Optimization is Not Enough: Why Problem Formulation Deserves Equal Attention

TL;DR

This paper highlights the importance of problem formulation and domain knowledge in black-box optimization, demonstrating through a case study that context-aware strategies outperform context-agnostic ones in engineering design.

Contribution

It provides a comparative analysis of concurrent versus sequential optimization strategies in topology optimization, emphasizing the role of problem formulation and domain knowledge.

Findings

Sequential optimization yields better, more interpretable designs.

Context-agnostic strategies often produce suboptimal or non-physical results.

Incorporating domain knowledge improves optimization outcomes.

Abstract

Black-box optimization is increasingly used in engineering design problems where simulation-based evaluations are costly and gradients are unavailable. In this context, the optimization community has largely analyzed algorithm performance in context-free setups, while not enough attention has been devoted to how problem formulation and domain knowledge may affect the optimization outcomes. We address this gap through a case study in the topology optimization of laminated composite structures, formulated as a black-box optimization problem. Specifically, we consider the design of a cantilever beam under a volume constraint, intending to minimize compliance while optimizing both the structural topology and fiber orientations. To assess the impact of problem formulation, we explicitly separate topology and material design variables and compare two strategies: a concurrent approach that optimizes all variables simultaneously without leveraging physical insight, and a sequential approach that optimizes variables of the same nature in stages. Our results show that context-agnostic strategies consistently lead to suboptimal or non-physical designs. In contrast, the sequential strategy yields better-performing and more interpretable solutions. These findings underscore the value of incorporating, when available, domain knowledge into the optimization process and motivate the development of new black-box benchmarks that reward physically informed and context-aware optimization strategies.