Optimization is everywhere, from engineering design to financial markets, from our daily activity to planning our holidays, and computer sciences to in dustrial applications. We always intend to maximize or minimize something. An organization wants to maximize its profits, minimize costs, and maximize performance. Even when we plan our holidays, we want to maximize our enjoyment with least cost (or ideally free). In fact, we are constantly search ing for the optimal solutions to every problem we meet, though we are not necessarily able to find such solutions.
It is no exaggeration to say that finding the solution to optimization prob lems, whether intentionally or subconsciously, is as old as human history itself. For example, the least effort principle can often explain many human behav iors. We know the shortest distance between any two different points on a plane is a straight line, though it often needs complex maths such as the cal culus of variations to formally prove that a straight line segment between the two points is indeed the shortest.
In fact, many physical phenomena are governed by the so-called least ac tion principle or its variants. For example, light travels and obeys Fermat's principle, that is to travel at the shortest time from one medium to another,