Algebraic Modeling Languages (AML) are high-level computer

Computer

A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...

 programming languages for describing and solving high complexity problems for large scale mathematical computation (i.e. large scale optimization

Optimization (mathematics)

In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....

 type problems). One particular advantage of some algebraic modeling languages like AIMMS

AIMMS

AIMMS is a software system designed for modeling and solving large-scale optimization and scheduling-type problems....

, AMPL

AMPL

AMPL, an acronym for "A Mathematical Programming Language", is an algebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computation AMPL, an acronym for "A Mathematical Programming Language", is an algebraic modeling language for describing and...

 or GAMS

General Algebraic Modeling System

The General Algebraic Modeling System is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to...

is the similarity of their syntax to the mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization, which is supported by certain language elements like sets, indices, algebraic expressions, powerful sparse index and data handling variables, constraints with arbitrary names. The algebraic formulation of a model does not contain any hints how to process it.

An AML does not solve those problems directly; instead, it calls appropriate external algorithms to obtain a solution. These algorithms are called solver

Solver

A solver is a generic term indicating a piece of mathematical software, possibly in the form of a stand-alone computer program or as a software library, that 'solves' a mathematical problem. A solver takes problem descriptions in some sort of generic form and calculate their solution...

s and can handle certain kind of mathematical problem

Mathematical problem

A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's...

s like:

• linear problems
• integer problems
• (mixed integer) quadratic problems
• mixed complementarity problem
  Mixed complementarity problem
  Mixed Complementarity Problem is a problem formulation in mathematical programming. Many well-known problem types are special cases of, or may be reduced to MCP...
  
  s
• mathematical programs with equilibrium constraints
• constrained nonlinear systems
• general nonlinear problems
• non-linear programs with discontinuous derivatives
• nonlinear integer problems
• global optimization problems
• stochastic optimization problems

Core Elements

The core elements of an AML are:

• a modeling language interpreter (the AML itself)
• solver links
• user interfaces (UI)
• data exchange facilities

Design Principles

Most AML follow certain design principles:

• a balanced mix of declarative and procedural elements
• open architecture and interfaces to other systems
• different layers with separation of:
  • model and data
  • model and solution methods
  • model and operating system
    Operating system
    An operating system is a set of programs that manage computer hardware resources and provide common services for application software. The operating system is the most important type of system software in a computer system...
    
    
  • model and interface

See also

• AIMMS
  AIMMS
  AIMMS is a software system designed for modeling and solving large-scale optimization and scheduling-type problems....
  
  
• AMPL
  AMPL
  AMPL, an acronym for "A Mathematical Programming Language", is an algebraic modeling language for describing and solving high-complexity problems for large-scale mathematical computation AMPL, an acronym for "A Mathematical Programming Language", is an algebraic modeling language for describing and...
  
   - a popular modeling language for large-scale linear, mixed integer and nonlinear optimization
• APMonitor
  APMonitor
  APMonitor, or "Advanced Process Monitor", is a modeling language for differential and algebraic equations. It is used for describing and solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and allows solutions of dynamic...
  
  
• ASCEND
  ASCEND
  ASCEND is a free, open source, mathematical modelling system developed at Carnegie Mellon University since the late 1978. ASCEND is an acronym which stands for Advanced System for Computations in ENgineering Design. Its main uses have been in the field of chemical process modelling although its...
  
  
• GAMS
  General Algebraic Modeling System
  The General Algebraic Modeling System is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to...
  
  
• OptimJ
  OptimJ
  OptimJ is an extension of the Java with language support for writing optimization models and abstractions for bulk data processing. OptimJ aims at providing a clear and concise algebraic notation for optimization modeling, removing compatibility barriers between optimization modeling and...
  
  - a Java-based modeling language