We present a framework to build a multiobjective algorithm from single-objective ones. This framework addresses the p × 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.
Publié le : 2019-07-13
Classification:
Hypervolume improvement,
CCS CONCEPTS • Mathematics of computing → Nonconvex optimization,
Multiobjective optimization,
Single-objective optimization,
Hypervolume,
Quality indicator,
Hypervolume contribution,
[INFO]Computer Science [cs],
[INFO.INFO-NE]Computer Science [cs]/Neural and Evolutionary Computing [cs.NE],
[MATH]Mathematics [math],
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-02103694,
author = {Tour\'e, Cheikh and Hansen, Nikolaus and Auger, Anne and Brockhoff, Dimo},
title = {Uncrowded Hypervolume Improvement: COMO-CMA-ES and the Sofomore framework},
journal = {HAL},
volume = {2019},
number = {0},
year = {2019},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-02103694}
}
Touré, Cheikh; Hansen, Nikolaus; Auger, Anne; Brockhoff, Dimo. Uncrowded Hypervolume Improvement: COMO-CMA-ES and the Sofomore framework. HAL, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/hal-02103694/