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Author Munoz, G.; Espinoza, D.; Goycoolea, M.; Moreno, E.; Queyranne, M.; Rivera Letelier, O. pdf  doi
openurl 
  Title A study of the Bienstock-Zuckerberg algorithm: applications in mining and resource constrained project scheduling Type
  Year 2018 Publication (up) Computational Optimization And Applications Abbreviated Journal Comput. Optim. Appl.  
  Volume 69 Issue 2 Pages 501-534  
  Keywords Column generation; Dantzig-Wolfe; Optimization; RCPSP  
  Abstract We study a Lagrangian decomposition algorithm recently proposed by Dan Bienstock and Mark Zuckerberg for solving the LP relaxation of a class of open pit mine project scheduling problems. In this study we show that the Bienstock-Zuckerberg (BZ) algorithm can be used to solve LP relaxations corresponding to a much broader class of scheduling problems, including the well-known Resource Constrained Project Scheduling Problem (RCPSP), and multi-modal variants of the RCPSP that consider batch processing of jobs. We present a new, intuitive proof of correctness for the BZ algorithm that works by casting the BZ algorithm as a column generation algorithm. This analysis allows us to draw parallels with the well-known Dantzig-Wolfe decomposition (DW) algorithm. We discuss practical computational techniques for speeding up the performance of the BZ and DW algorithms on project scheduling problems. Finally, we present computational experiments independently testing the effectiveness of the BZ and DW algorithms on different sets of publicly available test instances. Our computational experiments confirm that the BZ algorithm significantly outperforms the DW algorithm for the problems considered. Our computational experiments also show that the proposed speed-up techniques can have a significant impact on the solve time. We provide some insights on what might be explaining this significant difference in performance.  
  Address [Munoz, Gonzalo] Columbia Univ, Ind Engn & Operat Res, New York, NY USA, Email: marcos.goycoolea@uai.cl  
  Corporate Author Thesis  
  Publisher Springer Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0926-6003 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000426295000009 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 835  
Permanent link to this record
 

 
Author Barrera, J.; Moreno, E.; Munoz, G.; Romero, P. doi  openurl
  Title Exact reliability optimization for series-parallel graphs using convex envelopes Type
  Year 2022 Publication (up) Networks Abbreviated Journal Networks  
  Volume to appear Issue Pages  
  Keywords convex envelopes; network reliability; nonlinear optimization; reliability optimization; series-parallel graphs  
  Abstract Given its wide spectrum of applications, the classical problem of all-terminal network reliability evaluation remains a highly relevant problem in network design. The associated optimization problem-to find a network with the best possible reliability under multiple constraints-presents an even more complex challenge, which has been addressed in the scientific literature but usually under strong assumptions over failures probabilities and/or the network topology. In this work, we propose a novel reliability optimization framework for network design with failures probabilities that are independent but not necessarily identical. We leverage the linear-time evaluation procedure for network reliability in the series-parallel graphs of Satyanarayana and Wood (1985) to formulate the reliability optimization problem as a mixed-integer nonlinear optimization problem. To solve this nonconvex problem, we use classical convex envelopes of bilinear functions, introduce custom cutting planes, and propose a new family of convex envelopes for expressions that appear in the evaluation of network reliability. Furthermore, we exploit the refinements produced by spatial branch-and-bound to locally strengthen our convex relaxations. Our experiments show that, using our framework, one can efficiently obtain optimal solutions in challenging instances of this problem.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0028-3045 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000749651100001 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1513  
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Author Rivera Letelier, O.; Espinoza, D.; Goycoolea, M.; Moreno, E.; Munoz, G. doi  openurl
  Title Production scheduling for strategic open pit mine planning: A mixed integer programming approach Type
  Year 2020 Publication (up) Operations Research Abbreviated Journal Oper. Res.  
