Approximations on minimum weight pseudo-triangulations using ant colony optimization metaheuristic

Abstract

Globally optimal pseudo-triangulations are di cult to be found by deterministic methods as, for most type of criteria, no polynomial algorithm is known. In this work, we consider the Minimum Weight Pseudo-Triangulation (MWPT) problem of a given set of n points in the plane. This paper shows how the Ant Colony Optimization (ACO) metaheuristic can be used to nd optimal pseudo-triangulations of minimum weight. For the experimental study presented here we have created a set of instances for MWPT since no reference to benchmarks for these problems were found in the literature. We assess through the experimental evaluation the applicability of the ACO metaheuristic for MWPT.