Pymoo Visualization Reference

Comprehensive reference for visualization capabilities in pymoo.

Overview

Pymoo provides eight visualization types for analyzing multi-objective optimization results. All plots wrap matplotlib and accept standard matplotlib keyword arguments for customization.

Core Visualization Types

1. Scatter Plots

Purpose: Visualize objective space for 2D, 3D, or higher dimensions Best for: Pareto fronts, solution distributions, algorithm comparisons

Usage:

python

from pymoo.visualization.scatter import Scatter

# 2D scatter plot
plot = Scatter()
plot.add(result.F, color="red", label="Algorithm A")
plot.add(ref_pareto_front, color="black", alpha=0.3, label="True PF")
plot.show()

# 3D scatter plot
plot = Scatter(title="3D Pareto Front")
plot.add(result.F)
plot.show()

Parameters:

title: Plot title
figsize: Figure size tuple (width, height)
legend: Show legend (default: True)
labels: Axis labels list

Add method parameters:

color: Color specification
alpha: Transparency (0-1)
s: Marker size
marker: Marker style
label: Legend label

N-dimensional projection: For >3 objectives, automatically creates scatter plot matrix

2. Parallel Coordinate Plots (PCP)

Purpose: Compare multiple solutions across many objectives Best for: Many-objective problems, comparing algorithm performance

Mechanism: Each vertical axis represents one objective, lines connect objective values for each solution

Usage:

python

from pymoo.visualization.pcp import PCP

plot = PCP()
plot.add(result.F, color="blue", alpha=0.5)
plot.add(reference_set, color="red", alpha=0.8)
plot.show()

Parameters:

title: Plot title
figsize: Figure size
labels: Objective labels
bounds: Normalization bounds (min, max) per objective
normalize_each_axis: Normalize to [0,1] per axis (default: True)

Best practices:

Normalize for different objective scales
Use transparency for overlapping lines
Limit number of solutions for clarity (<1000)

3. Heatmap

Purpose: Show solution density and distribution patterns Best for: Understanding solution clustering, identifying gaps

Usage:

python

from pymoo.visualization.heatmap import Heatmap

plot = Heatmap(title="Solution Density")
plot.add(result.F)
plot.show()

Parameters:

bins: Number of bins per dimension (default: 20)
cmap: Colormap name (e.g., "viridis", "plasma", "hot")
norm: Normalization method

Interpretation:

Bright regions: High solution density
Dark regions: Few or no solutions
Reveals distribution uniformity

4. Petal Diagram

Purpose: Radial representation of multiple objectives Best for: Comparing individual solutions across objectives

Structure: Each "petal" represents one objective, length indicates objective value

Usage:

python

from pymoo.visualization.petal import Petal

plot = Petal(title="Solution Comparison", bounds=[min_vals, max_vals])
plot.add(result.F[0], color="blue", label="Solution 1")
plot.add(result.F[1], color="red", label="Solution 2")
plot.show()

Parameters:

bounds: [min, max] per objective for normalization
labels: Objective names
reverse: Reverse specific objectives (for minimization display)

Use cases:

Decision making between few solutions
Presenting trade-offs to stakeholders

5. Radar Charts

Purpose: Multi-criteria performance profiles Best for: Comparing solution characteristics

Similar to: Petal diagram but with connected vertices

Usage:

python

from pymoo.visualization.radar import Radar

plot = Radar(bounds=[min_vals, max_vals])
plot.add(solution_A, label="Design A")
plot.add(solution_B, label="Design B")
plot.show()

6. Radviz

Purpose: Dimensional reduction for visualization Best for: High-dimensional data exploration, pattern recognition

Mechanism: Projects high-dimensional points onto 2D circle, dimension anchors on perimeter

Usage:

python

from pymoo.visualization.radviz import Radviz

plot = Radviz(title="High-dimensional Solution Space")
plot.add(result.F, color="blue", s=30)
plot.show()

Parameters:

endpoint_style: Anchor point visualization
labels: Dimension labels

Interpretation:

Points near anchor: High value in that dimension
Central points: Balanced across dimensions
Clusters: Similar solutions

7. Star Coordinates

Purpose: Alternative high-dimensional visualization Best for: Comparing multi-dimensional datasets

Mechanism: Each dimension as axis from origin, points plotted based on values

Usage:

python

from pymoo.visualization.star_coordinate import StarCoordinate

plot = StarCoordinate()
plot.add(result.F)
plot.show()

Parameters:

axis_style: Axis appearance
axis_extension: Axis length beyond max value
labels: Dimension labels

8. Video/Animation

Purpose: Show optimization progress over time Best for: Understanding convergence behavior, presentations

Usage:

python

from pymoo.visualization.video import Video

# Create animation from algorithm history
anim = Video(result.algorithm)
anim.save("optimization_progress.mp4")

Requirements:

Algorithm must store history (use save_history=True in minimize)
ffmpeg installed for video export

Customization:

Frame rate
Plot type per frame
Overlay information (generation, hypervolume, etc.)

