Area Optimal Polygonization Using Simulated Annealing

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.