The Bernstein Branch-and-Bound Unconstrained Global Optimization Algorithm for MINLP Problems
In this work a Bernstein global optimization algorithm to solve unconstrained polynomial mixed-integer nonlinear programming (MINLP) problems is proposed. The proposed algorithm use a branch-and-bound framework and possesses several new features, such as a modified subdivision procedure, the Bernstein box consistency and the Bernstein hull consistency procedures to prune the solution search space. The performance of the proposed algorithm is numerically investigated and compared with previously reported Bernstein global optimization algorithm on a set of 10 test problems. The findings of the tests establishes the efficacy of the proposed algorithm over the previously reported Bernstein algorithm in terms of the chosen performance metrics.
- 1.The Mathworks Inc., MATLAB version 7.1 (R14), Natick, MA (2005)Google Scholar
- 6.GAMS Development Corp.: GAMS-The solver manuals, Washington, DC (2009)Google Scholar
- 13.Stahl, V.: Interval methods for bounding the range of polynomials and solving systems of nonlinear equations. Ph.D. thesis, Johannes Kepler University, Linz (1995)Google Scholar
- 15.Verschelde, J.: PHC pack, the database of polynomial systems. Technical report, Mathematics Department, University of Illinois, Chicago, USA (2001)Google Scholar
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