TY - GEN
T1 - Multiobjective Optimization with a Quadratic Surrogate-Assisted CMA-ES
AU - Gharafi, Mohamed
AU - Hansen, Nikolaus
AU - Brockhoff, Dimo
AU - Le Riche, Rodolphe
N1 - Publisher Copyright:
© 2023 ACM.
PY - 2023/7/15
Y1 - 2023/7/15
N2 - We present a surrogate-Assisted multiobjective optimization algorithm. The aggregation of the objectives relies on the Uncrowded Hypervolume Improvement (UHVI) which is partly replaced by a linear-quadratic surrogate that is integrated into the CMA-ES algorithm. Surrogating the UHVI poses two challenges. First, the UHVI is a dynamic function, changing with the empirical Pareto set. Second, it is a composite function, defined differently for dominated and nondominated points. The presented algorithm is thought to be used with expensive functions of moderate dimension (up to about 50) with a quadratic surrogate which is updated based on its ranking ability. We report numerical experiments which include tests on the COCO benchmark. The algorithm shows in particular linear convergence on the double sphere function with a convergence rate that is 6-20 times faster than without surrogate assistance.
AB - We present a surrogate-Assisted multiobjective optimization algorithm. The aggregation of the objectives relies on the Uncrowded Hypervolume Improvement (UHVI) which is partly replaced by a linear-quadratic surrogate that is integrated into the CMA-ES algorithm. Surrogating the UHVI poses two challenges. First, the UHVI is a dynamic function, changing with the empirical Pareto set. Second, it is a composite function, defined differently for dominated and nondominated points. The presented algorithm is thought to be used with expensive functions of moderate dimension (up to about 50) with a quadratic surrogate which is updated based on its ranking ability. We report numerical experiments which include tests on the COCO benchmark. The algorithm shows in particular linear convergence on the double sphere function with a convergence rate that is 6-20 times faster than without surrogate assistance.
KW - CMA-ES
KW - evolution strategies
KW - multiobjective optimization
KW - quadratic metamodel
KW - surrogate-Assisted optimization
UR - https://www.scopus.com/pages/publications/85167691769
U2 - 10.1145/3583131.3590492
DO - 10.1145/3583131.3590492
M3 - Conference contribution
AN - SCOPUS:85167691769
T3 - GECCO 2023 - Proceedings of the 2023 Genetic and Evolutionary Computation Conference
SP - 652
EP - 660
BT - GECCO 2023 - Proceedings of the 2023 Genetic and Evolutionary Computation Conference
PB - Association for Computing Machinery, Inc
T2 - 2023 Genetic and Evolutionary Computation Conference, GECCO 2023
Y2 - 15 July 2023 through 19 July 2023
ER -