Global optimization algorithm for mixed integer quadratically constrained quadratic program
Mixed integer quadratic programs with quadratic constraints (MIQQP) occur frequently in various areas of engineering practice and management science, but most solution methods for this kind of problems are often designed for its special cases. In this paper, we present a simple global optimization a...
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| Vydáno v: | Journal of computational and applied mathematics Ročník 319; s. 159 - 169 |
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Elsevier B.V
01.08.2017
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | Mixed integer quadratic programs with quadratic constraints (MIQQP) occur frequently in various areas of engineering practice and management science, but most solution methods for this kind of problems are often designed for its special cases. In this paper, we present a simple global optimization algorithm for solving problem (MIQQP). We first convert problem (MIQQP) into an equivalent generalized bilinear programming problem with integer variables (EIQQP). We next show that replacing the quadratic objective and constraint functions with their convex envelopes is dominated by an alternative methodology based on convexifying the range of the bilinear terms on the feasible region. Finally, by incorporating the reduction-correction techniques and sampling strategies into the branch and bound scheme, the proposed algorithm is developed for solving (MIQQP). Convergence and optimality of the algorithm are presented and numerical examples taken from some recent literature and MINLPLib2 are carried out to validate the performance of the proposed algorithm. |
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| AbstractList | Mixed integer quadratic programs with quadratic constraints (MIQQP) occur frequently in various areas of engineering practice and management science, but most solution methods for this kind of problems are often designed for its special cases. In this paper, we present a simple global optimization algorithm for solving problem (MIQQP). We first convert problem (MIQQP) into an equivalent generalized bilinear programming problem with integer variables (EIQQP). We next show that replacing the quadratic objective and constraint functions with their convex envelopes is dominated by an alternative methodology based on convexifying the range of the bilinear terms on the feasible region. Finally, by incorporating the reduction-correction techniques and sampling strategies into the branch and bound scheme, the proposed algorithm is developed for solving (MIQQP). Convergence and optimality of the algorithm are presented and numerical examples taken from some recent literature and MINLPLib2 are carried out to validate the performance of the proposed algorithm. |
| Author | Zhao, Yingfeng Liu, Sanyang |
| Author_xml | – sequence: 1 givenname: Yingfeng orcidid: 0000-0003-1581-8414 surname: Zhao fullname: Zhao, Yingfeng email: zhaoyingfeng6886@163.com organization: School of Mathematics and Statistics, Xidian University, Xi’an 710071, China – sequence: 2 givenname: Sanyang surname: Liu fullname: Liu, Sanyang email: liusanyang@126.com organization: School of Mathematics and Statistics, Xidian University, Xi’an 710071, China |
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| Cites_doi | 10.1007/s10898-012-9842-2 10.1287/mnsc.18.4.B220 10.1007/s10107-012-0555-6 10.1007/s10898-010-9630-9 10.1007/s10255-015-0456-6 10.1007/s10107-005-0582-7 10.1016/0098-1354(94)00097-2 10.1007/s101079900106 10.1016/j.ijepes.2014.04.048 10.1023/A:1008377529330 10.1080/10556780902883184 10.1007/s10898-011-9650-0 10.1016/j.jcss.2004.07.002 10.1007/s10957-010-9653-x 10.1007/BF01099462 10.1007/s10898-012-9874-7 |
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