Minimum enclosing rectangles: a comparative investigation of two optimizing criteria (reprise)

The minimum enclosing rectangle problem for convex polygons has been studied and solved for both area and perimeter as optimality criterion. A specialized problem instance based on the square is known to admit different solutions for each criterion. The lack of empirical data relating solutions to the two problems when problem instances were generated at random served as impetus to experiments reported earlier. In the present work, the authors report results of another variant of the experiment together with the earlier findings. Under the conditions in which the present experiments were run, the polygons that admit different solutions are rare, occurring only less than 5% of the time