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Entropy 2013, 15(9), 3592-3601; doi:10.3390/e15093592

A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs

Department of Industrial and Systems Engineering, University of Washington, Seattle, WA 98195, USA
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Received: 15 June 2013 / Revised: 30 August 2013 / Accepted: 30 August 2013 / Published: 4 September 2013
(This article belongs to the Special Issue Dynamical Systems)
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Abstract

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.
Keywords: large-scale binary integer programs; linear quadratic tracking; optimal control large-scale binary integer programs; linear quadratic tracking; optimal control
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Zhang, P.; Kohn, W.; Zabinsky, Z.B. A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs. Entropy 2013, 15, 3592-3601.

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