Pareto-optimality is everywhere: From engineering design, machine learning, to biological systems

This talk attempts to argue that almost all adaptive systems have multiple objectives to achieve. Very often, there is no single solution that can optimize all objectives, in which case, the concept of Pareto-optimization plays an important rule. Examples will be given ranging from engineering design, machine learning, to biological systems to show how Pareto-optimality can make a difference in analyzing these systems. The first example we will discuss is the aerodynamic design optimization of turbine blades, where energy efficiency in terms of pressure loss as well as the variation of pressure distribution must be minimized. One additional difficulty in aerodynamic design optimization is that the quality of candidate designs must be assessed by performing computational fluid dynamics analysis, which is very time consuming. To reduce computation time, computational techniques like parallel computation, and machine learning techniques, such as meta-modeling can be employed. Surprisingly interesting results will also be achieved when the concept of Pareto-optimality is applied to machine learning. Two cases will be provided to illustrate this idea. In the first case, we show how Pareto-based approach can address neural network regularization more elegantly, through which deeper insights into the problem can be gained. In the second case, we show that analysis of the Pareto-optimal solutions will help determine the optimal number of clusters in data clustering, which again shown how the Pareto front can disclose additional knowledge about the problem at hand. The final example is concerned with tradeoffs in simulated evolution of genetic representation. It has been argued that robustness is critical for biological evolution, because without certain degree of robustness to mutations, it is impossible for evolution to create new functionalities. Therefore, evolution must find representations that are sufficiently robust yet have the potential to innovate. Examples will be given to show that such tradeoff does exist in evolving both a stationary genotype-phenotype mapping, and also a gene regulatory network described by a random Boolean network.