There are not specific papers on these methods (from Open Babel). They are based, in part, on methods used in OpenEye OMEGA:
- Conformer Generation with OMEGA: Algorithm and Validation Using High Quality Structures from the Protein Databank and the Cambridge Structural Database J. Chem. Inf. Model. 2010, 50, 572-584. DOI: 10.1021/ci100031x
- Conformer Generation with OMEGA: Learning from the Data Set and the Analysis of Failures. J. Chem. Inf. Model. 2012 52, 2919–2936. DOI: 10.1021/ci300314k
The rulesets for finding rotatable bonds are similar between Open Babel (and thus Avogadro) and OMEGA.
The random rotor search method simply tries a set of random conformers and will preferentially pick the lowest.
The weighted rotor search method will adjust weights to particular bond rotations as it runs (e.g., if one conformer is low in energy, it will "learn" akin to Monte Carlo).