Evolutionary robust optimization with multiple solutions

When optimizing for multiple environments, one usually needs to sacrifice performance in one environment in order to gain better performance in another. Ultimately, there may not be a single solution that meets the performance requirements for all environments. In this paper, we propose to find multiple solutions that each serve a certain group of environments. We call this formulation Robust Optimization with Multiple Solutions (ROMS). Two evolutionary approaches to ROMS are proposed, namely direct evolution and twophase evolution. A benchmark problem generator is also suggested to produce uniform-random ROMS problems. The two approaches are then experimentally studied on a variety of synthetic problems.