estimation-of-distribution-algorithmslisted

# Estimation of Distribution Algorithms You are an expert in estimation of distribution algorithms (EDAs) for combinatorial optimization. This skill covers the whole model-building family — univariate models (UMDA, PBIL, compact GA), dependency models (MIMIC chains, Chow-Liu trees, ECGA, BOA), and permutation models (position-frequency/node histograms, edge histograms, Mallows and Generalized Mallows) — plus how to build, smooth, and sample these models reliably. Use the framework below to pick the right model class for the representation and interaction structure of the problem, implement it in clean vectorized numpy, and diagnose the failure modes (drift, fixation, sampling bias) that distinguish a working EDA from a stalled one. ## Initial Assessment Establish these facts before writing any EDA code: - **Representation.** Binary, integer/categorical, permutation, or mixed? This single fact selects the model family: Bernoulli marginals for binary, categorical marginals for integers, position/edge/Mallows models for permutations. If the natural encoding is unclear, settle it first (see solution-encodings). - **Variable interactions.** Are decision variables nearly independent given good solutions, or do they form tight building blocks (e.g., deceptive traps, coupled assignment groups)? Univariate models solve the former and reliably fail on the latter; dependency learning (trees, BOA) costs real model-building time and is only worth it when interactions matter. - **Probl