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DMulti-MADS: Mesh adaptive direct multisearch for blackbox multiobjective optimization

Jean Bigeon(jean.bigeon***at***grenoble-inp.fr)
Sébastien Le Digabel(sebastien.le.digabel***at***gerad.ca)
Ludovic Salomon(ludovic.salomon***at***gerad.ca)

Abstract: The context of this research is multiobjective optimization where conflicting objectives are present. In this work, these objectives are only available as the outputs of a blackbox for which no derivative information is available. This work proposes a new extension of the mesh adaptive direct search (MADS) algorithm to constrained multiobjective derivative-free optimization. This method does not aggregate objectives and keeps a list of non dominated points which converges to a (local) Pareto set as long as the algorithm unfolds. As in the single-objective optimization MADS algorithm, this method is built around a search step and a poll step. Under classical direct search assumptions, it is proved that the so-called DMulti-MADS algorithm generates multiple subsequences of iterates which converge to a set of local Pareto stationary points. Finally, computational experiments suggest that this approach is competitive compared to the state-of-the-art algorithms for multiobjective blackbox optimization.

Keywords: Multiobjective optimization, derivative-free optimization, blackbox optimization, mesh adaptive direct search, Clarke analysis.

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Other )

Category 3: Other Topics (Multi-Criteria Optimization )

Citation:

Download: [PDF]

Entry Submitted: 04/16/2020
Entry Accepted: 04/16/2020
Entry Last Modified: 04/16/2020

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