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Jun Ma, Optimization Services, June 23, 2005
Optimization Services (OS)
Jun Ma
Industrial Engineering and Management SciencesNorthwestern University
T.J. Watson Lab, IBM, 06/23/2005
-- A Framework for Optimization Software
-- A Computational Infrastructure
-- The Next Generation NEOS
-- The OR Internet
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Jun Ma, Optimization Services, June 23, 2005
OUTLINE
2. Demonstration
3. Optimization Services and Optimization Services Protocol
6. Optimization Services Protocol - Representation
10. Future and Derived Research
1. Motivations
7. Optimization Services Protocol - Communication
8. Optimization Services Protocol - Registry
5. Computing and Distributed Background
9. Optimization Services modeling Language (OSmL)
4. Optimization System Background
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Jun Ma, Optimization Services, June 23, 2005
MotivationFuture of Computing
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Jun Ma, Optimization Services, June 23, 2005
MotivationBut how… with so many type of components
1. Modeling Language Environment (MLE) (AIMMS, AMPL, GAMS, LINGO, LPL, MOSEL, MPL, OPL, OSmL, POAMS, PuLP, spreadsheets, GUIs )
2. Solver(Too many)
3. Analyzer/Preprocessor(Analyzer, MProbe, Dr. AMPL)
4. Simulation(Software that does heavy computation, deterministic or stochastic)
5. Server/Registry(NEOS, BARON, HIRON, NIMBUS, LPL, AMPL, etc.)
6. Interface/Communication Agent(COIN-OSI, CPLEX-Concert, AMPL/GAMS-Kestrel, etc.)
7. Low Level Instance Representation(Next page)
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Jun Ma, Optimization Services, June 23, 2005
Motivation
But how… with so many optimization types and representation formats
Linear Programming Quadratic ProgrammingMixed Integer Linear Programming
MPS, xMPS, LP, CPLEX, GMP, GLP, PuLP, LPFML, MLE instances
Nonlinearly Constrained OptimizationBounded Constrained OptimizationMixed Integer Nonlinearly Constrained OptimizationComplementarity ProblemsNondifferentiable OptimizationGlobal Optimization
MLE instancesSIF (only for Lancelot solver)
Semidefinite & Second Order Cone Programming
Sparse SDPA, SDPLR
Linear Network Optimization NETGEN, NETFLO, DIMACS, RELAX4
Stochastic Linear Programming sMPS
Stochastic Nonlinear Programming None
Combinatorial Optimization None (except for TSP input, only intended for solving Traveling Sales Person problems.
Constraint and Logic Programming None
Optimization with Distributed Data None
Optimization via Simulation None
OSiL
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Jun Ma, Optimization Services, June 23, 2005
MotivationLook at the NEOS server Web site
M X N drivers M + N drivers
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Jun Ma, Optimization Services, June 23, 2005
MotivationAs if it’s not bad enough …
1. Tightly-coupled implementation (OOP? Why not!)
2. Various operating systems
3. Various communication/interfacing mechanisms
4. Various programming languages
5. Various benchmarking standards
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Jun Ma, Optimization Services, June 23, 2005
MotivationNow…
• The key issue is communication, not solution!
• … and Optimization Services is intended to solve all the above issues.
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Jun Ma, Optimization Services, June 23, 2005
OUTLINE
2. Demonstration
3. Optimization Services and Optimization Services Protocol
6. Optimization Services Protocol - Representation
10. Future and Derived Research
1. Motivations
7. Optimization Services Protocol - Communication
8. Optimization Services Protocol - Registry
5. Computing and Distributed Background
9. Optimization Services modeling Language (OSmL)
4. Optimization System Background
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Jun Ma, Optimization Services, June 23, 2005
Demonstration
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Jun Ma, Optimization Services, June 23, 2005
OUTLINE
2. Demonstration
3. Optimization Services and Optimization Services Protocol
6. Optimization Services Protocol - Representation
10. Future and Derived Research
1. Motivations
7. Optimization Services Protocol - Communication
8. Optimization Services Protocol - Registry
5. Computing and Distributed Background
9. Optimization Services modeling Language (OSmL)
4. Optimization System Background
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Jun Ma, Optimization Services, June 23, 2005
Optimization Services (OS)What is happening behind?
