Global and Local Multiobjective Optimization using Direct Search

A solver for global multiobjective derivative-free optimization

The optimization of multimodal functions is a challenging task, in particular when derivatives are not available for use. MultiGLODS is a solver suited for global multiobjective constrained optimization which does not use any derivatives of the objective functions.

Using direct search of directional type, the algorithm alternates between a search step, where potentially good regions are located, and a poll step where the previously located promising regions are explored. Components of the objective function are not aggregated and new points are accepted using the concept of Pareto dominance. The initialized searches are not all conducted until the end, merging when start to be close to each other, this way keeping affordable computational budgets in terms of number of functions evaluations.

In the end of the optimization process, the set of all active points will define the approximations to the Pareto fronts of the problem (local and global).

  • MultiGLODS (Version 0.1, December 2016) is written in Matlab.
  • Version 0.1 (December 2016 of MultiGLODS can be obtained by sending an e-mail.

MultiGLODS is freely available for research, educational or commercial use, under a GNU lesser general public license.

References and complementary material:

  • A. L. Custódio and J. F. A. Madeira, MultiGLODS: Global and Local Multiobjective Optimization using Direct Search, Journal of Global Optimization, 72 (2018), 323 - 345 PDF

The MultiGLODS team:
Ana Luísa Custódio (Universidade Nova de Lisboa)
José F. Aguilar Madeira (ISEL and IDMEC-IST, Lisbon)