Approximations on Minimum Weight Pseudo-triangulation Problem Using Ant Colony Optimization Metaheuristic

Abstract

In this work, we consider the Minimum Weight Pseudo-Triangulation (MWPT) problem of a given set of $n$ points in the plane. Globally optimal pseudo-triangulations with respect to the $weight$, as optimization criteria, are difficult to be found by deterministic methods, since no polynomial algorithm is known. We show how the Ant Colony Optimization (ACO) metaheuristic can be used to find high quality pseudo-triangulations of minimum weight. We present the experimental and statistical study based on our own set of instances since no reference to benchmarks for these problems were found in the literature. Throughout the experimental evaluation, we appraise the ACO metaheuristic performance for MWPT problem.