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Zhongwei Li
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skills/pymoo/references/visualization.md
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skills/pymoo/references/visualization.md
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# Pymoo Visualization Reference
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Comprehensive reference for visualization capabilities in pymoo.
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## Overview
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Pymoo provides eight visualization types for analyzing multi-objective optimization results. All plots wrap matplotlib and accept standard matplotlib keyword arguments for customization.
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## Core Visualization Types
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### 1. Scatter Plots
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**Purpose:** Visualize objective space for 2D, 3D, or higher dimensions
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**Best for:** Pareto fronts, solution distributions, algorithm comparisons
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**Usage:**
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```python
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from pymoo.visualization.scatter import Scatter
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# 2D scatter plot
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plot = Scatter()
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plot.add(result.F, color="red", label="Algorithm A")
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plot.add(ref_pareto_front, color="black", alpha=0.3, label="True PF")
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plot.show()
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# 3D scatter plot
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plot = Scatter(title="3D Pareto Front")
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plot.add(result.F)
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plot.show()
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```
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**Parameters:**
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- `title`: Plot title
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- `figsize`: Figure size tuple (width, height)
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- `legend`: Show legend (default: True)
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- `labels`: Axis labels list
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**Add method parameters:**
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- `color`: Color specification
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- `alpha`: Transparency (0-1)
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- `s`: Marker size
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- `marker`: Marker style
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- `label`: Legend label
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**N-dimensional projection:**
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For >3 objectives, automatically creates scatter plot matrix
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### 2. Parallel Coordinate Plots (PCP)
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**Purpose:** Compare multiple solutions across many objectives
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**Best for:** Many-objective problems, comparing algorithm performance
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**Mechanism:** Each vertical axis represents one objective, lines connect objective values for each solution
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**Usage:**
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```python
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from pymoo.visualization.pcp import PCP
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plot = PCP()
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plot.add(result.F, color="blue", alpha=0.5)
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plot.add(reference_set, color="red", alpha=0.8)
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plot.show()
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```
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**Parameters:**
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- `title`: Plot title
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- `figsize`: Figure size
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- `labels`: Objective labels
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- `bounds`: Normalization bounds (min, max) per objective
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- `normalize_each_axis`: Normalize to [0,1] per axis (default: True)
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**Best practices:**
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- Normalize for different objective scales
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- Use transparency for overlapping lines
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- Limit number of solutions for clarity (<1000)
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### 3. Heatmap
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**Purpose:** Show solution density and distribution patterns
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**Best for:** Understanding solution clustering, identifying gaps
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**Usage:**
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```python
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from pymoo.visualization.heatmap import Heatmap
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plot = Heatmap(title="Solution Density")
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plot.add(result.F)
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plot.show()
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```
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**Parameters:**
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- `bins`: Number of bins per dimension (default: 20)
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- `cmap`: Colormap name (e.g., "viridis", "plasma", "hot")
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- `norm`: Normalization method
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**Interpretation:**
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- Bright regions: High solution density
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- Dark regions: Few or no solutions
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- Reveals distribution uniformity
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### 4. Petal Diagram
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**Purpose:** Radial representation of multiple objectives
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**Best for:** Comparing individual solutions across objectives
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**Structure:** Each "petal" represents one objective, length indicates objective value
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**Usage:**
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```python
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from pymoo.visualization.petal import Petal
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plot = Petal(title="Solution Comparison", bounds=[min_vals, max_vals])
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plot.add(result.F[0], color="blue", label="Solution 1")
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plot.add(result.F[1], color="red", label="Solution 2")
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plot.show()
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```
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**Parameters:**
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- `bounds`: [min, max] per objective for normalization
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- `labels`: Objective names
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- `reverse`: Reverse specific objectives (for minimization display)
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**Use cases:**
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- Decision making between few solutions
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- Presenting trade-offs to stakeholders
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### 5. Radar Charts
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**Purpose:** Multi-criteria performance profiles
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**Best for:** Comparing solution characteristics
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**Similar to:** Petal diagram but with connected vertices
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**Usage:**
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```python
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from pymoo.visualization.radar import Radar
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plot = Radar(bounds=[min_vals, max_vals])
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plot.add(solution_A, label="Design A")
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plot.add(solution_B, label="Design B")
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plot.show()
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```
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### 6. Radviz
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**Purpose:** Dimensional reduction for visualization
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**Best for:** High-dimensional data exploration, pattern recognition
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**Mechanism:** Projects high-dimensional points onto 2D circle, dimension anchors on perimeter
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**Usage:**
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```python
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from pymoo.visualization.radviz import Radviz
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plot = Radviz(title="High-dimensional Solution Space")
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plot.add(result.F, color="blue", s=30)
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plot.show()
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```
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**Parameters:**
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- `endpoint_style`: Anchor point visualization
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- `labels`: Dimension labels
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**Interpretation:**
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- Points near anchor: High value in that dimension
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- Central points: Balanced across dimensions
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- Clusters: Similar solutions
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### 7. Star Coordinates
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**Purpose:** Alternative high-dimensional visualization
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**Best for:** Comparing multi-dimensional datasets
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**Mechanism:** Each dimension as axis from origin, points plotted based on values
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**Usage:**
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```python
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from pymoo.visualization.star_coordinate import StarCoordinate
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plot = StarCoordinate()
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plot.add(result.F)
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plot.show()
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```
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**Parameters:**
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- `axis_style`: Axis appearance
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- `axis_extension`: Axis length beyond max value
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- `labels`: Dimension labels
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### 8. Video/Animation
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**Purpose:** Show optimization progress over time
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**Best for:** Understanding convergence behavior, presentations
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**Usage:**
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```python
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from pymoo.visualization.video import Video
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# Create animation from algorithm history
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anim = Video(result.algorithm)
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anim.save("optimization_progress.mp4")
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```
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**Requirements:**
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- Algorithm must store history (use `save_history=True` in minimize)
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- ffmpeg installed for video export
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**Customization:**
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- Frame rate
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- Plot type per frame
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- Overlay information (generation, hypervolume, etc.)
