Closed-Form Test Functions for Biophysical Sequence Optimization Algorithms

TL;DR

The paper addresses the lack of accessible benchmarks for biophysical sequence optimization by introducing Ehrlich functions, a closed-form, tunable benchmark family that encapsulates core geometric features such as feasibility constraints and non-additive motif interactions. It argues that well-designed benchmarks should be low-cost, well-characterized, and challenging, while remaining relevant to real applications, and it situates Ehrlich functions alongside other benchmark types. Through a simple genetic algorithm, the authors demonstrate how Ehrlich parameters control difficulty and how optimizer hyperparameters influence performance, including a Bayesian-optimization-led tuning that yields gains with trade-offs in feasibility. The work offers a practical, reproducible framework for rapid, scalable evaluation of optimization algorithms in biophysical design, with implications for deeper exploration of generative search strategies and future benchmark development.

Abstract

There is a growing body of work seeking to replicate the success of machine learning (ML) on domains like computer vision (CV) and natural language processing (NLP) to applications involving biophysical data. One of the key ingredients of prior successes in CV and NLP was the broad acceptance of difficult benchmarks that distilled key subproblems into approachable tasks that any junior researcher could investigate, but good benchmarks for biophysical domains are rare. This scarcity is partially due to a narrow focus on benchmarks which simulate biophysical data; we propose instead to carefully abstract biophysical problems into simpler ones with key geometric similarities. In particular we propose a new class of closed-form test functions for biophysical sequence optimization, which we call Ehrlich functions. We provide empirical results demonstrating these functions are interesting objects of study and can be non-trivial to solve with a standard genetic optimization baseline.

Figures (5)

• Figure 1: The Ackley function is widely used to evaluate black-box optimization algorithms such as Bayesian optimization that have been successfully applied to many real-world problems. The relevance of the Ackley function is not its semantic correspondence with real-world objective functions, but its geometric similarities, such as a multiplicity of local minima and changing local curvature.
• Figure 2: (a) Arginine and glutamate are complementary amino acids because they have a strong salt bridge interaction. (b - c) Antibodies that bind to a specific region of a target protein (the epitope) have many therapeutic and diagnostic uses. (d) Antibodies with different sequences can bind to the same epitope on two homologous proteins because they are structurally similar, which manifests as shared motifs in sequence space. Structures shown have RCSB codes 3gbn and 4fqi.
• Figure 3: Illustration of an epistatic second-order interaction.
• Figure 4: Here we show how the difficulty of the test problem can be controlled by varying Ehrlich function parameters, keeping the optimizer fixed to a robust GA baseline. Starting from a fixed set of reference parameters we vary each parameter individually. For this optimizer, the problem difficulty depends most strongly on the quantization parameter $q$.
• Figure 5: Here we show the effect of tuning the GA algorithm hyperparameters to optimize a fixed Ehrlich function with $k = 8$ and $q=4$. Configuration A is more aggressive than B, with higher values for $p_m$ and $p_r$. The optimal hyperparameter setting must trade off the depth of the search per iteration with the risk of violating the feasibility constraint.