Modeler
Model/Data Agent Solver
AMPL
OSmL
Parse to OSiL
XML-based standard
OS
Server
OS Server
location
Registry
OS Server
Simulation
Solver
Solver
Max f(x) :objective x :variabless.t. lb1 <= g1(x) <= ub2 :constraints lb2 <= g2(x) <= ub2
f(x) can be sin(x(1))+x(x(2))g1(x) can be if(x(1)>0) then x(2) else cost(x(2))g2(x) can be a metric from a finite element simulation (non-closed form black box function evaluator)
Analyzer
Raw Data
browser
Web page
Web Server
CGIsocket
Data in HTML Form
http/html
OSP -- OShL(OSiL)
Database/ App Service
HTML Checker
Web address
html form
OS Server
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Jun Ma, Optimization Services, June 23, 2005
Optimization ServicesWhat is it? – A framework for optimization software
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Jun Ma, Optimization Services, June 23, 2005
Optimization ServicesWhat is it? – A computational infrastructure
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Jun Ma, Optimization Services, June 23, 2005
Optimization ServicesWhat is it? – The next generation NEOS
•The NEOS server and its connected solvers uses the OS framework.•NEOS accepts the OSiL and other related OSP for problem submissions•NEOS becomes an OS compatible meta-solver on the OS network •NEOS hosts the OS registry
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Jun Ma, Optimization Services, June 23, 2005
Optimization ServicesWhat is it? – The OR Internet
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Jun Ma, Optimization Services, June 23, 2005
Optimization Services Protocol (OSP) What is it? – Application level networking protocol
– Interdisciplinary protocol between CS and OR
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Jun Ma, Optimization Services, June 23, 2005
Optimization Services Protocol (OSP) What does the protocol involve? – 20+ OSxL languages
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Jun Ma, Optimization Services, June 23, 2005
OUTLINE
2. Demonstration
3. Optimization Services and Optimization Services Protocol
6. Optimization Services Protocol - Representation
10. Future and Derived Research
1. Motivations
7. Optimization Services Protocol - Communication
8. Optimization Services Protocol - Registry
5. Computing and Distributed Background
9. Optimization Services modeling Language (OSmL)
4. Optimization System Background
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Jun Ma, Optimization Services, June 23, 2005
Optimization System Background What does an optimization system look like?
0x
tosubject
minimize
bAx
cxx
users
modelers
developers
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Jun Ma, Optimization Services, June 23, 2005
Optimization System Background What is the difference between a model and an instance?
0x
tosubject
minimize
bAx
cxx
model high-level, user-friendly
symbolic, general,
concise, understandable
AMPL
instance
MPS
OSiL
Low-level, computer-friendly
explicit, specific,
redundant, convenient
compile
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Jun Ma, Optimization Services, June 23, 2005
Optimization System Background What’s the difference between local interfacing and communication agent
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Jun Ma, Optimization Services, June 23, 2005
Optimization System Background More on local interface
9. “COIN OSI Solver” with GLPK Solvers (OSI is in fact a parser)
3.5 COIN-GLPKParser1. client (human or machine) construct COIN objects
Or1. MPS
2. MPS Reader
COINObj
COINObj
COINObj
COINObj
3. unified objectsor the MPSformat designedin COIN OSI
5. GLPK SolverGLPK
ObjGLPK
Obj
GLPKObj
GLPKObj
4. objectstaken byGLPKSolver
10 What we suggest for COIN OSI2 with any general solver, say “LANCELOT” or a new COIN Solver
5. LANCELOT(Existing)
<- x f(x) ->
5. A New COIN Solvermay just directly takethe objects created bythe OSiLReaderSo 3 and 4 are just thesame and there will beno 3.5
<- x f(x) ->
<- x f(x) ->
1. OSiL2. OSiLReader
expressiontrees
postfix
AMatrix
rowNum,colNum,rhs[], etc.
3.objectscreated byOSiLReader
3.5 COIN-LANCELOTOSiLReader <- x
f(x) ->
4. LANCELOT’sNLProblem
dF
Infix
AMatrix
iCol
for new COIN solver
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Jun Ma, Optimization Services, June 23, 2005
Optimization System Background Why is analyzer important?
