{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:32:29Z","timestamp":1760243549196,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2013,9,4]],"date-time":"2013-09-04T00:00:00Z","timestamp":1378252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Large-scale binary integer programs occur frequently in many real-world applications. For some binary integer problems, finding an optimal solution or even a feasible solution is computationally expensive. In this paper, we develop a discrete meta-control procedure to approximately solve large-scale binary integer programs efficiently. The key idea is to map the vector of n binary decision variables into a scalar function defined over a time interval [0; n] and construct a linear quadratic tracking (LQT) problem that can be solved efficiently. We prove that an LQT formulation has an optimal binary solution, analogous to a classical bang-bang control in continuous time. Our LQT approach can provide advantages in reducing computation while generating a good approximate solution. Numerical examples are presented to demonstrate the usefulness of the proposed method.<\/jats:p>","DOI":"10.3390\/e15093592","type":"journal-article","created":{"date-parts":[[2013,9,4]],"date-time":"2013-09-04T12:31:59Z","timestamp":1378297919000},"page":"3592-3601","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs"],"prefix":"10.3390","volume":"15","author":[{"given":"Pengbo","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Industrial and Systems Engineering, University of Washington, Seattle, WA 98195, USA"}]},{"given":"Wolf","family":"Kohn","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, University of Washington, Seattle, WA 98195, USA"}]},{"given":"Zelda","family":"Zabinsky","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, University of Washington, Seattle, WA 98195, USA"}]}],"member":"1968","published-online":{"date-parts":[[2013,9,4]]},"reference":[{"key":"ref_1","unstructured":"Wolsey, L.A. 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