MINLP Solver Technology

136 Pages·2015·9.08 MB·English

by  Stefan Vigerske

MINLP Solver Technology
Stefan Vigerske
10 March 2015
Outline
Solvers
Linear Relaxation of Non-Convex terms
More Relaxations for Quadratic programs
Even More Cuts ...
Reformulation / Presolving
Bound Tightening
Branching
Primal Heuristics
2/65
Outline
Solvers
Linear Relaxation of Non-Convex terms
More Relaxations for Quadratic programs
Even More Cuts ...
Reformulation / Presolving
Bound Tightening
Branching
Primal Heuristics
Solvers 3/65
BARON (Branch And Reduce Optimization Navigator)
(cid:73) by N. Sahinidis (CMU) and M. Tawarmalani (Purdue)
(cid:73) one of the first general purpose codes
(cid:73) available as commercial solver in AIMMS and GAMS
(cid:73) Tawarmalani and Sahinidis [2002, 2004, 2005]
Deterministic Global Optimization Solvers for MINLP
ANTIGONE (Algorithms for coNTinuous / Integer Global
Optimization of Nonlinear Equations)
(cid:73) by R. Misener (Imperial) and C.A. Floudas (Princeton)
(cid:73) originating from a solver for pooling problems
(cid:73) available as commercial solver in GAMS
(cid:73) Misener and Floudas [2012a,b, 2014], Misener [2012]
Solvers 4/65
Deterministic Global Optimization Solvers for MINLP
ANTIGONE (Algorithms for coNTinuous / Integer Global
Optimization of Nonlinear Equations)
(cid:73) by R. Misener (Imperial) and C.A. Floudas (Princeton)
(cid:73) originating from a solver for pooling problems
(cid:73) available as commercial solver in GAMS
(cid:73) Misener and Floudas [2012a,b, 2014], Misener [2012]
BARON (Branch And Reduce Optimization Navigator)
(cid:73) by N. Sahinidis (CMU) and M. Tawarmalani (Purdue)
(cid:73) one of the first general purpose codes
(cid:73) available as commercial solver in AIMMS and GAMS
(cid:73) Tawarmalani and Sahinidis [2002, 2004, 2005]
Solvers 4/65
LindoAPI
(cid:73) by Y. Lin and L. Schrage (LINDO Systems, Inc.)
(cid:73) supports many functions, incl. trigonometric (sin, cos)
(cid:73) available as commercial solver within LINDO and GAMS
(cid:73) Lin and Schrage [2009]
Deterministic Global Optimization Solvers for MINLP
Couenne (Convex Over and Under ENvelopes for Nonlinear
Estimation)
(cid:73) by P. Belotti (CMU, Clemson, now FICO)
(cid:73) COIN-OR open source solver based on Bonmin (based on
CBC and Ipopt)
(cid:73) supports also trigonometric functions (sin, cos)
(cid:73) available for AMPL and in GAMS and OS
(cid:73) Belotti, Lee, Liberti, Margot, and Wächter [2009]
Solvers 5/65
Deterministic Global Optimization Solvers for MINLP
Couenne (Convex Over and Under ENvelopes for Nonlinear
Estimation)
(cid:73) by P. Belotti (CMU, Clemson, now FICO)
(cid:73) COIN-OR open source solver based on Bonmin (based on
CBC and Ipopt)
(cid:73) supports also trigonometric functions (sin, cos)
(cid:73) available for AMPL and in GAMS and OS
(cid:73) Belotti, Lee, Liberti, Margot, and Wächter [2009]
LindoAPI
(cid:73) by Y. Lin and L. Schrage (LINDO Systems, Inc.)
(cid:73) supports many functions, incl. trigonometric (sin, cos)
(cid:73) available as commercial solver within LINDO and GAMS
(cid:73) Lin and Schrage [2009]
Solvers 5/65
Deterministic Global Optimization Solvers for MINLP
