This paper introduces MATRS, a novel matrix adaptation trust-region strategy designed to solve noisy derivative-free mixed-integer optimization problems with simple bounds in low dimensions. MATRS operates through a repeated cycle of five phases: mutation, selection, recombination, trust-region, and mixed-integer, executed in this sequence. But if in the mutation phase a new best point (the point with the lowest inexact function value among all evaluated points so far) is found, the selection, recombination, and trust-region phases are skipped. Similarly, if the recombination phase finds a new best point, the trust-region phase is skipped. The mixed-integer phase is always performed. To search for a new best point, the mutation and recombination phases use extrapolation whereas the mixed-integer phase performs a mixed-integer line search along directions estimated to go into a valley. Numerical
results on several collections of test problems show that MATRS is competitive with state-of-the-art derivative-free mixed-integer solvers.
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