Parallel distributed-memory simplex for large-scale stochastic LP problems
We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more rec...
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| Vydané v: | Computational optimization and applications Ročník 55; číslo 3; s. 571 - 596 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Springer US
01.07.2013
Springer Nature B.V |
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| ISSN: | 0926-6003, 1573-2894 |
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| Abstract | We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal basic solutions, which allow for efficient hot-starts (e.g., in a branch-and-bound context) and can provide important sensitivity information. Our approach exploits the dual block-angular structure of these problems inside the linear algebra of the revised simplex method in a manner suitable for high-performance distributed-memory clusters or supercomputers. While this paper focuses on stochastic LPs, the work is applicable to all problems with a dual block-angular structure. Our implementation is competitive in serial with highly efficient sparsity-exploiting simplex codes and achieves significant relative speed-ups when run in parallel. Additionally, very large problems with hundreds of millions of variables have been successfully solved to optimality. This is the largest-scale parallel sparsity-exploiting revised simplex implementation that has been developed to date and the first truly distributed solver. It is built on novel analysis of the linear algebra for dual block-angular LP problems when solved by using the revised simplex method and a novel parallel scheme for applying product-form updates. |
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| AbstractList | We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal basic solutions, which allow for efficient hot-starts (e.g., in a branch-and-bound context) and can provide important sensitivity information. Our approach exploits the dual block-angular structure of these problems inside the linear algebra of the revised simplex method in a manner suitable for high-performance distributed-memory clusters or supercomputers. While this paper focuses on stochastic LPs, the work is applicable to all problems with a dual block-angular structure. Our implementation is competitive in serial with highly efficient sparsity-exploiting simplex codes and achieves significant relative speed-ups when run in parallel. Additionally, very large problems with hundreds of millions of variables have been successfully solved to optimality. This is the largest-scale parallel sparsity-exploiting revised simplex implementation that has been developed to date and the first truly distributed solver. It is built on novel analysis of the linear algebra for dual block-angular LP problems when solved by using the revised simplex method and a novel parallel scheme for applying product-form updates. We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal basic solutions, which allow for efficient hot-starts (e.g., in a branch-and-bound context) and can provide important sensitivity information. Our approach exploits the dual block-angular structure of these problems inside the linear algebra of the revised simplex method in a manner suitable for high-performance distributed-memory clusters or supercomputers. While this paper focuses on stochastic LPs, the work is applicable to all problems with a dual block-angular structure. Our implementation is competitive in serial with highly efficient sparsity-exploiting simplex codes and achieves significant relative speed-ups when run in parallel. Additionally, very large problems with hundreds of millions of variables have been successfully solved to optimality. This is the largest-scale parallel sparsity-exploiting revised simplex implementation that has been developed to date and the first truly distributed solver. It is built on novel analysis of the linear algebra for dual block-angular LP problems when solved by using the revised simplex method and a novel parallel scheme for applying product-form updates.[PUBLICATION ABSTRACT] |
| Author | Lubin, Miles Anitescu, Mihai Petra, Cosmin G. Hall, J. A. Julian |
