What is multi-objective optimization?

The goal of single-objective optimization is simple. You have some kind of objective/function/metric/fitness/criterion that you would like to optimize (that is maximize or minimize) given some input parameters. Examples are optimizing the title (the input) of a youtube-video to maximize the number of views (the objective) or optimizing the route (the input) to minimize the traveling time (the objective).

While these tasks are examples of “high-level” problems, the use of optimization is also frequently used in different types of low-level engineering and/or mathematical problems. For instance, in most machine learning algorithms some kind of optimization algorithm is working under the hood to find the parameters. In neural networks, an optimization algorithm called backpropagation (you can read about it here) is used and in Gaussian mixture models an optimization algorithm called expectation–maximization (you can read more about it here) is used.

But in many problems (and in most real-world problems) there isn’t just a single objective. Take investing for instance, while naturally you would like to optimize the return, there is always the aspect of risk. If you decrease the risk you will often decrease the return and vice versa. Another example would be advertising; you would like…