Global optimization of mixed-integer nonlinear (polynomial) programming problems: the Bernstein polynomial approach |
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Authors: | Bhagyesh V Patil P S V Nataraj Sharad Bhartiya |
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Affiliation: | 1. Systems and Control Engineering Group, Indian Institute of Technology Bombay, Powai, Mumbai, 400 076, India 2. Chemical Engineering Department, Indian Institute of Technology Bombay, Powai, Mumbai, 400 076, India
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Abstract: | In this paper, we propose an algorithm for constrained global optimization of mixed-integer nonlinear programming (MINLP) problems. The proposed algorithm uses the Bernstein polynomial form in a branch-and-bound framework. Ingredients such as continuous relaxation, branching for integer decision variables, and fathoming for each subproblem in the branch-and-bound tree are used. The performance of the proposed algorithm is tested and compared with several state-of-the-art MINLP solvers, on two sets of test problems. The results of the tests show the superiority of the proposed algorithm over the state-of-the-art solvers in terms of the chosen performance metrics. |
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