| Author_xml | – sequence: 1 givenname: Miles surname: Lubin fullname: Lubin, Miles email: mlubin@mcs.anl.gov organization: Mathematics and Computer Science Division, Argonne National Laboratory – sequence: 2 givenname: J. A. Julian surname: Hall fullname: Hall, J. A. Julian organization: School of Mathematics, University of Edinburgh – sequence: 3 givenname: Cosmin G. surname: Petra fullname: Petra, Cosmin G. organization: Mathematics and Computer Science Division, Argonne National Laboratory – sequence: 4 givenname: Mihai surname: Anitescu fullname: Anitescu, Mihai organization: Mathematics and Computer Science Division, Argonne National Laboratory |
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| CitedBy_id | crossref_primary_10_1007_s12532_020_00185_4 crossref_primary_10_1007_s10589_014_9689_1 crossref_primary_10_1016_j_ejor_2017_02_005 crossref_primary_10_1007_s11227_020_03227_9 crossref_primary_10_1007_s10589_023_00493_0 crossref_primary_10_1016_j_jpdc_2018_10_009 crossref_primary_10_1007_s00186_020_00713_x crossref_primary_10_1287_ijoc_2022_1158 crossref_primary_10_1007_s10589_019_00074_0 crossref_primary_10_1137_130908737 crossref_primary_10_1016_j_ifacol_2017_08_339 crossref_primary_10_1007_s10107_016_1067_6 crossref_primary_10_1007_s10589_016_9882_5 |
| Cites_doi | 10.1007/978-1-4614-0237-4 10.1007/s10287-008-0090-3 10.1007/978-1-4615-0257-9 10.1287/ijoc.2.4.325 10.1007/BF01601939 10.1007/BF01581089 10.1287/mnsc.3.3.255 10.1007/s10589-008-9207-4 10.1137/1.9780898718881 10.1137/0909058 10.1007/BF01580108 10.1287/opre.14.4.636 10.1007/BF01584341 10.1007/BF01589114 10.1137/S1064827502401953 10.2307/2001993 10.1145/992200.992201 10.1007/BF01584548 10.1023/A:1018977102079 10.1145/1465482.1465560 10.1007/s10589-005-4802-0 10.1023/A:1021858008222 10.1007/BF02025534 10.1007/978-3-642-31464-3_15 |
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| Keywords | Parallel computing Stochastic optimization Simplex method Block-angular |
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| References | Lubin, Petra, Anitescu, Zavala (CR25) 2011 Golub, Van Loan (CR13) 1996 Hall, McKinnon (CR17) 2005; 32 Linderoth, Wright (CR24) 2003; 24 Aykanat, Pinar, Çatalyürek (CR2) 2004; 25 Lasdon (CR23) 1970 CR18 Amdahl (CR1) 1967 Forrest, Goldfarb (CR9) 1992; 57 Bennett (CR3) 1966; 14 Gill, Murray, Saunders, Wright (CR12) 1989; 45 Suhl, Suhl (CR30) 1993; 43 Koberstein (CR22) 2008; 41 Bisschop, Meeraus (CR5) 1977; 13 Forrest, Tomlin (CR10) 1972; 2 Maros (CR27) 2003 Gropp, Thakur, Lusk (CR16) 1999 Gondzio, Grothey (CR14) 2009; 6 Dantzig, Orchard-Hays (CR6) 1954; 8 Harris (CR19) 1973; 5 Vladimirou, Zenios (CR32) 1999; 90 Markowitz (CR26) 1957; 3 Gilbert, Peierls (CR11) 1988; 9 Grama, Karypis, Kumar, Gupta (CR15) 2003 Davis (CR7) 2006 CR21 Birge, Louveaux (CR4) 2011 Suhl, Suhl (CR31) 1990; 2 Stern, Vavasis (CR28) 1993; 12 Kall (CR20) 1979; 30 Strazicky (CR29) 1980 Duff, Scott (CR8) 2004; 30 P. Kall (9542_CR20) 1979; 30 L.S. Lasdon (9542_CR23) 1970 J. Gondzio (9542_CR14) 2009; 6 B. Strazicky (9542_CR29) 1980 G.H. Golub (9542_CR13) 1996 W. Gropp (9542_CR16) 1999 C. Aykanat (9542_CR2) 2004; 25 J. Linderoth (9542_CR24) 2003; 24 9542_CR18 U.H. Suhl (9542_CR31) 1990; 2 M. Lubin (9542_CR25) 2011 A. Grama (9542_CR15) 2003 P.M.J. Harris (9542_CR19) 1973; 5 T. Davis (9542_CR7) 2006 J.J. Forrest (9542_CR9) 1992; 57 L.M. Suhl (9542_CR30) 1993; 43 J. Birge (9542_CR4) 2011 I. Maros (9542_CR27) 2003 G.M. Amdahl (9542_CR1) 1967 J.R. Gilbert (9542_CR11) 1988; 9 A. Koberstein (9542_CR22) 2008; 41 G.B. Dantzig (9542_CR6) 1954; 8 J. Bisschop (9542_CR5) 1977; 13 J. Hall (9542_CR17) 2005; 32 J. Stern (9542_CR28) 1993; 12 H. Vladimirou (9542_CR32) 1999; 90 I.S. Duff (9542_CR8) 2004; 30 9542_CR21 H.M. Markowitz (9542_CR26) 1957; 3 J.M. Bennett (9542_CR3) 1966; 14 J.J.H. Forrest (9542_CR10) 1972; 2 P.E. Gill (9542_CR12) 1989; 45 |
| References_xml | – year: 2011 ident: CR4 publication-title: Introduction to Stochastic Programming doi: 10.1007/978-1-4614-0237-4 – year: 1999 ident: CR16 publication-title: Using MPI-2: Advanced Features of the Message Passing Interface – volume: 6 start-page: 135 year: 2009 end-page: 160 ident: CR14 article-title: Exploiting structure in parallel implementation of interior point methods for optimization publication-title: Comput. Manag. Sci. doi: 10.1007/s10287-008-0090-3 – ident: CR18 – start-page: 263 year: 1980 end-page: 274 ident: CR29 article-title: Some results concerning an algorithm for the discrete recourse problem publication-title: Stochastic Programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974) – year: 2003 ident: CR27 publication-title: Computational Techniques of the Simplex Method doi: 10.1007/978-1-4615-0257-9 – year: 1970 ident: CR23 publication-title: Optimization Theory for Large Systems – volume: 2 start-page: 325 issue: 