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An Improved Branch-and-Cut Algorithm for Mixed-Integer Nonlinear Systems Optimization Problem
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DOI：10.1002/aic.11616.png)
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Abstract
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Recent advances for global optimization and dynamic optimization of the mixed-integer systems have created an increasing demand for efficient and robust numerical algorithms for mixed-integer nonlinear programming (MINLP) problem. In this article, an improved branch-and-cut algorithm for 0-1 MINLP problems has been proposed by using our former critical finding (Zhu and Kuno, Ind Eng Chem Res. 2006;45:187196) of the disjunctive cutting plane for 0-1 MINLP. By virtue of the polyhedral outer approximation of the mixed-integer nonlinear set of the original MINLP problem at each enumeration node, a lift-and-project cutting planes that is valid for the original MINLP problem and cuts the fractional solution away can be generated by using the cut generating, lifting, and strengthening approach for MILP problem of Balas et al. (Math Program. 1993;58:295-324). The specific implementation issues of the cutting planes are discussed and incorporated into the algorithmic development of a branch-and-cut algorithm. The efficiency of the improved disjunctive cutting plane is demonstrated by the computational results for 11 systems optimization problems, and it is implied that the proposed branch-and-cut algorithm is very promising for practical MINLP problems as the interior-point solvers for nonlinear programming problems with many constraints are becoming mature gradually. (C) 2008 American Institute of Chemical Engineers AIChE J, 54: 3239-3247, 2008
Keywords:
systems optimization
MINLP
branch-and-cut
cutting plane
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