What is Optimization?

To optimize something generally means to make it the best it can possibly be. For a business, optimization might involve producing a product with the minimum, or, lowest cost possible. An athlete's optimal performance could be their fastest race, highest jump, or greatest number of points scored.

These are simple ways of looking at optimization--in many cases, optimization can be a fairly complicated thing. For example, a basketball player's optimal performance might not simply be "most points scored," but a combination of points scored, rebounds, and assists.

Why is optimization important?

One of the most important roles mathematics plays in the world is that of reducing complex problems to simple algorithms that an idiot (or a computer) could follow to the desired solution. In many, many real world applications, the object is to find the least expensive, or the most environmentally safe, or the fastest solution from a huge number of possible solutions. These are all optimization problems, each one with important bearing on the success of a business, the survival of an ecosystem, or an individual's daily schedule.

Why use a computer for optimization?

Many optimization problems require the selection of the best possibility from a staggeringly huge number of choices. Even when we can use some mathematical technique to narrow the field of choices a bit, that technique itself can require millions of computations. Since there is not always a graduate student available, these millions of computations are often assigned to a computer.

This document is an introduction to the general idea of optimization. If you are interested in classroom activities involving optimization, or a computer program (RealSim Surface) that performs an optimization, follow the appropriate link.