Quality Indicator Maximization in Multiobjective Optimization Via Single-Objective Solvers

author: Dimo Brockhoff, INRIA Saclay - Île-de-France
published: May 6, 2019,   recorded: April 2019,   views: 145
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Multiobjective Optimization problems appear frequently in practice when multiple objective functions need to be optimized simultaneously. Often, a multiobjective problem is approached by aiming to find a set of p solutions that maximizes a given quality, for example as defined by the hypervolume indicator. In this talk, I will present a new multiobjective framework which attacks the optimization of p solutions in a search space of dimension n towards the maximum of a quality indicator by successive dynamic (single-objective) subspace optimization of an n times p dimensional problem. When instantiated as the COMO-CMA-ES with an "unflattened" version of the hypervolume improvement and the well-known CMA-ES as single-objective solver, we observe linear convergence to the optimal placement of p solutions with respect to the hypervolume indicator on various bi-objective convex-quadratic problems. In addition to the general idea of the framework and details on the concrete COMO-CMA-ES, I will present in particular the intuition why the choice of the "unflattened" hypervolume is crucial to the performance of the algorithm. The presentation of benchmarking data from comparisons with other well-known multiobjective algorithms on the bbob-biobj suite of the COCO platform will top off the presentation. This presentation is based on work with Cheikh Touré, Anne Auger, and Nikolaus Hansen: "Unflattened Hypervolume Improvement for Multiobjective Problems: COMO-CMA-ES and the Sofomore framework", accepted at GECCO-2019

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