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

Giampaolo Liuzzi(giampaolo.liuzzi***at***iasi.cnr.it)
Stefano Lucidi(lucidi***at***dis.uniroma1.it)
Francesco Rinaldi(rinaldi***at***math.unipd.it)

Abstract: In this paper, we develop a new algorithmic framework that handles 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. We first describe and analyze a version of the algorithm that tackles problems with bound constraints. Then, we combine it with a penalty approach in order to solve problems with black box constraints. In both cases we prove finite convergence to a suitably defined local minimum of the problem (convergence to a global minimum can eventually be obtained by properly modifing a few instructions in the scheme). We report extensive numerical experiments based on a testbed of both bound constrained and generally constrained problems. We show the efficiency and robustness of the method when compared to two state-of-the-art solvers for black box optimization.

Keywords: Derivative Free Optimization Black Box Problems Integer variables Nonmonotone line search

Category 1: Integer Programming (Other )

Category 2: Optimization Software and Modeling Systems


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Entry Submitted: 02/16/2018
Entry Accepted: 02/16/2018
Entry Last Modified: 02/16/2018

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