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A fast global algorithm for singly linearly constrained separable binary quadratic program with partially identical parameters

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Abstract

The singly linearly constrained separable binary quadratic programming problem (SLSBQP) has a wide variety of applications in practice. In real-life applications, the coefficients in the objective function and constraints generally appear with symmetric structure. In this paper, we propose an extremely efficient global optimization algorithm for solving SLSBQP with symmetric structure. We first develop a reformulation of SLSBQP based on an aggregate function defined on the symmetric structure in the problem, and derive the convex envelop function for the aggregate function. A branch-and-bound algorithm is then proposed to find the global solution of the reformulation of SLSBQP. Computational experiments show that the proposed algorithm is able to solve test instances with thousands of variables in less than 0.04 seconds on average, whereas the current state-of-the-art algorithms may fail to solve the same test instances in 200 seconds. The superior performance of the proposed algorithm clearly indicates the potential of the proposed algorithm in real-life applications.

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Notes

  1. The optimal values of our numerical instances are generally larger than \(10^6\). An absolute error tolerance of 0.01 means that the relative error is less than \(10^{-8}\) for our test instances.

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Acknowledgements

Lu’s research has been supported by National Natural Science Foundation of China Grant Nos. 12171151 and 11701177. Deng’s research has been supported by a grant from MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation at UCAS, and National Natural Science Foundation of China Grant No. 11771287.

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Authors and Affiliations

  1. School of Economics and Management, North China Electric Power University, Beijing, 102206, China

    Cheng Lu,�Junhao Wu�&�Shaoze Li

  2. School of Economics and Management, University of Chinese Academy of Sciences, Beijing, 100190, China

    Zhibin Deng

  3. MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation at UCAS, Beijing, 100190, China

    Zhibin Deng

Authors
  1. Cheng Lu
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  2. Junhao Wu
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  3. Zhibin Deng
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  4. Shaoze Li
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Correspondence to Zhibin Deng.

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Lu, C., Wu, J., Deng, Z. et al. A fast global algorithm for singly linearly constrained separable binary quadratic program with partially identical parameters. Optim Lett 17, 613–628 (2023). https://doi.org/10.1007/s11590-022-01891-9

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  • DOI: https://doi.org/10.1007/s11590-022-01891-9

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