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Parallel strategies for Direct Multisearch

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Abstract

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. In DMS class, constraints are addressed with an extreme barrier approach, only evaluating feasible points. 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 strategies to improve the performance of BoostDMS, mainly through parallelization 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.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

Support for authors was provided by national funds through FCT – Fundação para a Ciência e a Tecnologia I. P., under the scope of projects PTDC/MAT-APL/28400/2017, UIDB/00297/2020, and UIDP/00297/2020, the last two only for second and third authors.

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Authors and Affiliations

  1. FCT NOVA, Campus de Caparica, Caparica, 2829-516, Portugal

    S. Tavares

  2. Department of Mathematics, FCT NOVA - CMA, Campus de Caparica, Caparica, 2829-516, Portugal

    C. P. Brás & A. L. Custódio

  3. Department of Computer Science, FCT NOVA - NOVA LINCS, Campus de Caparica, Caparica, 2829-516, Portugal

    V. Duarte & P. Medeiros

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  1. S. Tavares
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  2. C. P. Brás
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  3. A. L. Custódio
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  4. V. Duarte
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Correspondence to A. L. Custódio.

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Appendix.: Pareto front approximations for the styrene problem

Appendix.: Pareto front approximations for the styrene problem

Table 3

Table 3 Pareto front approximations for the styrene problem
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Tavares, S., Brás, C.P., Custódio, A.L. et al. Parallel strategies for Direct Multisearch. Numer Algor 92, 1757–1788 (2023). https://doi.org/10.1007/s11075-022-01364-1

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  • DOI: https://doi.org/10.1007/s11075-022-01364-1

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