Greedy and Local Search Heuristics to Build Area-Optimal Polygons

TL;DR

This paper introduces heuristic algorithms based on greedy and local search paradigms to construct area-optimal polygons with a given set of vertices, focusing on efficiency and solution quality.

Contribution

It presents novel heuristic methods for maximum and minimum area polygon problems using greedy and local search strategies, with implementation techniques for efficiency.

Findings

Effective heuristics for area-optimization of polygons

Strategies to avoid long edges improve solution quality

Implementation techniques reduce running time

Abstract

In this paper, we present our heuristic solutions to the problems of finding the maximum and minimum area polygons with a given set of vertices. Our solutions are based mostly on two simple algorithmic paradigms: greedy method and local search. The greedy heuristic starts with a simple polygon and adds vertices one by one, according to a weight function. A crucial ingredient to obtain good solutions is the choice of an appropriate weight function that avoids long edges. The local search part consists of moving consecutive vertices to another location in the polygonal chain. We also discuss the different implementation techniques that are necessary to reduce the running time.