On the effectiveness of the genetic paradigm for polygonization

A polygon is simple if it is a closed chain of straight line segments that do not self-intersect. Given a finite set P of input points in the Euclidean plane, the search for a simple polygon with vertex set P is a very well-known and studied computational problem, referred to as the simple polygonization. Its optimization version, that requires to find a simple polygon having either minimum or maximum area, is known to be NP-hard. Moreover, no bounded approximation algorithm is known for the minimization flavor, while the maximization one admits an algorithm guaranteeing [Formula presented] worst-case approximation ratio. In this work, we design a new algorithm to practically attack both the optimization problems, based on the genetic paradigm. We demonstrate its effectiveness through an extensive experimental evaluation that employs a reference test-bed set of input instances.