Recombinative approaches for the maximum happy vertices problem

Abstract

The maximum happy vertices problem involves taking a simple graph in which several vertices are precoloured. The aim is to colour the remaining vertices to maximise the number happy vertices, where a vertex is considered happy if and only if all of its neighbours are assigned the same colour as the vertex itself. Previous studies for this problem have investigated integer programming, tabu search and the construct, solve, merge & adapt (CMSA) matheuristic. In this study, we develop three different evolutionary approaches based on tabu search and also develop a CMSA-tabu search (CMSA-TS) hybrid. We conduct experiments on a wide range of d -regular and scale-free graphs and find that, overall, CMSA-TS is the most effective approach, nearly always finding the best-observed solutions. However, in special cases where problems have large numbers of vertices and low vertex degrees, the evolutionary algorithms have a distinct advantage.