Minimum enclosing rectangles: a comparative investigation of two optimizing criteria

The minimum-enclosing-rectangle problem for convex polygons has previously been studied and solved for both area and perimeter as the optimal criterion, but no empirical data are known to exist that relate to each other the solutions to the two problems. A specialized problem instance based on the square is known to admit different solutions for each criterion. The authors randomly generate a large set of problem instances, solve both types of optimization problems, and then tabulate the results to obtain a firmer idea of the relationship between the two solutions. It is found that, indeed, in the environment under which the experiment was run, the polygons that admit different solutions are rare, occurring only less than 5% of the time