Building AMPL Models into Applications

72 Pages·2014·3.64 MB·English

Building AMPL Models
into Applications
Robert Fourer, Victor Zverovich
[4er,viz]@ampl.com
AMPL Optimization Inc.
www.ampl.com — +1 773-336-AMPL
INFORMS Annual Meeting
San Francisco — 9-12 November 2014
Session SC56, Software Demonstrations
Robert Fourer, Victor Zverovich,Building AMPL Models Into Applications 1
INFORMS San Francisco —9-12 Nov 2014 —SC56 Software Demonstrations
Robert Fourer, Victor Zverovich,Building AMPL Models Into Applications 3
INFORMS San Francisco —9-12 Nov 2014 —SC56 Software Demonstrations
The Optimization Modeling Cycle
Steps
 Communicate with problem owner
 Build model
 Prepare data
 Generate optimization problem
 Submit problem to solver
 CPLEX, Gurobi, KNITRO, CONOPT, MINOS, . . .
 Report & analyze results
 Repeat!
Goals for optimization software
 Do this quickly and reliably
 Get results before client loses interest
 Deploy for application
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INFORMS San Francisco —9-12 Nov 2014 —SC56 Software Demonstrations
Optimization Modeling Languages
Two forms of an optimization problem
 Modeler’s form
 Mathematical description, easy for people to work with
 Algorithm’s form
 Explicit data structure, easy for solvers to compute with
Idea of a modeling language
 A computer-readable modeler’s form
 You write optimization problems in a modeling language
 Computers translate to algorithm’s form for solution
Advantages of a modeling language
 Faster modeling cycles
 More reliable modeling
 More maintainable applications
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INFORMS San Francisco —9-12 Nov 2014 —SC56 Software Demonstrations
Algebraic Modeling Languages
Formulation concept
 Define data in terms of sets & parameters
 Analogous to database keys & records
 Define decision variables
 Minimize or maximize a function of decision variables
 Subject to equations or inequalities
that constrain the values of the variables
Advantages
 Familiar
 Powerful
 Implemented
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INFORMS San Francisco —9-12 Nov 2014 —SC56 Software Demonstrations
The AMPL Modeling Language
Features
 Algebraic modeling language
 Variety of data sources
 Connections to all solver features
Advantages
 Powerful, general expressions
 Natural, easy-to-learn design
 Efficient processing scales well with problem size
3 ways to use
 Command language
 Scripting language
 Programming interface (API)
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INFORMS San Francisco —9-12 Nov 2014 —SC56 Software Demonstrations
Outline
Example: Multicommodity transportation
 Solution via command language
 Sensitivity analysis via scripting
Example: Roll cutting
 Pattern enumeration
 via scripting
 via MATLAB API
 via Java API
 Pattern generation
 via scripting
 via MATLAB API
Availability . . .
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INFORMS San Francisco —9-12 Nov 2014 —SC56 Software Demonstrations
Command Language
Multicommodity transportation . . .
 Products available at factories
 Products needed at stores
 Plan shipments at lowest cost
. . . with practical restrictions
 Cost has fixed and variable parts
 Shipments cannot be too small
 Factories cannot serve too many stores
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INFORMS San Francisco —9-12 Nov 2014 —SC56 Software Demonstrations
Multicommodity Transportation
Given
(cid:1841) Set of origins (factories)
(cid:1830) Set of destinations (stores)
(cid:1842) Set of products
and
(cid:1853) Amount available, for each (cid:1861) ∈ (cid:1841) and (cid:1868) ∈ (cid:1842)
(cid:3036)(cid:3043)
(cid:1854) Amount required, for each (cid:1862) ∈ (cid:1830) and (cid:1868) ∈ (cid:1842)
(cid:3037)(cid:3043)
(cid:1864) Limit on total shipments, for each (cid:1861) ∈ (cid:1841) and (cid:1862) ∈ (cid:1830)
(cid:1861)(cid:1862)
(cid:1855) Shipping cost per unit, for each (cid:1861) ∈ (cid:1841), (cid:1862) ∈ (cid:1830), (cid:1868) ∈ (cid:1842)
(cid:1861)(cid:1862)(cid:1868)
(cid:1856) Fixed cost for shipping any amount from (cid:1861) ∈ (cid:1841) to (cid:1862) ∈ (cid:1830)
(cid:1861)(cid:1862)
(cid:1871) Minimum total size of any shipment
(cid:1866) Maximum number of destinations served by any origin
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INFORMS San Francisco —9-12 Nov 2014 —SC56 Software Demonstrations
Multicommodity Transportation
Mathematical Formulation
Determine
(cid:1850) Amount of each (cid:1868) ∈ (cid:1842) to be shipped from (cid:1861) ∈ (cid:1841) to (cid:1862) ∈ (cid:1830)
(cid:1861)(cid:1862)(cid:1868)
(cid:1851) 1 if any product is shipped from (cid:1861) ∈ (cid:1841) to (cid:1862) ∈ (cid:1830)
(cid:1861)(cid:1862)
0 otherwise
to minimize
∑ ∑ ∑ (cid:1855) (cid:1850) (cid:3397) ∑ ∑ (cid:1856) (cid:1851)
(cid:3036)∈(cid:3016) (cid:3037)∈(cid:3005) (cid:3043)∈(cid:3017) (cid:3036)(cid:3037)(cid:3043) (cid:3036)(cid:3037)(cid:3043) (cid:3036)∈(cid:3016) (cid:3037)∈(cid:3005) (cid:3036)(cid:3037) (cid:3036)(cid:3037)
Total variable cost plus total fixed cost
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INFORMS San Francisco —9-12 Nov 2014 —SC56 Software Demonstrations