AIMMS

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

• the exchange of data with external data sources such as spreadsheets, databases, XML and text files
• data pre- and post-processing tasks around optimization models
• user interface event handling
• the construction of hybrid algorithms for problem types for which no direct efficient solvers are available.

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:

• Linear programming
• Quadratic programming
• Nonlinear programming
• Mixed-integer programming
• Mixed-integer nonlinear programming
• Global optimization
• Complementarity problems (MPECs)
• Stochastic programming
• Robust optimization
• Constraint programming

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

• Algebraic modeling language

References

External links

• AIMMS home page
• AIMMS user forum
• AIMMS blog: How-to, tips & tricks for AIMMS users
• AIMMS Open Solver Interface
• AIMMS 3 Software Review
• Comparison of modeling languages for optimization