This paper attempts to argue that most adaptive systems, such as evolutionary or learning systems, have inherently multiple objectives to deal with. Very often, there is no single solution that can optimize all the objectives. In this case, the concept of Pareto optimality is key to analyzing these systems.

To support this argument, we first present an example that considers the robustness and evolvability trade-off in a redundant genetic representation for simulated evolution. It is well known that robustness is critical for biological evolution, since without a sufficient degree of mutational robustness, it is impossible for evolution to create new functionalities. On the other hand, the genetic representation should also provide the chance to find new phenotypes, i.e., the ability to innovate. This example shows quantitatively that a trade-off between robustness and innovation does exist in the studied redundant representation.

Interesting results will also be given to show that new insights into learning problems can be gained when the concept of Pareto optimality is applied to machine learning. In the first example, a Pareto-based multi-objective approach is employed to alleviate catastrophic forgetting in neural network learning. We show that learning new information and memorizing learned knowledge are two conflicting objectives, and a major part of both information can be memorized when the multi-objective learning approach is adopted. In the second example, we demonstrate that a Pareto-based approach can address neural network regularizationmore elegantly. By analyzing the Pareto-optimal solutions, it is possible to identifying interesting solutions on the Pareto front.