Uncrowded Hypervolume Improvement: COMO-CMA-ES and the Sofomore framework
This work addresses multiobjective optimization for researchers and practitioners, presenting a novel framework but with incremental improvements as it builds on existing single-objective methods.
The authors tackled the problem of building a multiobjective optimization algorithm from single-objective ones by introducing the Sofomore framework, which uses dynamic subspace optimization to maximize an indicator, and instantiated it as COMO-CMA-ES, showing linear convergence on bi-objective convex-quadratic problems and comparing it to existing algorithms like MO-CMA-ES, NSGA-II, and SMS-EMOA.
We present a framework to build a multiobjective algorithm from single-objective ones. This framework addresses the $p \times n$-dimensional problem of finding p solutions in an n-dimensional search space, maximizing an indicator by dynamic subspace optimization. Each single-objective algorithm optimizes the indicator function given $p - 1$ fixed solutions. Crucially, dominated solutions minimize their distance to the empirical Pareto front defined by these $p - 1$ solutions. We instantiate the framework with CMA-ES as single-objective optimizer. The new algorithm, COMO-CMA-ES, is empirically shown to converge linearly on bi-objective convex-quadratic problems and is compared to MO-CMA-ES, NSGA-II and SMS-EMOA.