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An Improved Bernstein Global Optimization Algorithm for MINLP Problems with Application in Process Industry

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Abstract

We present an improved Bernstein global optimization algorithm to solve polynomial mixed-integer nonlinear programming (MINLP) problems. The algorithm is of branch-and-bound type, and uses the Bernstein form of the polynomials for the global optimization. The new ingredients in the algorithm include a modified subdivision procedure, a vectorized Bernstein cut-off test and a new branching rule for the decision variables. The performance of the improved algorithm is tested and compared with earlier reported Bernstein global optimization algorithm (to solve polynomial MINLPs) and with several state-of-the-art MINLP solvers on a set of 19 test problems. The results of the tests show the superiority of the improved algorithm over the earlier reported Bernstein algorithm and the state-of-the-art solvers in terms of the chosen performance metrics. Similarly, efficacy of the improved algorithm in handling a real-world MINLP problem is brought out via a trim-loss minimization problem from the process industry.

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Authors and Affiliations

  1. Laboratoire d’Informatique de Nantes Atlantique, BP 92208, 44322, Nantes, France

    Bhagyesh V. Patil

  2. Systems and Control Engineering Group, Indian Institute of Technology Bombay, Powai, Mumbai, 400 076, India

    P. S. V. Nataraj

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  1. Bhagyesh V. Patil
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  2. P. S. V. Nataraj
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Correspondence to Bhagyesh V. Patil.

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Patil, B.V., Nataraj, P.S.V. An Improved Bernstein Global Optimization Algorithm for MINLP Problems with Application in Process Industry. Math.Comput.Sci. 8, 357–377 (2014). https://doi.org/10.1007/s11786-014-0198-5

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  • DOI: https://doi.org/10.1007/s11786-014-0198-5

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