This deposit contains the PDF version of the article “GONM: A Layered Mathematical and Experimental Framework for Global Optimization on Noisy Multimodal Surfaces”. The work develops a layered mathematical and computational framework for global optimization on noisy multimodal landscapes. Its central idea is that difficult optimization problems should not be treated as homogeneous search spaces, but decomposed into structural, contractive, filtering, and terminal layers, each addressing a different source of instability or ambiguity in the search process. Within this framework, the article interprets global optimization as a sequence of coordinated mechanisms: structural basin organization inspired by the structural decomposition line, local contractive refinement derived from the principle of contractive propagation of perturbations, trajectory filtering informed by multiplicative and robust averaging ideas, and terminal statistical closure for noisy decision making. The work combines these ingredients into a composed layered operator, studies its qualitative stability under noise, and supports the framework with computational evidence on multimodal benchmark problems and Lennard-Jones molecular optimization. Main mathematical themes:- global optimization;- noisy multimodal landscapes;- layered optimization;- contractive refinement;- structural basin organization;- qualitative stability under noise.
Francisco Anderson de Sousa Oliveira (Sat,) studied this question.