A variable neighbourhood search algorithm to generate piano fingerings for polyphonic sheet music

A good piano fingering is essential for pianists to play a piece fluently. Some examples of algorithms to generate a piano fingering automatically can be found in the literature. However, the existing methods can only generate fingerings for small, monophonic piano pieces for the right hand, minimising the difficulty. In this paper, we develop a variable neighbourhood search (VNS) algorithm that can generate good fingerings for large pieces of polyphonic piano music considering both hands in an acceptable amount of calculation time. The algorithm calculates the difficulty based on a user-specific finger distance matrix. The set of rules considered in the literature in order to define the quality of a fingering is expanded to deal with specific finger combinations in polyphonic music. The VNS is a local search metaheuristic that searches in different neighbourhoods and performs a perturbation when a local optimum is reached. The selection of the optimal parameters of the VNS and the perturbation strategy are determined using thorough computational experiments and statistical analysis.