Inside the Black Box of Mathematical Optimization…
We are going to talk about mathematical optimization. This term is not to be confused with the word ‘optimization’ that we use in our everyday lives, for instance, improving the efficiency of a workflow. This kind of optimization means to find an optimal solution from a set of possible candidate solutions. An optimization problem is generally given in the following way: one, there is a set of variables we can play with, and two, there is an objective function that we wish to minimize or maximize.
Let’s build a better understanding of this concept through an example. For instance, let’s imagine that we have to cook a meal for our friends from a given set of ingredients. The question is, how much salt, vegetables and meat goes into the pan. These are our variables that we can adjust, and the goal is to choose the optimal amount of these ingredients to maximize the tastiness of the meal. Tastiness will be our objective function, and for a moment, we shall pretend that tastiness is an objective measure of a meal.
What does this mean in practice? In our cooking example, after making several meals, we would ask our guests about the tastiness of these meals. From their responses, we would recognize that adding a bit more salt led to very favorable results, and since these people are notorious meat eaters, decreasing the amount of vegetables and increasing the meat content also led to favorable reviews. Therefore, on the back of this newfound knowledge, will cook more with these variable changes in pursuit of the “best possible meal in the history of mankind”.