Area Optimal Polygonization Using Simulated Annealing

Abstract

We describe a practical method to find near-optimal solutions for the area-optimal simple polygonization problem: Given a set of points S in the plane, the objective is to find a simple polygon of minimum or maximum area defined by S . Our approach is based on the celebrated metaheuristic Simulated Annealing. The method consists of a modular pipeline of steps, where each step can be implemented in various ways and with several parameters controlling it. We have implemented several different algorithms and created an application that computes a polygon with minimal (or maximal) area. We experimented with the various algorithmic options and with the controlling parameters of each algorithm to tune up the pipeline. Then, we executed the application on each of the benchmark instances, exploiting a grid of servers, to obtain near optimal results.

Area-Optimal Simple Polygonalizations: The CG Challenge 2019

“…• Julien Lepagnot, Laurent Moalic, Dominique Schmitt: Optimal area polygonization by triangulation and raytracing [19] • Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard: Greedy and Local Search Solutions to the Minimum and Maximum Are [7] • Nir Goren, Efi Fogel, Dan Halperin: Area-optimal polygonization using simulated annealing [18] • Günther Eder, Martin Held, Steinpor Jasonarson, Philipp Mayer, Peter Palfrader: 2-Opt moves and flips for area-optimal polygonizations [9] • Natanael Ramos, Rai Caetan de Jesus, Pedro de Rezende, Cid de Souza, Fabio Luiz Usberti: Heuristics for area optimal polygonizations [29] In addition, there is one paper focusing on exact methods for computing provably optimal solutions.…”

“…2 0 1 9 -0 3 -0 1 2 0 1 9 -0 3 -1 5 2 0 1 9 -0 4 -0 1 2 0 1 9 -0 4 -1 5 2 0 1 9 -0 5 -0 1 2 0 1 9 -0 5 -1 5 2 0 1 9 -0 6 -0 1 (1) Team OMEGA/Mulhouse (France): Julien Lepagnot, Laurent Moalic, Dominique Schmitt [19] (2) Team lcrombez/Clermont Auvergne(France): Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard [7] (3) Team cgl@tau/Tel Aviv (Israel): Nir Goren, Efi Fogel, Dan Halperin [18] (4) Team CGA/Salzburg (France): Günther Eder, Martin Held, Steinthor Jasonarson, Philipp Mayer, Peter Palfrader [9].…”

Area-Optimal Simple Polygonalizations: The CG Challenge 2019

“…)-Loïc Crombez, Guilherme D. da Fonseca, Yan Gerard: Greedy and local search solutions to the minimum and maximum area[7]. -Nir Goren, Efi Fogel, Dan Halperin: Area-optimal polygonization using simulated annealing[18]. -Günther Eder, Martin Held, Steinpor Jasonarson, Philipp Mayer, Peter Palfrader: 2-Opt moves and flips for area-optimal polygonizations[9].…”