  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.