4 year: 1990 ident: CR31 article-title: Computing sparse LU factorizations for large-scale linear programming bases publication-title: ORSA J. Comput. doi: 10.1287/ijoc.2.4.325 – volume: 30 start-page: 261 year: 1979 end-page: 271 ident: CR20 article-title: Computational methods for solving two-stage stochastic linear programming problems publication-title: Z. Angew. Math. Phys. doi: 10.1007/BF01601939 – year: 2003 ident: CR15 publication-title: Introduction to Parallel Computing – start-page: 64:1 year: 2011 end-page: 64:64 ident: CR25 article-title: Scalable stochastic optimization of complex energy systems publication-title: Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’11 – volume: 57 start-page: 341 year: 1992 end-page: 374 ident: CR9 article-title: Steepest-edge simplex algorithms for linear programming publication-title: Math. Program. doi: 10.1007/BF01581089 – volume: 3 start-page: 255 issue: 3 year: 1957 end-page: 269 ident: CR26 article-title: The elimination form of the inverse and its application to linear programming publication-title: Manag. Sci. doi: 10.1287/mnsc.3.3.255 – volume: 41 start-page: 185 year: 2008 end-page: 204 ident: CR22 article-title: Progress in the dual simplex algorithm for solving large scale LP problems: techniques for a fast and stable implementation publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-008-9207-4 – ident: CR21 – year: 2006 ident: CR7 publication-title: Direct Methods for Sparse Linear Systems. Fundamentals of Algorithms doi: 10.1137/1.9780898718881 – volume: 9 start-page: 862 year: 1988 end-page: 874 ident: CR11 article-title: Sparse partial pivoting in time proportional to arithmetic operations publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0909058 – volume: 12 start-page: 199 year: 1993 end-page: 226 ident: CR28 article-title: Active set methods for problems in column block angular form publication-title: Comput. Appl. Math. – volume: 5 start-page: 1 year: 1973 end-page: 28 ident: CR19 article-title: Pivot selection methods of the DEVEX LP code publication-title: Math. Program. doi: 10.1007/BF01580108 – volume: 14 start-page: 636 issue: 4 year: 1966 end-page: 645 ident: CR3 article-title: An approach to some structured linear programming problems publication-title: Oper. Res. doi: 10.1287/opre.14.4.636 – volume: 13 start-page: 241 year: 1977 end-page: 254 ident: CR5 article-title: Matrix augmentation and partitioning in the updating of the basis inverse publication-title: Math. Program. doi: 10.1007/BF01584341 – volume: 45 start-page: 437 year: 1989 end-page: 474 ident: CR12 article-title: A practical anti-cycling procedure for linearly constrained optimization publication-title: Math. Program. doi: 10.1007/BF01589114 – volume: 25 start-page: 1860 year: 2004 end-page: 1879 ident: CR2 article-title: Permuting sparse rectangular matrices into block-diagonal form publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827502401953 – volume: 8 start-page: 64 issue: 46 year: 1954 end-page: 67 ident: CR6 article-title: The product form for the inverse in the simplex method publication-title: Math. Tables Other Aids Comput. doi: 10.2307/2001993 – volume: 30 start-page: 95 year: 2004 end-page: 117 ident: CR8 article-title: A parallel direct solver for large sparse highly unsymmetric linear systems publication-title: ACM Trans. Math. Softw. doi: 10.1145/992200.992201 – volume: 2 start-page: 263 year: 1972 end-page: 278 ident: CR10 article-title: Updated triangular factors of the basis to maintain sparsity in the product form simplex method publication-title: Math. Program. doi: 10.1007/BF01584548 – year: 1996 ident: CR13 publication-title: Matrix Computations – volume: 90 start-page: 87 year: 1999 end-page: 129 ident: CR32 article-title: Scalable parallel computations for large-scale stochastic programming publication-title: Ann. Oper. Res. doi: 10.1023/A:1018977102079 – start-page: 483 year: 1967 end-page: 485 ident: CR1 article-title: Validity of the single processor approach to achieving large scale computing capabilities publication-title: Proceedings of the April 18–20, 1967, Spring Joint Computer Conference, AFIPS ’67 (Spring) doi: 10.1145/1465482.1465560 – volume: 32 start-page: 259 year: 2005 end-page: 283 ident: CR17 article-title: Hyper-sparsity in the revised simplex method and how to exploit it publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-005-4802-0 – volume: 24 start-page: 207 year: 2003 end-page: 250 ident: CR24 article-title: Decomposition algorithms for stochastic