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

TL;DR

This paper introduces a realistic benchmark test suite for single and multi-objective optimization in human-powered aircraft design, capturing moderate multimodality and diverse Pareto front shapes across various difficulty levels.

Contribution

It provides a comprehensive, computationally inexpensive benchmark suite with 60 problems, incorporating realistic physics-based equations for meaningful optimization comparisons.

Findings

Moderate multimodality observed in problems

Diverse Pareto front shapes in multi-objective cases

Test suite effectively mimics real-world engineering challenges

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.