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 tha...

The Vertex Separation problem (VSP) is an NP-hard problem with practical applications in VLSI design, graph drawing and computer language compiler design. VSP belongs to a family of optimization problems in which the objective is to find the best separator of vertices or edges in a generic graph. In this paper, we propose different heuristic methods and embed them into a Variable Neighborhood S...