Affiliations: Facultad de Ciencias Físico Matemáticas y Naturales, Universidad Nacional de San Luis, San Luis, Argentina, {mgdorzan, oli, legui}@unsl.edu.ar | Universidad Politécnica de Madrid, Madrid, España, [email protected]
Note: [] Address for correspondence: Ejército de Los Andes 950 - D5700HHW - San Luis - Argentina
Abstract: Globally optimal triangulations and pseudo-triangulations are difficult 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 Triangulation (MWT) and Minimum Weight Pseudo-Triangulation (MWPT) problems of a given set of n points in the plane. This paper shows how the Ant Colony Optimization (ACO) metaheuristic can be used to find high quality triangulations and pseudo-triangulations of minimum weight. For the experimental study presented here we have created a set of instances for MWT and MWPT problems since no reference to benchmarks for these problems were found in the literature. Through the experimental evaluation, we assess the applicability of the ACO metaheuristic for MWT and MWPT problems considering greedy and Simulated Annealing algorithms.
