AIMMS

AIMMS
Designed by Johannes J. Bisschop
Marcel Roelofs
Developer AIMMS B.V. (formerly named Paragon Decision Technology B.V.[1])
First appeared 1993
Stable release
AIMMS 4.0 / July 7, 2014
OS Cross-platform with limitations such as Windows-only GUI
License Proprietary
Filename extensions .aimms .ams .prj .aim .amb .aimmspack .data .dat
Website AIMMS home page

AIMMS (an acronym for "Advanced Interactive Multidimensional Modeling System") is a software system designed for modeling and solving large-scale optimization and scheduling-type problems.[2][3] It consists of an algebraic modeling language, an integrated development environment for both editing models and creating a graphical user interface around these models, and a graphical end-user environment.[4] AIMMS is linked to multiple solvers through the AIMMS Open Solver Interface, not to be confused with COIN-OR Open Solver Interface (OSI) which unlike AIMMS OSI is an open-source project.[5] Supported solvers include CPLEX, Gurobi, MOSEK, CBC, Conopt, MINOS, IPOPT, SNOPT, KNITRO and CP Optimizer.

AIMMS is considered to be one of the five most important algebraic modeling languages (others are: AMPL, GAMS, LINDO/LINGO, and MPL), and the creator (Johannes J. Bisschop) has been awarded with INFORMS Impact Prize for his work in this language.[6]

Features

AIMMS features a mixture of declarative and imperative programming styles. Formulation of optimization models takes place through declarative language elements such as sets and indices, as well as scalar and multidimensional parameters, variables and constraints, which are common to all algebraic modeling languages, and allow for a concise description of most problems in the domain of mathematical optimization. Units of measurement are natively supported in the language, and compile- and runtime unit analysis may be employed to detect modeling errors.

Procedures and control flow statements are available in AIMMS for

To support the re-use of common modeling components, AIMMS allows modelers to organize their model in user model libraries.

AIMMS supports a wide range of mathematical optimization problem types:

Uncertainty can be taken into account in deterministic linear and mixed integer optimization models in AIMMS through the specification of additional attributes, such that stochastic or robust optimization techniques can be applied alongside the existing deterministic solution techniques.

Custom hybrid and decomposition algorithms can be constructed using the GMP system library which makes available at the modeling level many of the basic building blocks used internally by the higher level solution methods present in AIMMS, matrix modification methods, as well as specialized steps for customizing solution algorithms for specific problem types.

Optimization solutions created with AIMMS can be used either as a standalone desktop application or can be embedded as a software component in other applications.

Use in industry

AIMMS is used in a wide range of industries including oil and chemicals, steel production and agribusiness.[7][8][9]

Alstom Grid uses AIMMS as the modeling and optimization engine of its energy market clearing software.[10] Together with Alstom Grid, AIMMS (formerly known as Paragon Decision Technology) was part of the analytics team of Midwest ISO that won the Franz Edelman Award for Achievement in Operations Research and the Management Sciences of 2011 for successfully applying operations research in the Midwest ISO energy market.[11]

A sample model

A transportation problem[12] from George Dantzig is used to provide a sample AIMMS model. This problem finds the least cost shipping schedule that meets requirements at markets and supplies at factories. The textual representation of an AIMMS model presents the model as a tree of attributed identifier nodes. It reflects the way in which the model is presented to the modeler in the AIMMS IDE, and is typically generated by the AIMMS IDE.

MAIN MODEL Main_Transport

  DECLARATION SECTION 

    QUANTITY:
       identifier   :  QuantityLength
       base unit    :  mile ;

    QUANTITY:
       identifier   :  QuantityCurrency
       base unit    :  $ ;

    SET:
       identifier   :  Plants
       index        :  p ;

    SET:
       identifier   :  Markets
       index        :  m ;

    PARAMETER:
       identifier   :  Capacity
       index domain :  p ;

    PARAMETER:
       identifier   :  Demand
       index domain :  m ;

    PARAMETER:
       identifier   :  Distance
       index domain :  (p,m)
       unit         :  1000 * mile ;

    PARAMETER:
       identifier   :  Freight
       unit         :  $/(1000 * mile) ;

