BoTorch Constrained Multi-Objective Test Functions

Abstract

This package ports 6 constrained multi-objective test problems from BoTorch’s test_functions.multi_objective module to OptunaHub’s BaseProblem interface: BNH, CONSTR, ConstrainedBraninCurrin, OSY, SRN, and MW7. Each problem is reimplemented with plain Python and numpy only, so it can be evaluated without installing torch or botorch.

Conventions

• Parameters are named x0, x1, … following each problem’s input vector order.
• evaluate_constraints keys are named c0, c1, … following each problem’s constraint order.
• BoTorch’s constraint convention is that a slack c_i(x) >= 0 is feasible; OptunaHub’s BaseProblem convention is that a value <= 0 is feasible. So every constraint returned here is the negation of the corresponding BoTorch slack.
• OSY uses BoTorch’s raw _evaluate_true objectives verbatim (f0 already has its minus sign baked into the formula) with directions=[MINIMIZE, MINIMIZE], since BoTorch’s own negate=True recommendation is only about fitting its maximize-oriented ref_point/hypervolume convention, not the sign of f0 itself.

APIs

All 6 classes below share the same interface, inherited from optunahub.benchmarks.BaseProblem:

• search_space: Return the search space.

  • Returns: dict[str, optuna.distributions.BaseDistribution]

• directions: Return the optimization directions. Always [MINIMIZE, MINIMIZE] for every problem in this package.

  • Returns: list[optuna.study.StudyDirection]

• __call__(trial: optuna.Trial): Evaluate the objectives and constraints and return the objective values.

  • Args:
    • trial: Optuna trial object.
  • Returns: list[float]

• evaluate(params: dict[str, float]): Evaluate the objective functions.

  • Args:
    • params: Decision variable like {"x0": x0_value, "x1": x1_value, ..., "xn": xn_value}.
  • Returns: list[float] of length 2.

• evaluate_constraints(params: dict[str, float]): Evaluate the constraint functions.

  • Args:
    • params: Decision variable, same format as evaluate.
  • Returns: dict[str, float] keyed by c0, c1, …. A trial is feasible when every value is zero or less.

• BNH()

  • Dimension: 2. Constraints: 2. See (Garrido-Merchán & Hernández-Lobato, 2019).

• CONSTR()

  • Dimension: 2. Constraints: 2. See (Garrido-Merchán & Hernández-Lobato, 2019).

• ConstrainedBraninCurrin()

  • Dimension: 2. Constraints: 1. The Branin-Currin function with the disk constraint from (Gelbart et al., 2014).

• OSY()

  • Dimension: 6. Constraints: 6. See (Osyczka & Kundu, 1995).

• SRN()

  • Dimension: 2. Constraints: 2. See (Garrido-Merchán & Hernández-Lobato, 2019).

• MW7(dim: int)

  • dim: Number of decision variables. Must be at least 2.
  • Dimension: dim. Constraints: 2. Disconnected Pareto front. See (Ma & Wang, 2019).

Example

import optuna
import optunahub


cmo = optunahub.load_module("benchmarks/botorch_cmo_test_funcs")
problem = cmo.BNH()

study = optuna.create_study(
    sampler=optuna.samplers.NSGAIISampler(seed=42),
    directions=problem.directions,
)
study.optimize(problem, n_trials=100)
optuna.visualization.plot_pareto_front(study).show()

Tests can be performed by:

pytest package/benchmarks/botorch_cmo_test_funcs/tests

Reference

Garrido-Merchán, E. C., & Hernández-Lobato, D. (2019). Predictive Entropy Search for Multi-objective Bayesian Optimization with Constraints. Neurocomputing, 361, 50-68.

Gelbart, M. A., Snoek, J., & Adams, R. P. (2014). Bayesian Optimization with Unknown Constraints. UAI.

Osyczka, A., & Kundu, S. (1995). A New Method to Solve Generalized Multicriteria Optimization Problems Using the Simple Genetic Algorithm. Structural Optimization, 10, 94-99.

Ma, Z., & Wang, Y. (2019). Evolutionary Constrained Multiobjective Optimization: Test Suite Construction and Performance Comparisons. IEEE Transactions on Evolutionary Computation, 23(6), 972-986.