From Algorithm Names to Evidence: A Mechanism-First Framework for Reproducible Optimization Research

Optimization research contains hundreds of named algorithms, but different names do not necessarily represent different computational mechanisms, and reported performance often depends on the conditions under which an algorithm is evaluated. This study develops a mechanism-first framework for determining what an optimization method does, what evidence supports it, and what conclusions that evidence permits. A cross-paradigm census of 90 algorithm identities is organized into 42 source-backed mechanism fingerprints describing representation, information source, proposal geometry, memory, adaptation, selection, diversity control, constraint handling, derivative order, and model type. The framework separately records evidence completeness—documented, partial, contradictory, or untested—and evidence provenance, preventing missing evidence from being interpreted as algorithmic failure. Unresolved conditions are represented as evidence obligations specifying what additional observation is required to resolve them. The framework is demonstrated on all 24 noiseless COCO BBOB functions using Random Search, differential evolution, Nelder–Mead, and CMA-ES across dimensions 5, 10, 20, and 40. Discovery and held-out instances are separated, objective calls are independently recorded, and official cocopp outputs provide target-runtime and ECDF analyses. The results demonstrate how condition-specific evidence can be reproduced and interpreted without extending conclusions beyond the experimental design. The framework thereby connects algorithm mechanism, evidence, reproducible experimentation, and admissible scientific claims within a single auditable structure.