    PARAMETER:
       identifier   :  TransportCost
       index domain :  (p,m)
       unit         :  1000 * $
       definition   :  Freight * Distance(p,m) ;

    VARIABLE:
       identifier   :  Shipment
       index domain :  (p,m)
       range        :  nonnegative ;

    CONSTRAINT:
       identifier   :  SatisfyCapacity
       index domain :  p
       definition   :  sum(m, Shipment(p,m)) <= Capacity(p) ;

    CONSTRAINT:
       identifier   :  MeetDemand
       index domain :  m
       definition   :  sum(p, Shipment(p,m)) >= Demand(m) ;

    VARIABLE:
       identifier   :  TotalCost
       unit         :  1000 * $
       definition   :  sum((p,m), TransportCost(p,m)*Shipment(p,m)) ;

    MATHEMATICAL PROGRAM:
       identifier   :  TransportModel
       objective    :  TotalCost
       direction    :  minimize
       constraints  :  AllConstraints
       variables    :  AllVariables ;

  ENDSECTION  ;

  PROCEDURE
    identifier :  MainInitialization
    body       :  
      Plants := data { seattle, san-diego };
      Markets := data { new-york, Chicago, topeka };
      
      Capacity(p) := data { seattle : 350, san-diego : 600 };
      Demand(m) := data { new-york : 325, Chicago : 300, topeka : 275 };
      
      Distance(p,m) := data
      { ( seattle, new-york ) :  2.5,  ( seattle, Chicago  ) :  1.7,  ( seattle, topeka   ) :  1.8,
        ( san-diego, new-york ) :  2.5,  ( san-diego, Chicago  ) :  1.8,  ( san-diego, topeka   ) :  1.4 };
      
      Freight := 90 [$/(1000*mile)];

  ENDPROCEDURE  ;

  PROCEDURE
    identifier :  MainExecution
    body       :  
      solve TransportModel;

  ENDPROCEDURE  ;

ENDMODEL Main_Transport ;

See also

References

  1. ↑ "We are moving forward, from now on you can call us AIMMS", "Archived copy". Archived from the original on 2013-10-29. Retrieved 2013-10-23.
  2. ↑ Kallrath, Joseph (2004). Modeling Languages in Mathematical Optimization. Kluwer Academic Publishing. ISBN 978-1-4020-7547-6.
  3. ↑ Roelofs, Marcel (2010). AIMMS Language Reference (PDF). lulu.com. ISBN 978-0-557-42456-6.
  4. ↑ Roelofs, Marcel (2010). AIMMS User's Guide (PDF). lulu.com. ISBN 978-0-557-06360-4.
  5. ↑ Paragon Decision Technology (2009). "AIMMS Open Solver Interface API".
  6. ↑ http://www.informs.org/Blogs/E-News-Blog/INFORMS-Impact-Prize
  7. ↑ Lasschuit, Winston; Thijssen, Nort (15 June 2004). "Supporting supply chain planning and scheduling decisions in the oil and chemical industry" (PDF). Computers & Chemical Engineering (Volume 28, Issues 6-7, FOCAPO 2003 Special issue): 863–870. doi:10.1016/j.compchemeng.2003.09.026.
  8. ↑ "Integration and Optimisation of Crude Planning and Scheduling in the Hydrocarbon Supply Chain" (Press release). Shell Global Solutions. January 17, 2011.
  9. ↑ Medeiros Milanez, Eduardo (April 2010). "25 years of O.R. in Brazil". OR/MS Today.
  10. ↑ Streiffert, D.; Philbrick, R.; Ott, A. (August 1, 2005). "A mixed integer programming solution for market clearing and reliability analysis" (PDF). Power Engineering Society General Meeting, 2005. IEEE. pp. 2724–2731 Vol. 3. doi:10.1109/PES.2005.1489108.
  11. ↑ "Midwest ISO Wins INFORMS Edelman Award" (Press release). INFORMS. April 11, 2011.
  12. ↑ Dantzig, G B (1963). "Chapter 3.3". Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey. ISBN 978-0-691-05913-6.

External links


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