Global optimization of bilinear programs with a multiparametric disaggregation technique

被引：108

作者：

Kolodziej, Scott ^{[1
]}

Castro, Pedro M. ^{[2
]}

Grossmann, Ignacio E. ^{[1
]}

机构：

[1] Carnegie Mellon Univ, Dept Chem Engn, Pittsburgh, PA 15213 USA

[2] Unidade Modelacaoe Otimizacao Sistemas, Lab Nacl Energia & Geol, P-1649038 Lisbon, Portugal

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2013年 / 57卷 / 04期

基金：

美国国家科学基金会;

关键词：

Global optimization; Mixed integer linear programming; Mixed integer nonlinear programming; Quadratic optimization; Disjunctive programming; MIXED-INTEGER; WATER NETWORKS; RELAXATIONS; HIERARCHY; ALGORITHM;

D O I：

10.1007/s10898-012-0022-1

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this paper, we present the derivation of the multiparametric disaggregation technique (MDT) by Teles et al. (J. Glob. Optim., 2011) for solving nonconvex bilinear programs. Both upper and lower bounding formulations corresponding to mixed-integer linear programs are derived using disjunctive programming and exact linearizations, and incorporated into two global optimization algorithms that are used to solve bilinear programming problems. The relaxation derived using the MDT is shown to scale much more favorably than the relaxation that relies on piecewise McCormick envelopes, yielding smaller mixed-integer problems and faster solution times for similar optimality gaps. The proposed relaxation also compares well with general global optimization solvers on large problems.

引用

页码：1039 / 1063

页数：25

共 49 条

[11]

Brook A., 1988, ACM SIGNUM NEWSLETT, V23

[12]

Drud A. S., 1994, ORSA Journal on Computing, V6, P207, DOI 10.1287/ijoc.6.2.207

[13] Computational Comparison of Piecewise-Linear Relaxations for Pooling Problems [J].