into a smoother function that approximates the original function and has fewer local minima. The algorithm builds a hierarchy of increasingly smooth functions by iteratively applying a transformation. In a next step, employs Newton’s method as a local optimization on the smoothest function and then traces this solution back to the original objective function, applying a local optimization on each level. Liberti [*et al.*]{}state that the algorithm “has several advantages: it is efficient, effective for small-to-medium-sized instances, and, more importantly, can be naturally extended to solve iMDGP instances” [@liberti2014survey p. 23]. On the downside, on large-scale instances the solution quality decreases (while the running time remains reasonable). An et al. [@an2003large; @an2003solving] use a different continuation approach which improves the solution quality compared to . In their experiments the running time of their algorithm for proteins larger than atoms lies between and s. The double variable neighborhood search with smoothing (DVS) algorithm by Liberti et al. [@liberti2009double] combines the ideas of and variable neighborhood search into one algorithm. In their comparison to the quality of DVS was significantly better, but the running time two orders of magnitude slower already for small inputs.

Biswas [*et al.*]{} [@biswas2008distributed] proposed the DAFGL algorithm 