A Cautionary Note on Optimization [Antenna Designer's Notebook]

It is always nice to be told that one's solution to a problem is optimal. We like to think we have the best solution, even though as engineers, we should be aware that for very few problems is the quality of the solution really a uni-dimensional variable with a unique maximum. In the real world, a "best solution" is usually the result of painstaking exploration of a Pareto frontier, the dimensions of which do not in general lend themselves to being neatly bundled a priori in some scalar function.