Optimization in the shopping mall

Assume we are planning to visit a shopping mall, and the plan is to get ourselves a new fancy dress.

Universe and problem parameters

There are a number of boutiques and department stores,
offering all sorts of clothes. This is called the problem universe. Our
particular problem depends on the problem parameters, such as size, weight, age, and the fact we want a dress rather than a hat.

Search space and candidates

The collection of all dresses in the universe that fit
our body make up our personal search space. Each of them is a candidate we
might choose.

Optimization objectives

Since we want to choose one of the candidate dresses, we should have a clearly defined objective.

We may choose the cheapest or the most elegant, the most sincere or the one most resembling beloved worn-out rag in our home closet. There are hundreds of objectives.

Common objectives:

- the deepest blue
- the most fashionable design
- the best ratio of elegance over price

Not so common, but perfectly legal:

- buy everything (everything that fits - remember the rest is not in our search space)
- buy all the black ones
- buy nothing, but take a picture of everything and a complete list of prices.

Persuing our objective means to evaluate each candidate to obtain some rating, often called a score, and eventually make a choice based on all scores.

Summary

In face of an optimization problem, we use the following terminology

- Problem universe: Everything that could be considered a solution.
- Problem parameters: Define a particular instance of the problem.
- Problem search space: The candidates in the universe that fit to the problem parameters.
- Problem objective: Each candidate is evaluated and yields some score. Based on the scores, we make a choice.

The rules of the game

To keep things straight, we strictly adhere to the following rules:

- For given problem parameters, we will always consider
__all__the candidates in the search space, but__no__other elements in the universe. - Our choice will be based on the scores, and no other attributes of the candidate.