User-Defined Adapters and Hardware-Scalable Search in Refined Math

Refined Math allows domain experts to define new optimization problems for a reusable search engine. An adapter specifies how to represent a candidate solution, evaluate it, change it and check the answer. In a partitioning problem with six items, imported exchange operators reduced the difference between group totals from 10 to the optimum of 0. In a quadratic assignment with four facilities, an imported Rust module reduced cost from 200 to 120. Disabling the operators left both examples at their initial objective values. Six further adapter programs produced results that matched reference checks on twelve instances. The paper examines how additional hardware can support more runs, wider beams, more candidates per state and deeper local improvement within a fixed time. For 24 polynomial-selection inputs, selecting the best of five seeded CPU searches by the search objective improved the score on a separate evaluation sample for 14 inputs, matched the first search on eight and scored lower on two. The architecture is particularly relevant when an expert can evaluate candidates but lacks a suitable dedicated optimizer. Proposed applications include molecular candidate selection with an external AlphaFold 3 workflow and cooling-channel design using thermal and flow simulation. This work follows Robopol Refined: A Universal Guided Search Engine for Combinatorial Optimization (DOI 10.5281/zenodo.20273854). Refined Math product pageTry Refined Math Online Free The manuscript was written in collaboration with GPT Astra, an AI assistant. This deposit contains the English manuscript, version 0.1. The CSV supplement cited in the manuscript is not included in this deposit.