programming on a computational grid publication-title: Comput. Optim. Appl. doi: 10.1023/A:1021858008222 – volume: 43 start-page: 33 year: 1993 end-page: 47 ident: CR30 article-title: A fast LU update for linear programming publication-title: Ann. Oper. Res. doi: 10.1007/BF02025534 – volume: 13 start-page: 241 year: 1977 ident: 9542_CR5 publication-title: Math. Program. doi: 10.1007/BF01584341 – volume: 57 start-page: 341 year: 1992 ident: 9542_CR9 publication-title: Math. Program. doi: 10.1007/BF01581089 – volume: 3 start-page: 255 issue: 3 year: 1957 ident: 9542_CR26 publication-title: Manag. Sci. doi: 10.1287/mnsc.3.3.255 – volume: 43 start-page: 33 year: 1993 ident: 9542_CR30 publication-title: Ann. Oper. Res. doi: 10.1007/BF02025534 – volume-title: Direct Methods for Sparse Linear Systems. Fundamentals of Algorithms year: 2006 ident: 9542_CR7 doi: 10.1137/1.9780898718881 – volume: 24 start-page: 207 year: 2003 ident: 9542_CR24 publication-title: Comput. Optim. Appl. doi: 10.1023/A:1021858008222 – volume: 32 start-page: 259 year: 2005 ident: 9542_CR17 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-005-4802-0 – volume: 30 start-page: 261 year: 1979 ident: 9542_CR20 publication-title: Z. Angew. Math. Phys. doi: 10.1007/BF01601939 – volume: 8 start-page: 64 issue: 46 year: 1954 ident: 9542_CR6 publication-title: Math. Tables Other Aids Comput. doi: 10.2307/2001993 – volume: 90 start-page: 87 year: 1999 ident: 9542_CR32 publication-title: Ann. Oper. Res. doi: 10.1023/A:1018977102079 – start-page: 64:1 volume-title: Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’11 year: 2011 ident: 9542_CR25 – start-page: 263 volume-title: Stochastic Programming (Proc. Internat. Conf., Univ. Oxford, Oxford, 1974) year: 1980 ident: 9542_CR29 – ident: 9542_CR18 doi: 10.1007/978-3-642-31464-3_15 – start-page: 483 volume-title: Proceedings of the April 18–20, 1967, Spring Joint Computer Conference, AFIPS ’67 (Spring) year: 1967 ident: 9542_CR1 doi: 10.1145/1465482.1465560 – volume-title: Introduction to Stochastic Programming year: 2011 ident: 9542_CR4 doi: 10.1007/978-1-4614-0237-4 – volume: 2 start-page: 325 issue: 4 year: 1990 ident: 9542_CR31 publication-title: ORSA J. Comput. doi: 10.1287/ijoc.2.4.325 – volume: 6 start-page: 135 year: 2009 ident: 9542_CR14 publication-title: Comput. Manag. Sci. doi: 10.1007/s10287-008-0090-3 – volume-title: Introduction to Parallel Computing year: 2003 ident: 9542_CR15 – volume: 41 start-page: 185 year: 2008 ident: 9542_CR22 publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-008-9207-4 – volume: 5 start-page: 1 year: 1973 ident: 9542_CR19 publication-title: Math. Program. doi: 10.1007/BF01580108 – volume-title: Optimization Theory for Large Systems year: 1970 ident: 9542_CR23 – volume: 14 start-page: 636 issue: 4 year: 1966 ident: 9542_CR3 publication-title: Oper. Res. doi: 10.1287/opre.14.4.636 – volume-title: Using MPI-2: Advanced Features of the Message Passing Interface year: 1999 ident: 9542_CR16 – volume: 12 start-page: 199 year: 1993 ident: 9542_CR28 publication-title: Comput. Appl. Math. – ident: 9542_CR21 – volume-title: Matrix Computations year: 1996 ident: 9542_CR13 – volume: 2 start-page: 263 year: 1972 ident: 9542_CR10 publication-title: Math. Program. doi: 10.1007/BF01584548 – volume: 9 start-page: 862 year: 1988 ident: 9542_CR11 publication-title: SIAM J. Sci. Stat. Comput. doi: 10.1137/0909058 – volume: 25 start-page: 1860 year: 2004 ident: 9542_CR2 publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827502401953 – volume: 30 start-page: 95 year: 2004 ident: 9542_CR8 publication-title: ACM Trans. Math. Softw. doi: 10.1145/992200.992201 – volume-title: Computational Techniques of the Simplex Method year: 2003 ident: 9542_CR27 doi: 10.1007/978-1-4615-0257-9 – volume: 45 start-page: 437 year: 1989 ident: 9542_CR12 publication-title: Math. Program. doi: 10.1007/BF01589114 |
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| SubjectTerms | Algorithms Blocking Computation Computer science Convex and Discrete Geometry Decomposition Linear algebra Linear programming Management Science Mathematical analysis Mathematical models Mathematics Mathematics and Statistics Methods Operations Research Operations Research/Decision Theory Optimization Random variables Simplex method Sparsity Statistics Stochasticity Studies |
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| Title | Parallel distributed-memory simplex for large-scale stochastic LP problems |
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