Basin: Efficient and Extensible Numerical Optimization in Rust

We introduce BASIL, a user-friendly desktop application for process optimization. BASIL employs a Bayesian approach, incorporating special acquisition functions that can be used to solve both single and multi-objective optimization problems. It provides a graphical interface that enables users to input their experimental parameters, optimization objectives, and legacy data. This is then used to build surrogate models, which are coupled with acquisition functions to guide and optimize a process towards a desired objective. To facilitate model building, BASIL provides a variety of predefined surrogate model templates. BASIL can be used to optimize any arbitrary experiment or process with known, user-defined input variables, optimization objectives, and defined output.

Global optimization is a challenging problem, with plenty of algorithms displaying empirical success, but scarce theoretical backing. In this work, we propose a new theoretical framework called Proximal Basin Hopping (PBH), carefully tailored to combine proximal optimization and local minimization. We use it to construct a practical algorithm that converges to the global minimizer with high probability, when using a finite amount of samples. Proximal Basin Hopping outperforms well known algorithms with theoretical backing on standard synthetic hard functions, and real problems such as fitting scaling laws for deep learning. Furthermore, the higher the dimension, the better the performance gap.

Can a single LLM-based optimization system match specialized tools across fundamentally different domains? We show that when optimization problems are formulated as improving a text artifact evaluated by a scoring function, a single AI-based optimization system-supporting single-task search, multi-task search with cross-problem transfer, and generalization to unseen inputs-achieves state-of-the-art results across six diverse tasks. Our system discovers agent architectures that nearly triple Gemini Flash's ARC-AGI accuracy (32.5% to 89.5%), finds scheduling algorithms that cut cloud costs by 40%, generates CUDA kernels where 87% match or beat PyTorch, and outperforms AlphaEvolve's reported circle packing solution (n=26). Ablations across three domains reveal that actionable side information yields faster convergence and substantially higher final scores than score-only feedback, and that multi-task search outperforms independent optimization given equivalent per-problem budget through cross-task transfer, with benefits scaling with the number of related tasks. Together, we show for the first time that text optimization with LLM-based search is a general-purpose problem-solving paradigm, unifying tasks traditionally requiring domain-specific algorithms under a single framework. We open-source optimize_anything with support for multiple backends as part of the GEPA project at https://github.com/gepa-ai/gepa .