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Jun Ma, Optimization Services, June 23, 2005
Optimization System Background What’s the difference between a server and a registry
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Jun Ma, Optimization Services, June 23, 2005
Optimization System Background What’s a simulation?
0,0x
932tosubject
2 minimize
21
21
22
21
x
xx
xxx
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Jun Ma, Optimization Services, June 23, 2005
Optimization System Background AMPL, NEOS and Kestrel
ampl: option optimizationservices on
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Jun Ma, Optimization Services, June 23, 2005
OUTLINE
2. Demonstration
3. Optimization Services and Optimization Services Protocol
6. Optimization Services Protocol - Representation
10. Future and Derived Research
1. Motivations
7. Optimization Services Protocol - Communication
8. Optimization Services Protocol - Registry
5. Computing and Distributed Background
9. Optimization Services modeling Language (OSmL)
4. Optimization System Background
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Jun Ma, Optimization Services, June 23, 2005
Computing and Distributed Background What we used in our implementation
1. Java, Open Source Libraries, Object-oriented Programming (OS library)
2. Networking Protocols: HTTP, SOAP, OSP (OS server: Tomcat, Axis, OS library)
3. Eclipse IDE for JAVA development
4. XML Spy for XML Schema design
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Jun Ma, Optimization Services, June 23, 2005
Computing and Distributed Background XML and XML Dialect (e.g. MathML, OSiL)
MathML
OSiL
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Jun Ma, Optimization Services, June 23, 2005
Computing and Distributed Background XML Schema
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Jun Ma, Optimization Services, June 23, 2005
Computing and Distributed Background Other XML Technologies
1. Parsing: SAX and DOM models
2. Transformation: XSL style sheet
3. Lookup: XPath and XQuery
4. Communication: SOAP, WSDL, UDDI
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Jun Ma, Optimization Services, June 23, 2005
Computing and Distributed Background Web services and SOAP
Protocol ViewArchitecture View
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Jun Ma, Optimization Services, June 23, 2005
OUTLINE
2. Demonstration
3. Optimization Services and Optimization Services Protocol
6. Optimization Services Protocol - Representation
10. Future and Derived Research
1. Motivations
7. Optimization Services Protocol - Communication
8. Optimization Services Protocol - Registry
5. Computing and Distributed Background
9. Optimization Services modeling Language (OSmL)
4. Optimization System Background
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Jun Ma, Optimization Services, June 23, 2005
Optimization Services RepresentationOptimization Services general Language (OSgL)
General data structures; Included in other schemas
Optimization Services instance Language (OSiL)
All major optimization types
Optimization Services nonlinear Language (OSnL)
Provides 200+ function/operator/operand nodes for OSiL
arithmetic, elementary function, statistic/probability, constants, optimization, terminals, trigonometric, logic/relational, special
Optimization Services result Language (OSrL)
Multiple solutions; built-in standard results, solver-specific, analysis result
Optimization Services option Language (OSoL)
Few built-in standard options; well-scalable design structure for specific options
Optimization Services simulation Language (OSsL)
Both simulation input and output; supports values and links
Optimization Services transformation Language (OStL)
XSL transformation style sheet;
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Jun Ma, Optimization Services, June 23, 2005
OSiL and OSrL
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Jun Ma, Optimization Services, June 23, 2005
OUTLINE
2. Demonstration
3. Optimization Services and Optimization Services Protocol
6. Optimization Services Protocol - Representation
10. Future and Derived Research
1. Motivations
7. Optimization Services Protocol - Communication
8. Optimization Services Protocol - Registry
5. Computing and Distributed Background
9. Optimization Services modeling Language (OSmL)
4. Optimization System Background
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Jun Ma, Optimization Services, June 23, 2005
Optimization Services CommunicationOptimization Services hookup Language (OShL)
Hookup to solvers, and analyzers
Optimization Services instance Language (OScL)
Call simulations
Optimization Services flow Language (OSfL)
Orchestrate flow logics;
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Jun Ma, Optimization Services, June 23, 2005
OUTLINE
2. Demonstration
3. Optimization Services and Optimization Services Protocol
6. Optimization Services Protocol - Representation
10. Future and Derived Research
1. Motivations
7. Optimization Services Protocol - Communication
8. Optimization Services Protocol - Registry
5. Computing and Distributed Background
9. Optimization Services modeling Language (OSmL)
4. Optimization System Background
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Jun Ma, Optimization Services, June 23, 2005
Optimization Services Registryregistration
Optimization Services entity Language (OSeL, representation)
Static service entity information
Optimization Services process Language (OSpL, , representation)
Dynamic service process information
Optimization Services benchmark Language (OSbL, , representation)
Score based benchmarks?
