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An algorithmic framework based on primitive directions and nonmonotone line searches for black-box optimization problems with integer variables

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Abstract

In this paper, we develop a new algorithmic framework to solve black-box problems with integer variables. The strategy included in the framework makes use of specific search directions (so called primitive directions) and a suitably developed nonmonotone line search, thus guaranteeing a high level of freedom when exploring the integer lattice. First, we describe and analyze a version of the algorithm that tackles problems with only bound constraints on the variables. Then, we combine it with a penalty approach in order to solve problems with simulation constraints. In both cases we prove finite convergence to a suitably defined local minimum of the problem. We report extensive numerical experiments based on a test bed of both bound-constrained and generally-constrained problems. We show the effectiveness of the method when compared to other state-of-the-art solvers for black-box integer optimization.

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Notes

  1. A new version of NOMAD with better functionalities, e.g. the Nelder Mead search and the possibility to specify the direction type for poll intensification, was released while this paper was under review (for further details visit the website https://www.gerad.ca/nomad/).

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Authors and Affiliations

  1. Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, 00185, Rome, Italy

    Giampaolo Liuzzi

  2. Dipartimento di Ingegneria Informatica Automatica e Gestionale “A. Ruberti”, “Sapienza” Università di Roma, Via Ariosto 25, 00185, Rome, Italy

    Stefano Lucidi

  3. Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Via Trieste, 63, 35121, Padua, Italy

    Francesco Rinaldi

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  1. Giampaolo Liuzzi
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  2. Stefano Lucidi
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  3. Francesco Rinaldi
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Correspondence to Giampaolo Liuzzi.

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Liuzzi, G., Lucidi, S. & Rinaldi, F. An algorithmic framework based on primitive directions and nonmonotone line searches for black-box optimization problems with integer variables. Math. Prog. Comp. 12, 673–702 (2020). https://doi.org/10.1007/s12532-020-00182-7

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