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.

中文翻译：

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贪婪和局部搜索启发式构建区域最优多边形

在本文中，我们提出了我们的启发式解决方案，用于寻找具有给定顶点集的最大和最小面积多边形的问题。我们的解决方案主要基于两个简单的算法范式：贪婪方法和局部搜索。贪心启发式从一个简单的多边形开始，并根据权重函数一个一个地添加顶点。获得良好解决方案的一个关键因素是选择合适的权重函数，以避免长边。局部搜索部分包括将连续顶点移动到多边形链中的另一个位置。我们还讨论了减少运行时间所需的不同实现技术。