2008
DOI: 10.1021/ie071316j
|View full text |Cite
|
Sign up to set email alerts
|

Global Optimization of Reverse Osmosis Network for Wastewater Treatment and Minimization

Abstract: Reverse osmosis (RO) has shown itself to be a viable technology for the treatment and minimization of industrial and domestic wastewater streams. The current research presents a deterministic branchand-bound global optimization-based algorithm for the solution of the reverse osmosis network (RON) synthesis problem. The mathematical programming model describes the RON through nonconvex mixedinteger nonlinear programs (MINLPs). A piecewise mixed-integer linear program (MILP) is derived based on the convex relaxa… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1

Citation Types

0
45
0

Year Published

2011
2011
2013
2013

Publication Types

Select...
8

Relationship

1
7

Authors

Journals

citations
Cited by 46 publications
(45 citation statements)
references
References 12 publications
0
45
0
Order By: Relevance
“…Our previous work integrated piecewise-linear underestimators into the global optimization branch-and-bound tree based on computational experimentation determining the best formulations for these underestimators [29,65,66,73,93,98,99,100,101,107,119,139]. After extensive testing on process networks and point packing problems [99], we suggested that using the piecewise-linear relaxation scheme increases the probability that MIQCQP will solve to ε-global optimality within a given time limit.…”
Section: Piecewise-linear Underestimatorsmentioning
confidence: 99%
See 2 more Smart Citations
“…Our previous work integrated piecewise-linear underestimators into the global optimization branch-and-bound tree based on computational experimentation determining the best formulations for these underestimators [29,65,66,73,93,98,99,100,101,107,119,139]. After extensive testing on process networks and point packing problems [99], we suggested that using the piecewise-linear relaxation scheme increases the probability that MIQCQP will solve to ε-global optimality within a given time limit.…”
Section: Piecewise-linear Underestimatorsmentioning
confidence: 99%
“…The GloMIQO reformulation uses the observation that disaggregating bilinear terms tightens the relaxation of MIQCQP and actively takes advantage of any redundant linear constraints added to the model. It is standard to use termwise convex/concave envelopes [11,91] to relax MIQCQP, but many tighter relaxations have been developed based on: polyhedral facets of edge-concave multivariable term aggregations [17,26,34,94,95,96,99,111,130,131,132], eigenvector projections [38,106,113,122], piecewise-linear underestimators [29,65,66,73,93,98,99,100,101,107,119,139], outer approximation of convex terms [32,48,47], and semidefinite programming (SDP) relaxations [16,25,35,122,121]. GloMIQO incorporates several of these advanced relaxations.…”
Section: Literature Reviewmentioning
confidence: 99%
See 1 more Smart Citation
“…Hasan and Karimi [2010] studied the possibility of bivariate partitioning, that is, segmenting both variables participating in each bilinear term. Other groups who have used piecewise-linear underestimators include: Bergamini et al [2008] in their Outer Approximation for Global Optimization Algorithm; Saif et al [2008], in a reverse osmosis network case study; and Pham et al [2009], in a fast-solving algorithm that generates near-optimal solutions.…”
Section: Literature Reviewmentioning
confidence: 99%
“…Nonconvex quadratically-constrained quadratic programs (nonconvex QCQP) and those admitting integer variables (MIQCQP), are ubiquitous in process systems applications including heat integration networks, separation systems, reactor networks, reactor-separator-recycle systems, and batch processes (e.g., [2,5,18,24,26,28,29,31,33,42,44,45,47,48,50,66,67,70,71,88,91]). …”
Section: Introductionmentioning
confidence: 99%