units="cm", lower_bound=0, upper_bound=10) ) result.add_variable_metadata( DesignVariable(name="x3_depth", units="cm", lower_bound=0, upper_bound=10) ) result.add_variable_metadata( DesignVariable(name="x4_thickness", units="mm", lower_bound=0, upper_bound=10) ) result.add_variable_metadata( DesignVariable(name="iteration", units=None, lower_bound=0, upper_bound=n_points) ) result.add_variable_metadata( Objective(name="f1_cost", units="$", direction=OptimizationDirection.MINIMIZE) ) result.add_variable_metadata( Objective(name="f2_weight", units="kg", direction=OptimizationDirection.MINIMIZE) ) result.add_variable_metadata( Objective(name="f3_volume", units="cm³", direction=OptimizationDirection.MINIMIZE) ) result.add_variable_metadata( Constraint( name="g1_size_constraint", constraint_type=ConstraintType.INEQUALITY, reference_value=0 ) ) result.add_variable_metadata( Constraint( name="g2_dimensional_constraint", constraint_type=ConstraintType.INEQUALITY, reference_value=0, ) ) result.add_variable_metadata( Constraint( name="h1_balance", constraint_type=ConstraintType.EQUALITY, reference_value=0, tolerance=0.5, ) ) return result def setup_result_sets(result): """Create useful result sets for visualization.""" # 1. Find feasible solutions feasible_mask = check_feasibility(result) feasible_indices = np.where(feasible_mask)[0].tolist() result.create_set( name="feasible", indices=feasible_indices, created_by="constraint_filter", description="Solutions satisfying all constraints", color="#2ecc71", ) # 2. Create Pareto set pareto_mask = identify_pareto_front( result.objectives, directions=result.optimization_directions, mask=feasible_mask, ) pareto_indices = np.where(pareto_mask)[0].tolist() pareto_set = result.create_set( name="pareto_front", indices=pareto_indices, created_by="smart_filter", description="Pareto optimal solutions", color="#e74c3c", ) # 3. Knee points if pareto_set and len(pareto_set) >= 5: pareto_objectives = result.objectives.iloc[pareto_indices][["f1_cost", "f2_weight"]] knee_indices_relative = detect_knee_points( pareto_objectives, method="angle", n_knees=3, normalize=True ) knee_indices = [pareto_indices[i] for i in knee_indices_relative] result.create_set( name="knee_points", indices=knee_indices, created_by="knee_detection", description="Knee points on Pareto front", color="#9b59b6", ) return result

In [4]:

print("Generating test data...")
result = generate_test_problem(n_points=200)
print("Setting up result sets...")
result = setup_result_sets(result)

print("Generating test data...") result = generate_test_problem(n_points=200) print("Setting up result sets...") result = setup_result_sets(result)

Generating test data...
Setting up result sets...

1. 2D Pareto Front¶

Visualize the trade-off between two objectives.

In [5]:

fig_2d = plot_pareto_front_2d(
    result,
    obj_x="f1_cost",
    obj_y="f2_weight",
    pareto_set="pareto_front",
    additional_sets=["knee_points", "feasible"],
    show_dominated=False,
    show_ideal_nadir=False,
    title="2D Pareto Front (Cost vs. Weight)",
)
fig_2d.show()

fig_2d = plot_pareto_front_2d( result, obj_x="f1_cost", obj_y="f2_weight", pareto_set="pareto_front", additional_sets=["knee_points", "feasible"], show_dominated=False, show_ideal_nadir=False, title="2D Pareto Front (Cost vs. Weight)", ) fig_2d.show()

2. 3D Pareto Front¶

Visualize the trade-off between three objectives.

In [6]:

fig_3d = plot_pareto_front_3d(
    result,
    obj_x="f1_cost",
    obj_y="f2_weight",
    obj_z="f3_volume",
    pareto_set="pareto_front",
    show_dominated=True,
    show_surface=False,
    title="3D Pareto Front",
)
fig_3d.show()

fig_3d = plot_pareto_front_3d( result, obj_x="f1_cost", obj_y="f2_weight", obj_z="f3_volume", pareto_set="pareto_front", show_dominated=True, show_surface=False, title="3D Pareto Front", ) fig_3d.show()

3. Parallel Coordinates¶

Visualize high-dimensional data.

In [7]:

fig_pc = plot_parallel_coordinates(
    result,
    include_design_vars=True,
    include_objectives=True,
    include_constraints=False,
    result_sets=["pareto_front", "feasible"],
    title="Parallel Coordinates Plot",
)
fig_pc.show()

fig_pc = plot_parallel_coordinates( result, include_design_vars=True, include_objectives=True, include_constraints=False, result_sets=["pareto_front", "feasible"], title="Parallel Coordinates Plot", ) fig_pc.show()

4. Scatter Matrix (SPLOM)¶

Visualize pairwise relationships between variables.

In [8]:

fig_splom = plot_scatter_matrix(
    result,
    include_objectives=True,
    include_design_vars=True,
    max_vars=6,
    highlight_feasible=True,
    show_distributions=True,
    show_correlations=True,
    marker_size=4,
    title="Scatter Plot Matrix",
)
fig_splom.show()

fig_splom = plot_scatter_matrix( result, include_objectives=True, include_design_vars=True, max_vars=6, highlight_feasible=True, show_distributions=True, show_correlations=True, marker_size=4, title="Scatter Plot Matrix", ) fig_splom.show()

5. Correlation Heatmap¶

Visualize correlations between variables.

In [9]:

fig_corr = plot_correlation_heatmap(
    result,
    include_objectives=True,
    include_design_vars=True,
    method="pearson",
    title="Pearson Correlation Heatmap",
)
fig_corr.show()

fig_corr = plot_correlation_heatmap( result, include_objectives=True, include_design_vars=True, method="pearson", title="Pearson Correlation Heatmap", ) fig_corr.show()

6. Time Series¶

Visualize the evolution of variables over iterations.

In [10]:

fig_ts = plot_time_series(
    result,
    columns=["x1_width", "x2_height", "x3_depth", "x4_thickness"],
    data_attr="design_variables",
    title="Design Variables Evolution",
    show_markers=True,
    line_width=2,
    marker_size=4,
)
fig_ts.show()

fig_ts = plot_time_series( result, columns=["x1_width", "x2_height", "x3_depth", "x4_thickness"], data_attr="design_variables", title="Design Variables Evolution", show_markers=True, line_width=2, marker_size=4, ) fig_ts.show()

7. Optimization History¶

Visualize the full history of the optimization process.

In [11]:

figs_hist = plot_optimization_history(
    result,
    variables=["x1_width", "x2_height"],
    objectives=["f1_cost", "f2_weight", "f3_volume"],
    constraints=["g1_size_constraint", "h1_balance"],
    observables=["efficiency", "total_mass"],
    show_markers=True,
    line_width=2,
    marker_size=4,
)

# Display one of the figures
figs_hist["objectives"].show()

figs_hist = plot_optimization_history( result, variables=["x1_width", "x2_height"], objectives=["f1_cost", "f2_weight", "f3_volume"], constraints=["g1_size_constraint", "h1_balance"], observables=["efficiency", "total_mass"], show_markers=True, line_width=2, marker_size=4, ) # Display one of the figures figs_hist["objectives"].show()