Metaheuristics for the Minimum Gap Graph Partitioning Problem

Abstract The Minimum Gap Graph Partitioning Problem (MGGPP) consists in partitioning a vertex-weighted undirected graph into a given number of connected subgraphs with the minimum difference between the largest and the smallest weight in each subgraph. We propose a two-level Tabu Search algorithm and an Adaptive Large Neighborhood Search algorithm to solve the MGGPP in reasonable time on instances with up to about 23 000 vertices. The quality of the heuristic solutions is assessed comparing them with the solutions of a polynomially solvable combinatorial relaxation.