Objectives

Objectives define the properties you want to optimize. Each objective has a direction (maximize or minimize) and represents a measurable quantity returned by the evaluation function.

Basic Syntax

yaml

objectives:
  - name: tensile_strength
    direction: maximize
    unit: MPa

  - name: cost
    direction: minimize
    unit: USD/kg

Objective Fields

Single-Objective Optimization

When only one objective is specified, MatCraft performs single-objective optimization. CMA-ES directly optimizes this objective and returns the single best solution:

yaml

objectives:
  - name: conductivity
    direction: maximize
    unit: S/cm

Multi-Objective Optimization

When two or more objectives are specified, MatCraft performs multi-objective optimization and returns the Pareto front — the set of solutions where no objective can be improved without worsening another:

yaml

objectives:
  - name: energy_density
    direction: maximize
    unit: Wh/kg

  - name: power_density
    direction: maximize
    unit: W/kg

  - name: cycle_life
    direction: maximize
    unit: cycles

MatCraft supports up to 5 simultaneous objectives. Beyond 3 objectives, the Pareto front becomes a high-dimensional surface and visualization becomes more challenging. Consider whether all objectives are truly independent.

Reference Points

The hypervolume indicator requires a reference point — a point in objective space that is dominated by all Pareto-optimal solutions. MatCraft auto-computes reference points, but you can specify them explicitly for consistent comparison across campaigns:

yaml

objectives:
  - name: permeability
    direction: maximize
    unit: L/(m2*h*bar)
    reference_point: 0.0

  - name: selectivity
    direction: maximize
    unit: "-"
    reference_point: 0.0

For maximize objectives, the reference point should be at or below the worst expected value. For minimize objectives, it should be at or above the worst expected value.

Objective Weights

When scalarization is needed (e.g., for certain convergence criteria), weights control relative importance:

yaml

objectives:
  - name: strength
    direction: maximize
    weight: 2.0   # Twice as important as cost

  - name: cost
    direction: minimize
    weight: 1.0

Weights do not affect Pareto computation. They are only used when the optimizer needs a scalar fitness value, such as for CMA-ES internal population ranking.

Evaluation Return Format

The domain plugin's evaluation function must return values for every declared objective. The return type is a dictionary mapping objective names to float values:

python

def evaluate(params: dict) -> dict:
    # Physics simulation or model prediction
    strength = compute_strength(params)
    cost = compute_cost(params)
    return {
        "tensile_strength": strength,
        "cost": cost,
    }

If an evaluation returns None or NaN for any objective, the candidate is marked as failed and excluded from surrogate training.

Common Objective Pairs

Many material optimization problems involve well-known trade-offs:

See the Multi-Objective Optimization guide for strategies to navigate these trade-offs.