Achieving Diversity in Objective Space for Sample-efficient Search of Multiobjective Optimization Problems

As mathematical, statistical, and machine learning algorithms leverage increasingly powerful computational hardware to perform elaborate tasks, simulation has grown to play a key role in fields such as materials science, operations research, industrial engineering, aerodynamics, pharmaceuticals, image processing, and many others. In particular, a key use of these simulations is to serve as a surrogate for the eventual implementation and/or manufacturing during the design optimization; running a computational simulation is likely much cheaper than actually conducting a physical experiment or fabrication (Forrester et al. 2008; Negoescu et al. 2011; Molesky et al. 2018; Haghanifar et al. 2020). Computational simulations can, however, easily run for hours or days, making simulation itself an often costly proposition. The high cost of a single simulation is compounded by the frequent need to simulate many different systems to search for a set of desirable outcomes. This is the motivating force behind simulation optimization, which seeks to identify suitable system parameters to achieve a satisfactory system or effective simulation in a sample-efficient fashion, i.e., with as few simulations conducted as possible. In practical situations, simulations almost always have multiple competing objectives which define success, and thus it is important for users to understand trade-offs between these competing objectives in order to make an informed design decision. Multiobjective optimization tackles this problem by identifying the Pareto frontier, which is the manifold in objective space such that improving one objective cannot occur without harming another. Unfortunately, using the Pareto frontier as the measurement of success may be limiting in engineering and design applications.