Multi-objective¶

This page loads results that have two or more objectives, trains a model for each, and asks for the next experiments that push the Pareto front outward. The web app loads and trains; the multi-objective suggestion and the Pareto front are in Python for now.

Loading a file with two objective columns. The file has no Output column, so ALchemist asks which columns are the targets.

What works where¶

Theory, including the reference point, is in Acquisition functions.

1. Load data with several targets¶

The file holds one column for each variable and one for each objective. ALchemist reads a column named Output as the single objective and asks nothing, so name the objective columns something else.

1. Define the variables (Define variables).
2. In the Experiment Data panel, choose Load CSV and pick the file.
3. In Select Target Column(s), choose Multi-Objective instead of Single-Objective. A list of every column in the file appears under Target Columns.
4. Tick the columns that hold objectives, at least two. Do not tick the variable columns, which the list also offers. Confirm stays disabled until two are ticked.

In the web app and over REST a single goal, maximize or minimize, applies to every objective. Python takes one direction per objective.

import numpy as np
import pandas as pd
from alchemist_core import OptimizationSession

rng = np.random.default_rng(11)
session = OptimizationSession()
session.add_variable("temperature", "real", bounds=(200.0, 300.0), unit="°C")
session.add_variable("pressure", "real", bounds=(20.0, 80.0), unit="bar")
session.add_variable("whsv", "real", bounds=(1.5, 18.0))

rows = []
for p in session.generate_initial_design("lhs", n_points=12, random_seed=11):
    t = (p["temperature"] - 200) / 100
    q = (p["pressure"] - 20) / 60
    w = (p["whsv"] - 1.5) / 16.5
    rows.append({
        **p,
        "conversion": 100 * (0.2 + 0.7 * t * (1 - 0.4 * w) + 0.1 * q) + rng.normal(0, 1),
        "selectivity": 100 * (0.9 - 0.5 * t**2 + 0.1 * q - 0.1 * w) + rng.normal(0, 1),
    })
pd.DataFrame(rows).to_csv("two_objectives.csv", index=False)

session.load_data("two_objectives.csv", target_columns=["conversion", "selectivity"])
print(session.is_multi_objective, session.objective_names)

POST /api/v1/sessions/{session_id}/experiments/upload?target_columns=conversion,selectivity

2. Train a model for each objective¶

1. In the Model tab, choose BoTorch. The scikit-learn backend supports one objective and refuses the data with an error.
2. Choose Train Model. A message reports "Model trained successfully (2 objectives)", and Trained Model Info reads "Trained 2 objectives. Cross-validation metrics aren't computed for multi-objective models yet."

ALchemist fits one Gaussian process per objective. The hyperparameters in View Hyperparameters list them by objective name.

results = session.train_model(backend="botorch")
print(results["metrics"], results["n_objectives"])

POST /api/v1/sessions/{session_id}/model/train
Content-Type: application/json

{"backend": "botorch"}

3. Suggest the next experiments¶

The only strategies for several objectives are qEHVI and qNEHVI, which score a candidate by the hypervolume it is expected to add above a reference point. qNEHVI also allows for noise in the observed values. Any other strategy is refused with "multi-objective optimization requires 'qEHVI' or 'qNEHVI'".

The web app's Acquisition tab lists neither strategy, so Run Acquisition Strategy cannot suggest for a multi-objective session there, and Find Model Optimum returns an error. Use Python, or REST for a suggestion.

Find Model Optimum and POST /api/v1/sessions/{session_id}/acquisition/find-optimum return one point, so on a multi-objective session they answer 400. Use find_optimum in Python, below, for the Pareto frontier.

suggestions = session.suggest_next(
    strategy="qNEHVI",
    goal=["maximize", "maximize"],
    n_suggestions=2,
    ref_point=[0.0, 0.0],
)
print(suggestions)

best = session.find_optimum(goal=["maximize", "maximize"])
print(best["n_pareto"], best["objective_names"])
print(best["pareto_frontier"][["conversion", "selectivity"]].round(1))

fig = session.plot_pareto_frontier(directions=["maximize", "maximize"], ref_point=[0.0, 0.0])
fig.savefig("pareto.png")

POST /api/v1/sessions/{session_id}/acquisition/suggest
Content-Type: application/json

{"strategy": "qNEHVI", "goal": "maximize", "n_suggestions": 2}