In daily life we are faced with an enormous number of decisions. Some of these decisions may be more important than others but imagine you could nail the best choice for all of them. Eating the breakfast that gets you through to lunch without feeling hungry or over-full, avoiding the motorway to get home 20 minutes earlier, and choosing the contract that saves your company millions.

## The basics

Optimisation is about finding the smallest, biggest, cheapest, most efficient, most valuable or least error prone solution to a problem. This can be achieved by a range of methods including finding direct mathematical solutions, searching through all of the possible solutions to find the best one or by using some really cool algorithm. Optimisation is about finding the best available answer as efficiently as possible.

## What does it look like?

One of the most famous optimisation problems, and a good example to get an understanding of how optimisation works is the travelling salesman problem. Imagine you’re a self employed salesperson who needs to visit a number of cities for sales meetings, and then get home at the end. You want to find the cheapest route you can because your travel expenses come out of the profits from the sales of your product.

“#Optimisation is about finding the best available answer to your problem as efficiently as possible.”

There is a “correct” cheapest answer to what order you should visit the cities, but when you have to visit more locations, it becomes really hard to find that answer. The number of possible routes you could take grows unbelievably quickly, while there is still only one shortest path. Optimisation seeks to overcome the complexity of the problem and still provide the best answer possible.

## Cheat sheet

Optimisation is a field of advanced research, and delving into the topic can lead you to all sorts of difficult terminology. We’ve got some common terms for you here to get you started.

Goal | The goal of an optimisation problem is the solution to be found, for example the order of travel which provides the cheapest route in the travelling salesman problem. |

Constraint | Some rule which must be taken into account which limits which solutions are possible. For example, you may only be able to get a flight to city A from city B. This will influence which solution is returned as the optimum. |

Approximation | Some optimisation problems get very complicated, just like the travelling salesman problem above when there are many places to visit. These problems can take an extremely long time to solve, even with the fastest supercomputers. Approximation involves finding a solution which will be close to the optimum, but can be found much more efficiently. |

Closed form solution | A closed form solution is an optimum solution which can be found directly using a mathematical equation. This is the ideal scenario as enormous problems can be solved as quickly as little ones, and the correct answer is guaranteed. |