Participants will navigate a black-box search space with four objectives:

### Objectives
- **y1, y2, y3, y4** — all to be minimized.  
- **Correlations**:
  - y1 and y2 are positively correlated.  
  - y1 and y2 are anticorrelated with y3.  
- **Noise**:
  - y1, y2, and y3 are stochastic with heteroskedastic, parameter-free noise.  
  - y4 is deterministic but still black-box.  
  - This means repeated evaluations with the same parameters will yield different y1, y2, and y3 values, but the same y4.

---

### Objective Thresholds
A solution is automatically considered **bad** if:  
- y1 > 0.2  
- y2 > 0.7  
- y3 > 1800  
- y4 > 40e6  

These thresholds guide participants to avoid unpromising regions of the search space and focus on meaningful trade-offs.

---

### Search Space
- **Parameter bounds**:  
  - x1 … x20 ∈ [0, 1]  
  - c1 ∈ {c1_0, c1_1}  
  - c2 ∈ {c2_0, c2_1}  
  - c3 ∈ {c3_0, c3_1, c3_2}  
- **Fidelity parameter**: `fidelity1` ∈ [0, 1]  
  - Higher fidelity → more expensive evaluations but better quality.  
  - fidelity1 and y3 are correlated.

---

### Constraints
- x19 < x20  
- x6 + x15 ≤ 1.0  
- All interaction must go through the provided package.

---

### Workflow Example

```python
# Import the package
import kagglehub

package = kagglehub.package_import('amanichabouni/crabnet-package/versions/19')

# Create a campaign
campaign = package.Model()

# Evaluate the objectives
campaign.predict(
    0.5, 0.5, 1, 1, 1, 0, 1, 1, 1, 1,
    1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
    'c1_0', 'c2_0', 'c3_0', 1
)

# Export the history
package.Model.export_history()
```


### Why This Task
- Real-world optimization problems rarely have a single objective; trade-offs between competing criteria must be managed.  
- The stochasticity in y1, y2, and y3 simulates **noisy real-world conditions**, forcing participants to handle uncertainty.  
- Constraints and fidelity make the search space **non-trivial**, requiring careful planning and sample-efficient exploration.  
- This competition is a **bridge to real-world multi-objective problems**, consolidating skills from previous competitions in the series.

---

### Context in the Series
This is the **6th and final competition** in the series. Previous tasks included:  

- **Multi-Task Optimization**  
- **Multi-Fidelity Branin Optimization**  
- **Noisy Vanilla Branin Optimization**  


The final task challenges participants to handle **multi-objective, noisy, constrained black-box optimization**—a realistic scenario in scientific and engineering applications.