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

TL;DR

This work introduces a real-world-inspired optimization benchmark for engineering design focusing on human-powered aircraft (HPA). It defines 60 problems across three difficulty levels by deriving objective functions and constraints from aerodynamics and CFRP mechanics, with a wing-segmentation parameter $n$ to scale dimensionality, and provides both constrained and penalty-based unconstrained variants. The authors conduct extensive single- and multi-objective experiments using a range of evolutionary and Bayesian methods, revealing moderate multimodality and diverse Pareto-front shapes; AGE-MOEA-II often performs best across many many-objective cases, while other algorithms excel in specific objective counts. The benchmark is computationally light (evaluation under ~0.15 s) and accompanied by open-source Python code, offering a practical, scalable platform for benchmarking black-box optimization methods in realistic, high-dimensional engineering settings.

Abstract

The landscapes of real-world optimization problems can vary strongly depending on the application. In engineering design optimization, objective functions and constraints are often derived from governing equations, resulting in moderate multimodality. However, benchmark problems with such moderate multimodality are typically confined to low-dimensional cases, making it challenging to conduct meaningful comparisons. To address this, we present a benchmark test suite focused on the design of human-powered aircraft for single and multi-objective optimization. This test suite incorporates governing equations from aerodynamics and material mechanics, providing a realistic testing environment. It includes 60 problems across three difficulty levels, with a wing segmentation parameter to scale complexity and dimensionality. Both constrained and unconstrained versions are provided, with penalty methods applied to the unconstrained version. The test suite is computationally inexpensive while retaining key characteristics of engineering problems. Numerical experiments indicate the presence of moderate multimodality, and multi-objective problems exhibit diverse Pareto front shapes.

Figures (8)

• Figure 1: Human-powered aircraft.
• Figure 2: Wing shape definition.
• Figure 3: Variables defining the stacking sequence of CFRP pipes.
• Figure 4: Relationship between wing deflection at parked and flight conditions, dihedral angle, and tension force of the flying wires.
• Figure 5: Pareto front shapes with reference points for $\text{IGD}^+$ in each difficulty level.