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## Advanced Features
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### Multiple Dataset Overlay
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All plot types support adding multiple datasets:
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```python
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plot = Scatter(title="Algorithm Comparison")
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plot.add(nsga2_result.F, color="red", alpha=0.5, label="NSGA-II")
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plot.add(nsga3_result.F, color="blue", alpha=0.5, label="NSGA-III")
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plot.add(true_pareto_front, color="black", linewidth=2, label="True PF")
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plot.show()
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```
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### Custom Styling
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Pass matplotlib kwargs directly:
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```python
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plot = Scatter(
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title="My Results",
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figsize=(10, 8),
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tight_layout=True
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)
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plot.add(
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result.F,
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color="red",
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marker="o",
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s=50,
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alpha=0.7,
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edgecolors="black",
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linewidth=0.5
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)
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```
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### Normalization
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Normalize objectives to [0,1] for fair comparison:
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```python
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plot = PCP(normalize_each_axis=True, bounds=[min_bounds, max_bounds])
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```
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### Save to File
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Save plots instead of displaying:
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```python
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plot = Scatter()
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plot.add(result.F)
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plot.save("my_plot.png", dpi=300)
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```
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## Visualization Selection Guide
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**Choose visualization based on:**
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| Problem Type | Primary Plot | Secondary Plot |
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|--------------|--------------|----------------|
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| 2-objective | Scatter | Heatmap |
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| 3-objective | 3D Scatter | Parallel Coordinates |
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| Many-objective (4-10) | Parallel Coordinates | Radviz |
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| Many-objective (>10) | Radviz | Star Coordinates |
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| Solution comparison | Petal/Radar | Parallel Coordinates |
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| Algorithm convergence | Video | Scatter (final) |
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| Distribution analysis | Heatmap | Scatter |
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**Combinations:**
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- Scatter + Heatmap: Overall distribution + density
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- PCP + Petal: Population overview + individual solutions
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- Scatter + Video: Final result + convergence process
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## Common Visualization Workflows
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### 1. Algorithm Comparison
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```python
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from pymoo.visualization.scatter import Scatter
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plot = Scatter(title="Algorithm Comparison on ZDT1")
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plot.add(ga_result.F, color="blue", label="GA", alpha=0.6)
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plot.add(nsga2_result.F, color="red", label="NSGA-II", alpha=0.6)
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plot.add(zdt1.pareto_front(), color="black", label="True PF")
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plot.show()
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```
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### 2. Many-objective Analysis
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```python
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from pymoo.visualization.pcp import PCP
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plot = PCP(
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title="5-objective DTLZ2 Results",
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labels=["f1", "f2", "f3", "f4", "f5"],
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normalize_each_axis=True
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)
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plot.add(result.F, alpha=0.3)
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plot.show()
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```
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### 3. Decision Making
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```python
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from pymoo.visualization.petal import Petal
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# Compare top 3 solutions
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candidates = result.F[:3]
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plot = Petal(
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title="Top 3 Solutions",
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bounds=[result.F.min(axis=0), result.F.max(axis=0)],
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labels=["Cost", "Weight", "Efficiency", "Safety"]
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)
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for i, sol in enumerate(candidates):
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plot.add(sol, label=f"Solution {i+1}")
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plot.show()
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```
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### 4. Convergence Visualization
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```python
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from pymoo.optimize import minimize
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# Enable history
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result = minimize(
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problem,
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algorithm,
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('n_gen', 200),
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seed=1,
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save_history=True,
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verbose=False
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)
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# Create convergence plot
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from pymoo.visualization.scatter import Scatter
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plot = Scatter(title="Convergence Over Generations")
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for gen in [0, 50, 100, 150, 200]:
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F = result.history[gen].opt.get("F")
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plot.add(F, alpha=0.5, label=f"Gen {gen}")
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plot.show()
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```
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## Tips and Best Practices
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1. **Use appropriate alpha:** For overlapping points, use `alpha=0.3-0.7`
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2. **Normalize objectives:** Different scales? Normalize for fair visualization
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3. **Label clearly:** Always provide meaningful labels and legends
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4. **Limit data points:** >10000 points? Sample or use heatmap
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5. **Color schemes:** Use colorblind-friendly palettes
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6. **Save high-res:** Use `dpi=300` for publications
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7. **Interactive exploration:** Consider plotly for interactive plots
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8. **Combine views:** Show multiple perspectives for comprehensive analysis
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