Constraints

Constraints

Constraints define hard feasibility conditions that candidate materials must satisfy. Unlike objectives (which are optimized), constraints act as binary filters — a candidate either satisfies all constraints or is rejected.

Basic Syntax

constraints:
  - expression: temperature >= 300
    description: Minimum processing temperature

  - expression: pressure <= 50.0
    description: Equipment pressure limit

  - expression: weight_a + weight_b + weight_c <= 1.0
    description: Composition fractions cannot exceed 100%

Constraint Fields

| Field | Required | Type | Description | |———-|—————|———|——————-| | expression | Yes | string | Inequality expression using parameter names | | description | No | string | Human-readable explanation | | tolerance | No | number | Numerical tolerance for equality (default: 1e-6) |

Supported Operators

The constraint expression parser supports:

| Operator | Meaning | Example | |—————|————-|————-| | >= | Greater than or equal | thickness >= 20 | | <= | Less than or equal | cost <= 100 | | > | Strictly greater than | concentration > 0 | | < | Strictly less than | porosity < 1.0 | | == | Equal (with tolerance) | ratio == 0.5 | | + | Addition | a + b <= 1.0 | | - | Subtraction | max_temp - min_temp >= 50 | | | Multiplication | length width <= 500 | | / | Division | flow / area >= 10 |

Composition Constraints

The most common constraint type in materials science is a composition constraint. When optimizing component fractions, they must sum to a fixed value:

parameters:
  - name: ni_fraction
    type: continuous
    bounds: [0.0, 1.0]
  - name: mn_fraction
    type: continuous
    bounds: [0.0, 1.0]
  - name: co_fraction
    type: continuous
    bounds: [0.0, 1.0]

constraints:
  - expression: ni_fraction + mn_fraction + co_fraction <= 1.0
    description: Total transition metal fraction cannot exceed stoichiometry

Equipment and Process Constraints

Constraints can enforce physical or practical limits:

constraints:
  - expression: sintering_temp <= 1400
    description: Furnace maximum temperature is 1400 C

  - expression: film_thickness >= 5
    description: Deposition tool minimum thickness is 5 nm

  - expression: precursor_cost * batch_size <= 10000
    description: Maximum reagent budget per batch

How Constraints Are Enforced

MatCraft enforces constraints at two levels:

1. Candidate generation: During CMA-ES acquisition, proposed candidates are checked against constraints. Infeasible candidates are either repaired (projected back to the feasible region) or discarded and resampled.

1. Post-evaluation filtering: After evaluation, any candidate that violates constraints is excluded from the Pareto front and marked as infeasible in the results.

The repair mechanism uses a simple projection: for linear inequality constraints, infeasible points are projected onto the constraint boundary. For complex nonlinear constraints, rejection sampling is used instead.

Constraint Violation Reporting

After a campaign, you can inspect constraint violations:

materia results --show-violations

This reports how many candidates were rejected and which constraints were most frequently violated, helping you assess whether the design space is overly constrained.

Best Practices

• Keep constraints simple: Use linear inequalities when possible. Complex nonlinear constraints slow down candidate generation.
• Avoid redundant constraints: If a parameter has bounds: [10, 100], you do not need a constraint param >= 10.
• Use constraints for cross-parameter relationships: Bounds handle single-parameter limits; constraints handle relationships between parameters.
• Set reasonable tolerances: For equality constraints, the default tolerance of 1e-6 works for most cases. Increase it if your evaluation function has limited numerical precision.

Limitations

• Constraint expressions cannot reference objective values — they can only reference parameters.
• The expression parser does not support functions like sin, exp, or log. For complex feasibility conditions, implement them in a custom domain plugin's is_feasible() method.
• Maximum of 20 constraints per MDL file.