Advanced Features

Multiple Dataset Overlay

All plot types support adding multiple datasets:

python

plot = Scatter(title="Algorithm Comparison")
plot.add(nsga2_result.F, color="red", alpha=0.5, label="NSGA-II")
plot.add(nsga3_result.F, color="blue", alpha=0.5, label="NSGA-III")
plot.add(true_pareto_front, color="black", linewidth=2, label="True PF")
plot.show()

Custom Styling

Pass matplotlib kwargs directly:

python

plot = Scatter(
    title="My Results",
    figsize=(10, 8),
    tight_layout=True
)
plot.add(
    result.F,
    color="red",
    marker="o",
    s=50,
    alpha=0.7,
    edgecolors="black",
    linewidth=0.5
)

Normalization

Normalize objectives to [0,1] for fair comparison:

python

plot = PCP(normalize_each_axis=True, bounds=[min_bounds, max_bounds])

Save to File

Save plots instead of displaying:

python

plot = Scatter()
plot.add(result.F)
plot.save("my_plot.png", dpi=300)

Visualization Selection Guide

Choose visualization based on:

Problem Type	Primary Plot	Secondary Plot
2-objective	Scatter	Heatmap
3-objective	3D Scatter	Parallel Coordinates
Many-objective (4-10)	Parallel Coordinates	Radviz
Many-objective (>10)	Radviz	Star Coordinates
Solution comparison	Petal/Radar	Parallel Coordinates
Algorithm convergence	Video	Scatter (final)
Distribution analysis	Heatmap	Scatter

Combinations:

Scatter + Heatmap: Overall distribution + density
PCP + Petal: Population overview + individual solutions
Scatter + Video: Final result + convergence process

Common Visualization Workflows

1. Algorithm Comparison

python

from pymoo.visualization.scatter import Scatter

plot = Scatter(title="Algorithm Comparison on ZDT1")
plot.add(ga_result.F, color="blue", label="GA", alpha=0.6)
plot.add(nsga2_result.F, color="red", label="NSGA-II", alpha=0.6)
plot.add(zdt1.pareto_front(), color="black", label="True PF")
plot.show()

2. Many-objective Analysis

python

from pymoo.visualization.pcp import PCP

plot = PCP(
    title="5-objective DTLZ2 Results",
    labels=["f1", "f2", "f3", "f4", "f5"],
    normalize_each_axis=True
)
plot.add(result.F, alpha=0.3)
plot.show()

3. Decision Making

python

from pymoo.visualization.petal import Petal

# Compare top 3 solutions
candidates = result.F[:3]

plot = Petal(
    title="Top 3 Solutions",
    bounds=[result.F.min(axis=0), result.F.max(axis=0)],
    labels=["Cost", "Weight", "Efficiency", "Safety"]
)
for i, sol in enumerate(candidates):
    plot.add(sol, label=f"Solution {i+1}")
plot.show()

4. Convergence Visualization

python

from pymoo.optimize import minimize

# Enable history
result = minimize(
    problem,
    algorithm,
    ('n_gen', 200),
    seed=1,
    save_history=True,
    verbose=False
)

# Create convergence plot
from pymoo.visualization.scatter import Scatter

plot = Scatter(title="Convergence Over Generations")
for gen in [0, 50, 100, 150, 200]:
    F = result.history[gen].opt.get("F")
    plot.add(F, alpha=0.5, label=f"Gen {gen}")
plot.show()

Tips and Best Practices

Use appropriate alpha: For overlapping points, use alpha=0.3-0.7
Normalize objectives: Different scales? Normalize for fair visualization
Label clearly: Always provide meaningful labels and legends
Limit data points: >10000 points? Sample or use heatmap
Color schemes: Use colorblind-friendly palettes
Save high-res: Use dpi=300 for publications
Interactive exploration: Consider plotly for interactive plots
Combine views: Show multiple perspectives for comprehensive analysis