- The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. - Claude Shannon
- Here information can be thought of a being transmitted across time (by taking photographs of an event to document it) or across space (from Mumbai to Delhi) The way I imagine information theory can be used in optimization is best explained using an analogy. Suppose a man treks across a particularly tricky piece of terrain. There are numerous life-threatening obstacles in our mans path but being the intrepid traveler that he is, he successfully crosses the terrain. Now with that knowledges gained from his trek, the traveler sends information across space by using a transmitter to communicate to his team mates the safest path through the terrain. Or he may send information across time by putting up placards warning of the particularly dangerous bits of the terrain. So, how does this have anything to do with optimization?
- Usually, in practical business settings where optimization is used on a a regular basis we solve the same problem frequently with data changing across instances. Let us imagine that we are responsible for the scheduling production jobs for a small firm manufacturing firm. We use a constraint programming solver to create schedules which minimize the makespan. We use the solver every week to create schedules. After creating schedules for a bout a year, we realise that the solver runs and tries to solve the same problem, albeit with different demands, every week. The solver run of today does not consult with the solver run of yesterday. The question is useful to do so?