TY - JOUR
T1 - Uncrowded Hypervolume-Based Multiobjective Optimization with Gene-Pool Optimal Mixing
AU - Maree, S. C.
AU - Alderliesten, T.
AU - Bosman, P. A. N.
N1 - Funding Information: This work is part of the research programme IPPSI-TA with project number 628.006.003, which is financed by the Dutch Research Council (NWO) and Elekta. We acknowledge financial support of the Nijbakker-Morra Foundation for a high-performance computing system. Publisher Copyright: © 2022, MIT Press Journals. All rights reserved.
PY - 2022/9/1
Y1 - 2022/9/1
N2 - Domination-based multiobjective (MO) evolutionary algorithms (EAs) are today arguably the most frequently used type of MOEA. These methods, however, stagnate when the majority of the population becomes nondominated, preventing further convergence to the Pareto set. Hypervolume-based MO optimization has shown promising results to overcome this. Direct use of the hypervolume, however, results in no selection pressure for dominated solutions. The recently introduced Sofomore framework overcomes this by solving multiple interleaved single-objective dynamic problems that iteratively improve a single approximation set, based on the uncrowded hypervolume improvement (UHVI). It thereby however loses many advantages of population-based MO optimization, such as handling multimodality. Here, we reformulate the UHVI as a quality measure for approximation sets, called the uncrowded hypervolume (UHV), which can be used to directly solve MO optimization problems with a single-objective optimizer. We use the state-of-the-art gene-pool optimal mixing evolutionary algorithm (GOMEA) that is capable of efficiently exploiting the intrinsically available grey-box properties of this problem. The resulting algorithm, UHV-GOMEA, is compared with Sofomore equipped with GOMEA, and the domination-based MO-GOMEA. In doing so, we investigate in which scenarios either domination-based or hypervolume-based methods are preferred. Finally, we construct a simple hybrid approach that combines MO-GOMEA with UHV-GOMEA and outperforms both.
AB - Domination-based multiobjective (MO) evolutionary algorithms (EAs) are today arguably the most frequently used type of MOEA. These methods, however, stagnate when the majority of the population becomes nondominated, preventing further convergence to the Pareto set. Hypervolume-based MO optimization has shown promising results to overcome this. Direct use of the hypervolume, however, results in no selection pressure for dominated solutions. The recently introduced Sofomore framework overcomes this by solving multiple interleaved single-objective dynamic problems that iteratively improve a single approximation set, based on the uncrowded hypervolume improvement (UHVI). It thereby however loses many advantages of population-based MO optimization, such as handling multimodality. Here, we reformulate the UHVI as a quality measure for approximation sets, called the uncrowded hypervolume (UHV), which can be used to directly solve MO optimization problems with a single-objective optimizer. We use the state-of-the-art gene-pool optimal mixing evolutionary algorithm (GOMEA) that is capable of efficiently exploiting the intrinsically available grey-box properties of this problem. The resulting algorithm, UHV-GOMEA, is compared with Sofomore equipped with GOMEA, and the domination-based MO-GOMEA. In doing so, we investigate in which scenarios either domination-based or hypervolume-based methods are preferred. Finally, we construct a simple hybrid approach that combines MO-GOMEA with UHV-GOMEA and outperforms both.
KW - Multiobjective optimization
KW - black-box optimization
KW - hypervolume indicator
UR - http://www.scopus.com/inward/record.url?scp=85137136391&partnerID=8YFLogxK
U2 - https://doi.org/10.1162/evco_a_00303
DO - https://doi.org/10.1162/evco_a_00303
M3 - Article
C2 - 34878530
SN - 1063-6560
VL - 30
SP - 329
EP - 353
JO - Evolutionary Computation
JF - Evolutionary Computation
IS - 3
ER -