Dr. Ampl A Meta Solver for Optimization Dominique Orban Bob Fourer École Polytechnique de Montréal Northwestern University Dominique.Orban@polymtl.ca 4er@iems.northwestern.edu Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 1/36
Outline ■ Numerical Optimization ● Outline ● Numerical Optimization Software Model analysis The DAG Bounds Convexity Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 2/36
Outline ■ Numerical Optimization ● Outline ● Numerical Optimization ■ Current software challenges Software Model analysis The DAG Bounds Convexity Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 2/36
Outline ■ Numerical Optimization ● Outline ● Numerical Optimization ■ Current software challenges Software ■ The NEOS Server Model analysis The DAG Bounds Convexity Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 2/36
Outline ■ Numerical Optimization ● Outline ● Numerical Optimization ■ Current software challenges Software ■ The NEOS Server Model analysis ■ The AMPL modeling language The DAG Bounds Convexity Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 2/36
Outline ■ Numerical Optimization ● Outline ● Numerical Optimization ■ Current software challenges Software ■ The NEOS Server Model analysis ■ The AMPL modeling language The DAG ■ The DrAmpl meta solver Bounds Convexity Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 2/36
Outline ■ Numerical Optimization ● Outline ● Numerical Optimization ■ Current software challenges Software ■ The NEOS Server Model analysis ■ The AMPL modeling language The DAG ■ The DrAmpl meta solver Bounds Convexity ■ Numerical results Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 2/36
Outline ■ Numerical Optimization ● Outline ● Numerical Optimization ■ Current software challenges Software ■ The NEOS Server Model analysis ■ The AMPL modeling language The DAG ■ The DrAmpl meta solver Bounds Convexity ■ Numerical results Classification ■ Future directions of research Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 2/36
Numerical Optimization A general problem, representable in a modeling language may ● Outline ● Numerical Optimization be written as Software Model analysis The DAG minimize objective f ( x ) Bounds c L ≤ c ( x ) ≤ c U subject to general constraints Convexity x L ≤ x ≤ x U explicit bounds Classification Preprocessing Solver choice where f : R n → R , c : R n → R m ∈ C 2 . Final notes Bounds may be equal or infinite, some c i ( x ) may be linear. Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 3/36
Current software challenges ■ Myriad of solvers available for most classes of optimization ● Outline ● Numerical Optimization problems Software ■ Competing solvers designed to tackle the same class of ● Current software challenges ● Consequences problems, with varying subtelties ● More software challenges ● The NEOS Optimization Server ● The AMPL modeling language ■ Competing general-purpose solvers ● Some typical AMPL commands ● DrAmpl is a meta solver ■ Competing free and commercial codes Model analysis ■ Competing modeling languages and environments The DAG ■ Often, solvers have limited compatibility with modeling Bounds environments or interfaces do not exist Convexity Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 4/36
Consequences ■ Much confusion arising from so much choice ● Outline ● Numerical Optimization ■ Much room for remote or local software offering guidance Software and bridging the abyssal gap between problem classes and ● Current software challenges ● Consequences solvers ● More software challenges ● The NEOS Optimization Server ● The AMPL modeling language ■ Much need for tools to help bridge this gap, by compiling lists ● Some typical AMPL commands ● DrAmpl is a meta solver of available software, classifying the possible problem Model analysis instances, linking them together The DAG ■ Much need for software able to associate a given problem Bounds instance with a general class and a general class with a few Convexity solvers. Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 5/36
More software challenges ■ Modeling languages are often commercial ● Outline ● Numerical Optimization ■ Optimization software is often commercial Software ● Current software challenges ■ Software may be problematic to install locally ● Consequences ● More software challenges ■ Need to learn how to use the software ● The NEOS Optimization Server ● The AMPL modeling language ■ Trial versions are often available with various limitations ● Some typical AMPL commands ● DrAmpl is a meta solver Model analysis The DAG Bounds Convexity Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 6/36
The NEOS Optimization Server ■ Remote optimization software repository ● Outline ● Numerical Optimization ■ Problems modelled locally, solved remotely Software ● Current software challenges ■ Solution may be returned for later local examination ● Consequences ● More software challenges ■ Accepts problems in several modeling languages; AMPL, ● The NEOS Optimization Server ● The AMPL modeling language GAMS, SIF, SeDuMi, Sparse SDPA, C and Fortran ● Some typical AMPL commands ● DrAmpl is a meta solver ■ 43 solvers for 12 classes of optimization problems Model analysis ■ Optimization tree... last updated in March 1996. The DAG ■ 2723 submissions from May 2–May 9, up to 5430/week Bounds Convexity ■ Alleviates the need to install some solvers locally Classification ■ Allows to test solvers before purchasing or downloading Preprocessing ■ Free of charge Solver choice ■ E-mail, Web, TCP/IP submission clients Final notes How to best make use of all those resources? Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 7/36
The AMPL modeling language ■ Fourer, Gay, Kernighan book ● Outline ● Numerical Optimization ■ Flexible and powerful language to model linear, nonlinear, Software mixed-integer and constraint programming ● Current software challenges ● Consequences ● More software challenges ■ Provides some level of preprocessing ● The NEOS Optimization Server ● The AMPL modeling language ■ Provides automatic differentiation ● Some typical AMPL commands ● DrAmpl is a meta solver ■ Size-limited student version available free of charge Model analysis ■ Source code of AMPL library available on NetLib to facilitate The DAG interfacing with solvers and exploring the AMPL data Bounds structures Convexity Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 8/36
Some typical AMPL commands Select a model, a solver and solve. ● Outline ● Numerical Optimization Software ● Current software challenges ampl: model mymodel.mod; ● Consequences ● More software challenges ampl: data mymodel.dat; ● The NEOS Optimization Server ● The AMPL modeling language ampl: option solver lancelot; ● Some typical AMPL commands ● DrAmpl is a meta solver ampl: solve; Model analysis The DAG Bounds What is a solver to AMPL? Any program which can receive a Convexity model, possibly manipulate it and return some result. Classification Preprocessing Make a distinction between a solver and a meta solver. Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 9/36
DrAmpl is a meta solver The purposes of DrAmpl are to ● Outline ● Numerical Optimization Software ● Current software challenges ■ Analyze a given model ● Consequences ● More software challenges ● The NEOS Optimization Server ■ Provide bounds on expressions appearing in the model ● The AMPL modeling language ● Some typical AMPL commands ■ Assess convexity of expressions appearing in the model ● DrAmpl is a meta solver ■ Classify the model Model analysis The DAG ■ Provide some level of "nonlinear preprocessing" Bounds ■ Assist in the choice of an appropriate solver Convexity Classification Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 10/36
Analysis of a model Problem statistics ● Outline ● Numerical Optimization ------------------ Software # Objectives: [1 ] Model analysis # Nonlinear objectives: 0 ● Analysis of a model ● Analysis of a model # Linear objectives: 1 ● Analysis of a model ● Analysis of a model The DAG Sparsity statistics Bounds ------------------- Convexity # nnz in Jacobian: 4000 Classification # nnz in obj. gradients: 800 Preprocessing Solver choice Final notes Dominique Orban, May 21, 2004 The DrAmpl meta solver - p. 11/36
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