BoostDFO: Improving the performance and moving to newer dimensions in Derivative-Free Optimization

Research grant PTDC/MAT-APL/28400/2017 funded by 

October 2018 - September 2021 

Doctoral Members: 
Ana Luísa Custódio (PI), Pedro Medeiros (co-PI), Maria do Carmo Brás, Rohollah Garmanjani, and Vítor Duarte

Students: Aboozar Mohammadi, Sérgio Tavares
Milagros Loreto (University of Washington Bothell) and Luís Nunes Vicente (Lehigh University)


The goal of this project is to develop efficient and robust algorithms for Global and/or Multiobjective Derivative-free Optimization. This type of optimization is typically required in complex scientific/industrial applications, where the function evaluation is time consuming and derivatives are not available for use, neither can be numerically approximated. Often problems present several conflicting objectives or users aspire to obtain global solutions.

Inspired by successful approaches used in single objective local Derivative-free Optimization, and resourcing to parallel/cloud computing, new numerical algorithms will be proposed and analyzed. As result, an integrated toolbox for solving multi/single objective, global/local Derivative-free Optimization problems will be available, taking advantage of parallelization and cloud computing, providing an easy access to several efficient and robust algorithms, and allowing to tackle harder Derivative-free Optimization problems.


Related publications:

R. G. Begiato, A. L. Custódio, and M. A. Gomes-Ruggiero, A global hybrid derivative-free method for high-dimensional systems of nonlinear equations, Computational Optimization and Applications, 2019, (online published) DOI 10.1007/s10589-019-00149-y

C. P. Brás and A. L. Custódio, On the use of polynomial models in multiobjective directional direct search, 2019 (submitted)

A. L. Custódio, Y. Diouane, R. Garmanjani, and E. Riccietti, Worst-case complexity bounds of directional direct-search methods for multiobjective derivative-free optimization, 2019 (submitted)


Computational codes:

BoostDMS is a multiobjective optimization solver which does not use any derivatives of the objective functions. The algorithm defines a search step based on quadratic polynomial models for Direct Multisearch (DMS).

Problem class: derivative-free multiobjective optimization problems with (or without) any type of constraints

Version 0.1, August 2019 (written in Matlab; request by sending an e-mail)