  Volume 68 Issue 5 Pages 1425-1444  
  Keywords  
  Abstract Given a discretized representation of an ore body known as a block model, the open pit mining production scheduling problem that we consider consists of defining which blocks to extract, when to extract them, and how or whether to process them, in such a way as to comply with operational constraints and maximize net present value. Although it has been established that this problem can be modeled with mixed-integer programming, the number of blocks used to represent real-world mines (millions) has made solving large instances nearly impossible in practice. In this article, we introduce a new methodology for tackling this problem and conduct computational tests using real problem sets ranging in size from 20,000 to 5,000,000 blocks and spanning 20 to 50 time periods. We consider both direct block scheduling and bench-phase scheduling problems, with capacity, blending, and minimum production constraints. Using new preprocessing and cutting planes techniques, we are able to reduce the linear programming relaxation value by up to 33\%, depending on the instance. Then, using new heuristics, we are able to compute feasible solutions with an average gap of 1.52% relative to the previously computed bound. Moreover, after four hours of running a customized branch-and-bound algorithm on the problems with larger gaps, we are able to further reduce the average from 1.52% to 0.71%  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0030-364X ISBN Medium  
  Area Expedition Conference  
  Notes Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1052  
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Author Letelier, O.R.; Espinoza, D.; Goycoolea, M.; Moreno, E.; Munoz, G. doi  openurl
  Title Production Scheduling for Strategic Open Pit Mine Planning: A Mixed-Integer Programming Approach Type
  Year 2020 Publication (up) Operations Research Abbreviated Journal Oper. Res.  
  Volume 68 Issue 5 Pages 1425-1444  
  Keywords open pit mining; production scheduling; column generation; heuristics; cutting planes; integer programming applications  
  Abstract Given a discretized representation of an ore body known as a block model, the open pit mining production scheduling problem that we consider consists of defining which blocks to extract, when to extract them, and how or whether to process them, in such a way as to comply with operational constraints and maximize net present value. Although it has been established that this problem can be modeled with mixed-integer programming, the number of blocks used to represent real-world mines (millions) has made solving large instances nearly impossible in practice. In this article, we introduce a new methodology for tackling this problem and conduct computational tests using real problem sets ranging in size from 20,000 to 5,000,000 blocks and spanning 20 to 50 time periods. We consider both direct block scheduling and bench-phase scheduling problems, with capacity, blending, and minimum production constraints. Using new preprocessing and cutting planes techniques, we are able to reduce the linear programming relaxation value by up to 33%, depending on the instance. Then, using new heuristics, we are able to compute feasible solutions with an average gap of 1.52% relative to the previously computed bound. Moreover, after four hours of running a customized branch-and-bound algorithm on the problems with larger gaps, we are able to further reduce the average from 1.52% to 0.71%.  
  Address [Rivera Letelier, Orlando] Univ Adolfo Ibanez, Doctoral Program Ind Engn & Operat Res, Santiago 7941169, Chile, Email: orlando.rivera@uai.cl;  
  Corporate Author Thesis  
  Publisher Informs Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0030-364x ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000574409100008 Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1250  
Permanent link to this record
 

 
Author Barrera, J.; Moreno, E.; Munoz, G. doi  openurl
  Title Convex envelopes for ray-concave functions Type
  Year 2022 Publication (up) Optimization Letters Abbreviated Journal Optim. Let.  
  Volume to appear Issue Pages  
  Keywords Convex envelopes; Nonlinear programming; Convex optimization  
  Abstract Convexification based on convex envelopes is ubiquitous in the non-linear optimization literature. Thanks to considerable efforts of the optimization community for decades, we are able to compute the convex envelopes of a considerable number of functions that appear in practice, and thus obtain tight and tractable approximations to challenging problems. We contribute to this line of work by considering a family of functions that, to the best of our knowledge, has not been considered before in the literature. We call this family ray-concave functions. We show sufficient conditions that allow us to easily compute closed-form expressions for the convex envelope of ray-concave functions over arbitrary polytopes. With these tools, we are able to provide new perspectives to previously known convex envelopes and derive a previously unknown convex envelope for a function that arises in probability contexts.  
  Address  
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  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000752153900001 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1525  
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