SCIP (Solving Constraint Integer Programs)
(cid:73) by Zuse Institute Berlin, TU Darmstadt, ...
(cid:73) part of a constraint integer programming framework
(cid:73) free for academic use, available for AMPL and in GAMS
(cid:73) Berthold, Gleixner, Heinz, and Vigerske [2012], Vigerske [2013]
MIP
(cid:73) LPrelaxation MIP,GO,CP,andSAT
(cid:73) cuttingplanes (cid:73) branch-and-bound
(cid:73) columngeneration
GO(cid:73) spatialbranching implicsbiinntatroyprobingtrivial cfnifxciplpccgmpRseadeorpbzplppmsosrlspol ccmlcifioqlrovuweergomoryzheSaibrmeloofpupanlridaesdtstorcroignntgobrejdcmosrclectafoaypdrcinddle
CP(cid:73) domainpropagation esthiedmysdubtafabirstmslioefhduirixnfetbdsdtffassrtseNlPeocrdteeosrolver Di·sp·l·ay cIamtipolnis TreeSCIPPricer PgarotopVraRareilaabxlpesoebujdroevrdobcoootusntdzadicirtvociounnngscdorvoesrsddvcieivvocifielnneefagngsdpiunmspfiixnfrafaencrddivinHggdPeuiruviidrimniesgadtilinctdisvhiinifngttingblrinaldoneicvscaehinalinrgsdpcughisbovcnciomntlspagtunteatoiobodnjnipvesioncpogtst
defaultdefault Dialog Cutpool Conflict Event default ucnovdeerr ttrwyosoolpttrirvosiuiamnldpilnegsphrifotp&shirftoiunngdingrdroiionvtsinsogl rens
SA(cid:73)(cid:73)T cpoenrifloidcitcarneastlyasritss sqpsxonxopnrsemskLPcpx clp sestops1pcsobcqsaouvotuaasinrd2cdrxorCHoannsdtrlaerianntddbcikosssonauojuucalnncsknpditanct.doirilcnauttemigvurealrceolsptsrandomBrapnscchsaotlsrltfounlmglosstftruiolnlenlfaiegnsntfceienrf
toorpbei orlogicolrinkinglinear
Solvers 6/65
MINOTAUR (Mixed-Integer Nonconvex Optimization
Toolbox – Algorithms, Underestimators, Relaxations)
(cid:73) by A. Mahajan, S. Leyffer, J. Linderoth, J. Luedtke,
T. Munson, et.al. (Argonne, Wisconsin-Madison, IIT Bombay)
(cid:73) open source with AMPL interface
(cid:73) branch-and-bound with NLP relaxation (or its QP
approximation); facilities to handle and manipulate
algebraic expression are in place
(cid:73) Mahajan and Munson [2010], Mahajan et al. [2012]
Upcoming Deterministic Global Solvers for MINLP
COCONUT (COntinuous CONstraints – Updating the Technology)
(cid:73) by A. Neumaier, H. Schichl, E. Monfroy (Vienna), et.al.
(cid:73) rigorous calculations via interval arithmetics, thus avoiding
floating point roundoff errors
(cid:73) still in development, no stable release so far
(cid:73) Neumaier [2004], Bliek et al. [2001]
Solvers 7/65
Upcoming Deterministic Global Solvers for MINLP
COCONUT (COntinuous CONstraints – Updating the Technology)
(cid:73) by A. Neumaier, H. Schichl, E. Monfroy (Vienna), et.al.
(cid:73) rigorous calculations via interval arithmetics, thus avoiding
floating point roundoff errors
(cid:73) still in development, no stable release so far
(cid:73) Neumaier [2004], Bliek et al. [2001]
MINOTAUR (Mixed-Integer Nonconvex Optimization
Toolbox – Algorithms, Underestimators, Relaxations)
(cid:73) by A. Mahajan, S. Leyffer, J. Linderoth, J. Luedtke,
T. Munson, et.al. (Argonne, Wisconsin-Madison, IIT Bombay)
(cid:73) open source with AMPL interface
(cid:73) branch-and-bound with NLP relaxation (or its QP
approximation); facilities to handle and manipulate
algebraic expression are in place
(cid:73) Mahajan and Munson [2010], Mahajan et al. [2012]
Solvers 7/65