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

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

Received: 15 June 2013; in revised form: 30 August 2013 / Accepted: 30 August 2013 / Published: 4 September 2013
(This article belongs to the Special Issue Dynamical Systems)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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
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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.

AMA Style

Zhang P, Kohn W, Zabinsky ZB. A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs. Entropy. 2013; 15(9):3592-3601.

Chicago/Turabian Style

Zhang, Pengbo; Kohn, Wolf; Zabinsky, Zelda B. 2013. "A Discrete Meta-Control Procedure for Approximating Solutions to Binary Programs." Entropy 15, no. 9: 3592-3601.

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