I am looking some problem, which would be:
- Easy to understand
- Hard to solve intuitively
- Touch our everyday lives
I am doing research in optimization using evolutionary computation. When people ask me what I do, I have no problem to explain evolutionary computation, but it is hard to get across the idea of optimization. It seems that optimization has many meanings in the real world, such as "optimize your daily routine", "optimize the landing page"... and these meaning are very different from the formal concept of mathematical optimization.
I think I could get my point across better if I used some example from the real world. Something that has real impact on the lives of people and something that they are in contact with every day. One such example is the optimization of the shape of the nose of the Shinkansen bullet train. The nose has a very complicated shape that tries to optimize several aerodynamic criteria. The problem is that to explain this problem I would have to explain how a shape can be parametrized and converted to numbers. And again I would have to explain how the aerodynamic properties of a given shape are tested using physics simulations.
I thought about the Travelling salesman problem, but this sounds like a toy problem, since there are no more travelling salesmen. I am aware that TSP has many industrial applications, but explaining those applications takes us away from everyday life.
Similarly the Knapsack problem seems to be a toy problem, since when we are packing to go somewhere usually we can solve the problem very nicely using our intuition. Moreover, when we pack for a vacation, we do not follow the maximization of utility procedure, but a more complicated mental process. Also, someone always finds the solution of just inserting the item with the highest value/mass ratio, until we reach the mass limit and it is hard to persuade the person, that this is not necessarily optimal.