As the name implies, multi-objective optimization problems are a class of problems in which one seeks to optimize over multiple, conflicting objectives.

Optimizing over one objective is relatively easy: given information on traffic, a navigation app can suggest which route it expects to be the fastest. But if you have multiple objectives this problem become complicated: if, for example, you want a reasonably fast route that won’t use too much gas and gives you time to take in the view outside your window.

Or, perhaps, you have multiple deadlines pending and you want to do perfectly on all of them, but you also have limited time and would like to eat and maybe sleep sometime, too. How do you prioritize your time? How do you optimize over all the possible things you could be doing?

This is not easy.

Rather than having a single, optimal solution, these problems have a set of solutions, known as the Pareto front. Each of these solutions is equally optimal mathematically, but each represents a different trade-off in optimization of the features.

Using 3D Rad-Viz, Ibrahim et al. have visualized the complexity of the Pareto front, showing the bumpy landscape these solution spaces have.

Chen et al. take a somewhat different approach – designing a tool to allow a user to interact with the Pareto front, visually seeing the trade-offs each solution implicitly makes and allowing a user to select the solutions they see as best meeting their needs: