On the use of polynomial models in multiobjective directional direct search

Brás, Carmo P.; Custódio, A. L.

doi:10.1007/s10589-020-00233-8

Cited by 10 publications

(14 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, many extensions could be implemented to improve performance of DMulti-MADS: search strategies assisted by surrogate models [14,19] or global search strategies [21], parallelism, taking into account general inequality constraints [31] and so on. An integration of this algorithm in NOMAD is also planned.…”

Section: Discussionmentioning

confidence: 99%

DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization

2021

View full text Add to dashboard Cite

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 multiobjective derivative-free optimization with bound constraints. 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.

show abstract

Section: Discussionmentioning

confidence: 99%

DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization

2021

View full text Add to dashboard Cite

show abstract

“…BoostDMS [10] is a numerical implementation of a Direct Multisearch [15] algorithm, where the individual or joint minimization of quadratic polynomial models, built for each component of the objective function, is used in the definition of a search step.…”

Section: Boostdms Implementation Of Direct Multisearchmentioning

confidence: 99%

“…A simplified description of BoostDMS is provided in Algorithm 1. For a detailed description see [10,15].…”

Section: Boostdms Implementation Of Direct Multisearchmentioning

confidence: 99%

“…denotes the Lebesgue measure of a q-dimensional set of points and [x, U p ] denotes the interval box with lower corner x and upper corner U p . The approach proposed in [23] was used for its computation, after scaling all the hypervolume values to the interval [0, 1] (see [10] for details).…”

Section: Parallelization Strategiesmentioning

confidence: 99%

“…However, since its first version, in 2010, new releases corresponded to small improvements of the original implementation, with no major changes. Exception occurred in [10], where the definition of a search step based on the minimization of quadratic polynomial models was proposed. This new version of the code was named as Boost-DMS.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Parallel Strategies for Direct Multisearch

Tavares¹,

Brás²,

Custódio³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Direct Multisearch (DMS) is a Derivative-free Optimization class of algorithms suited for computing approximations to the complete Pareto front of a given Multiobjective Optimization problem. It has a well-supported convergence analysis and simple implementations present a good numerical performance, both in academic test sets and in real applications. Recently, this numerical performance was improved with the definition of a search step based on the minimization of quadratic polynomial models, corresponding to the algorithm BoostDMS.In this work, we propose and numerically evaluate the performance of parallelization strategies for this solver, applied to the search and to the poll steps. The final parallelized version not only considerably decreases the computational time required for solving a Multiobjective Optimization problem, but also increases the quality of the computed approximation to the Pareto front. Extensive numerical results will be reported in an academic test set and in a chemical engineering application.

show abstract