Optimization Services yellow-page Language (OSyL, , representation)
OS registry database; native XML; A sequence of [OSeL, OSpL, OSbL] triplets
Optimization Services join Language (OSjL, communication)
Join the OS registry (manual and automatic process) with entity (OSeL) information.
Optimization Services knock Language (OSkL, communication)
“Knock” at the services for run time dynamitic process (OSpL) information
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Jun Ma, Optimization Services, June 23, 2005
Optimization Services Registrydiscovery
Optimization Services query Language (OSqL, representation)
Like SQL for relational database; can use XQuery, OSaL (analysis), predefined
Optimization Services discover Language (OSdL, communication)
send the query to the OS registry to discover services
Optimization Services uri Language (OSuL, representation)
A sequence of uri (url) addresses for service locations with degree of fitness
Optimization Services validate Language (OSvL, validate)
A validation service provided by the OS registry that validates all OSxL instances
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Jun Ma, Optimization Services, June 23, 2005
OUTLINE
2. Demonstration
3. Optimization Services and Optimization Services Protocol
6. Optimization Services Protocol - Representation
10. Future and Derived Research
1. Motivations
7. Optimization Services Protocol - Communication
8. Optimization Services Protocol - Registry
5. Computing and Distributed Background
9. Optimization Services modeling Language (OSmL)
4. Optimization System Background
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Jun Ma, Optimization Services, June 23, 2005
Optimization Services modeling Language(OSmL)
A derived research
Open source and general purposeStandard based (XQuery input; OSiL output)Suitable for distributed optimization
XML data is ubiquitous
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Jun Ma, Optimization Services, June 23, 2005
Optimization Services modeling Language
#set, parameter, and variable constructionsparam T;set PROD;set LINKS = {PROD, 1..T};param HC {PROD} ;param FXC {PROD} ;param CAP {1..T} ;param DEM {LINKS};param PCOST {PROD, 1..T} ;
#VARIABLE DECLARATIONvar x {PROD, 1..T} >= 0;var I {PROD, 0..T} >=0;var y {PROD, 1..T}binary;
#OBJECTIVE CONSTRUCTIONminimize Total_Cost: sum {i in PROD} I[i, 0] + sum {i in PROD, t in 1..T} (PCOST[i, t]*x[i, t] + HC[i]*I[i, t] + FXC[i]*y[i, t]);
# INITIAL INVENTORY CONSTRAINTSsubject to Init_Inv {i in PROD}: I[i, 0] = 0.0;
# DEMAND CONSTRAINTSsubject to Balance {i in PROD, t in 1..T}: x[i, t] + I[i, t - 1] - I[i, t] = DEM[i, t];
# FIXED CHARGE CONSTRAINTSsubject to Fixed_Charge {i in PROD, t in 1..T}: x[i, t] <= CAP[ t]*y[i, t];
# CAPACITY CONSTRAINTS subject to Capacity {t in 1..T}: sum {i in PROD} x[i, t] <= CAP[ t];
(: set and parameter constructions:)let $capacity := doc("./lotsizeData.xml")/lotSizeData/periodCapacity/capacitylet $products := doc("./xml/ds800m.xml")/lotSizeData/productlet $N := count($products)let $T := count($capacity[periodID])let $FXC := data($products/@fixedCost)let $HC := data($products/@holdCost)let $PCOST := data($products/@prodCost)let $CAP := data($capacity/text())let $DEM := $products/period/demandlet $PROD := (1 to $N)return <mathProgram> (: VARIABLE DECLARATION :)<variables>{ for $i in (1 to $N), $t in (1 to $T) return (<var name="X[{$i},{$t}]"/>, <var name="I[{$i},{$t}]"/>, <var name="Y[{$i},{$t}]" type="B" />) }</variables>
(: OBJECTIVE FUNCTION :)<obj maxOrMin="min" name="Total_Cost">SUM(for $i in (1 to $N), $t in (1 to $T) return{$PCOST[$i]}*X[{$i},{$t}] + {$FXC[$i]}*Y[{$i},{$t}] + {$HC[$i]}*I[{$i},{$t}])</obj>
