Single and Multi-objective Optimization Benchmark Problems Focusing on Human-Powered Aircraft Design

Abstract

The benchmark for human-powered aircraft (hpa) design is introduced in the paper Single and Multi-Objective Optimization Benchmark Problems Focusing on Human-Powered Aircraft Design. The original benchmark is available here. This package serves as a wrapper for the original benchmark.

APIs

class ConstrainedProblem(problem_name: str, n_div: int = 4, level: int = 0 )

• problem_name: The name of a benchmark problem. All problem names and their explanations are provided here.
• n_div: The wing segmentation number and alters the problem’s dimension. It must be an integer greater than 0. Concretely, the number of sections in this figure. The default value used in the paper is 4.
• level: The difficulty level of the problem. It must be in [0, 1, 2]

Note that Problem also receives the same set of arguments.

Method and Properties

• search_space: Return the search space.
  • Returns: dict[str, optuna.distributions.BaseDistribution]
• directions: Return the optimization directions.
  • Returns: list[optuna.study.StudyDirection]
• metric_names: Return the objective names in the order returned by evaluate.
  • Returns: list[str] of length self.nf.
• constraint_names: Return the constraint names used as the keys of evaluate_constraints. This property is only available in ConstrainedProblem.
  • Returns: list[str] of length self.ng.
• evaluate(params: dict[str, float]): Evaluate the objective function given a dictionary of parameters.
  • Args:
    • params: A dictionary representing decision variable like {"x0": x1_value, "x1": x1_value, ..., "xn": xn_value}. The number of parameters must be equal to self.nx. xn_value must be a float in [0, 1].
  • Returns: List of length self.nf.
• evaluate_constraints(params: dict[str, float]): Evaluate the constraint functions and return the constraint function values keyed by their names. This method is only available in ConstrainedProblem.
  • Args:
    • params: A dictionary representing the decision variables, with the same format and value range as in evaluate.
  • Returns: Dictionary of length self.ng. A trial is feasible when every value is zero or less.

The properties and functions of classes in hpa.problem are also available such as nx.

Objective and Constraint Names

Each problem uses a subset of the 11 fundamental objectives and the 5 constraints defined in Table 1 of the paper. The names below carry the paper’s f_i and g_j indices as a prefix, so metric_names and constraint_names can be read directly against Table 2 of the paper. Which subset a problem uses can also be inspected at runtime via problem.metric_names and problem.constraint_names.

Objectives (all minimized)

Since the paper maximizes the cruise speed, the wing efficiency, and the payload, the corresponding objectives are negated and prefixed with negative_.

Constraints (feasible when zero or less)

Note that evaluate_constraints preserves the order of the original implementation, which is not sorted by the constraint index. For example, ConstrainedProblem("HPA131").constraint_names is ["g1_max_strain", "g3_parked_wingtip_deflection", "g2_wingtip_dihedral_angle"].

In the unconstrained problems, the constraints are folded into the objectives as penalty terms following Eq. (5) of the paper, so Problem exposes only metric_names.

Installation

The dependencies can be installed via:

pip install pandas scipy optunahub

Or you can install the required packages from optunahub as well.

pip install -r https://hub.optuna.org/benchmarks/hpa/requirements.txt

Example

from __future__ import annotations

import optuna
import optunahub


hpa = optunahub.load_module("benchmarks/hpa")
problem = hpa.ConstrainedProblem("HPA131") 
study = optuna.create_study(directions=problem.directions)
study.optimize(problem, n_trials=10)


if len(problem.directions) == 1:
    print(study.best_trial)
else:
    print(study.best_trials)

Reference

@inproceedings{namura2025single,
  title={Single and multi-objective optimization benchmark problems focusing on human-powered aircraft design},
  author={Namura, Nobuo},
  booktitle={International Conference on Evolutionary Multi-Criterion Optimization},
  pages={195--210},
  year={2025},
  organization={Springer}
}