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New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

Author

Listed:
  • Loay Alkhalifa

    (Department of Mathematics, College of Sciences and Arts, Qassim University, Ar Rass 51921, Saudi Arabia)

  • Hans Mittelmann

    (School of Math & Stat Sciences, Arizona State University, Tempe, AZ 85287, USA)

Abstract

Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform nonlinear problems into linear ones. This paper will introduce PLA with brief a background and literature review, followed by describing our contribution before presenting the results of computational experiments and our findings. The goals of this paper are (a) improving PLA models by using nonuniform domain partitioning, and (b) proposing an idea of applying PLA partially on MINLP problems, making them easier to handle. The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate solutions and required less time compared to PLA with uniform partition.

Suggested Citation

  • Loay Alkhalifa & Hans Mittelmann, 2022. "New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation," Mathematics, MDPI, vol. 10(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:198-:d:720880
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    References listed on IDEAS

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    1. Pei, Mingyang & Lin, Peiqun & Du, Jun & Li, Xiaopeng & Chen, Zhiwei, 2021. "Vehicle dispatching in modular transit networks: A mixed-integer nonlinear programming model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
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    Cited by:

    1. Tubagus Robbi Megantara & Sudradjat Supian & Diah Chaerani & Abdul Talib Bon, 2024. "The Application of the Piecewise Linear Method for Non-Linear Programming Problems in Ride-Hailing Assignment Based on Service Level, Driver Workload, and Fuel Consumption," Mathematics, MDPI, vol. 12(14), pages 1-23, July.

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