<constraints>(: INITIAL INVENTORY CONSTRAINTS :){for $i in $PROD return <con name="inventory[{$i}]"> I[{$i},0] = 0 </con> }
(: DEMAND CONSTRAINTS :){for $i in $PROD, $t in (1 to $T)let $demand := ($products[$i]/period[@periodID=$t]/demand/text()) return<con name="demand[{$i},{$t }]"> X[{$i},{$t}] + I[{$i},{$t - 1}] - I[{$i},{$t}] = {$demand} </con> }
(: FIXED CHARGE CONSTRAINTS :){for $t in (1 to $T), $i in (1 to $N) return<con name="fixed_charge[{$i},{$t }]" > X[{$i},{$t}]-{$CAP[$t]}*Y[{$i},{$t}] <= 0</con> }
(: CAPACITY CONSTRAINTS :){for $t in (1 to $T) return <con name="capacity[{$t}]"> SUM(for $i in (1 to $N) return X[{$i},{$t}])<= {$CAP[$t]} </con>}</constraints> </mathProgram>
AMPLOSmL
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Jun Ma, Optimization Services, June 23, 2005
Optimization Services modeling Language4 ways of combining XML with optimization
1. Use XML to represent the instance of a mathematical program
2. Develop an XML modeling language dialect
3. Enhance modeling languages with XML features such as XPath
4. Use XML technologies to transform XML data into a problem instance
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Jun Ma, Optimization Services, June 23, 2005
OUTLINE
2. Demonstration
3. Optimization Services and Optimization Services Protocol
6. Optimization Services Protocol - Representation
10. Future and Derived Research
1. Motivations
7. Optimization Services Protocol - Communication
8. Optimization Services Protocol - Registry
5. Computing and Distributed Background
9. Optimization Services modeling Language (OSmL)
4. Optimization System Background
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Jun Ma, Optimization Services, June 23, 2005
Future and Derived Research• The Optimization Services project• Standardization • Problem repository building • OS server software, library enhancement• Derived research in distributed systems (coordination, scheduling and congestion control)• Derived research in decentralized systems (registration,
discovery, analysis, control)• Derived research in local systems (OSI? OSiI, OSrI, OSoI?)• Derived research in optimization servers (NEOS)• Derived research in computational software
(AMPL, Knitro, Lindo/Lingo, IMPACT, OSmL, MProbe, Dr. AMPL, etc. )• Derived research in computational algorithm
Parallel computing
Optimization via simulation
Optimization job scheduling
Analyzing optimization instances according to the needs of the OS registry.
Modeling and compilation
Efficient OSxL instance parsing and preprocessing algorithms.
Effective Optimization Services process orchestration.
Promote areas where lack of progress are partly due to lack of representation schemes• Derived business model
Modeling language developers, solver developers, and analyzer developers
Library developers, registry/server developers, and other auxiliary developers
Computing on demand and “result on demand”
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Jun Ma, Optimization Services, June 23, 2005
Acknowledgement • Robert Fourer (advisor)• Kipp Martin (co-advisor)• Tom Tirpak, Motorola Advanced Technology Center• Professor Mehrotra’s group• NEOS/OTC team at Argonne National Lab• Professor John Birge• Professor Horand Gassmann• Jorge Nocedal & Richard Waltz, Knitro/Ziena• Professors at Northwestern IEMS (Mark Daskin, Wally Hopp, Barry Nelson)• Professor Gordon Bradley• Bjarni Kristjansson, MPL• Linus Schrage, Lindo
http://www.optimizationservices.org (.net)
INFORMS New Orleans Cluster: Optimization Services and Open Source Software