AMPL is a computer language for describing production, distribution,
blending, scheduling and many other kinds of problems known generally as
large-scale optimization or mathematical programming.
AMPL's familiar algebraic notation and interactive command environment are
designed to help formulate models, communicate with a wide variety of solvers,
and examine solutions.
AMPL's flexibility and convenience make it ideal for rapid prototyping and
development of models, while its speed and generality provide the resources
required by repeated production runs.
AMPL is one of several optimization modeling systems that are designed around
specialized algebraic modeling languages. These languages employ adaptations of
familiar mathematical notation to describe optimization problems as
- the minimization or maximization of algebraic expressions in numerical
decision variables,
- subject to constraints expressed as equalities or inequalities between
algebraic expressions in the decision variables.
Advanced interpreters
and interfaces for these languages provide support for simplifying and analyzing
models. Some also provide language extensions for describing algorithmic schemes
that attack difficult problems by alternately solving interrelated subproblems.
Some of the other commercially distributed algebraic modeling languages are:
- GAMS, one of the first such languages, now widely used in a number of
industries.
- MGG, another early language with a long history of support.
- LINGO, a more powerful sibling of the LINDO language widely used in
elementary instruction.
- MPL, notable for its associated graphical interface and database links.
- AIMMS, providing a graphical application development environment and a
GAMS compatibility mode supplementing its own language.
AMPL is
designed to combine and extend the expressive abilities of these languages,
while remaining easy to use for elementary applications. AMPL is particularly
notable for the naturalness of its syntax and for the generality of its set and
indexing expressions.
AMPL provides strong support for validation, verification and reporting of
optimal solutions, through numerous alternatives for presenting data and
results. AMPL's extensive preprocessing routines can automatically carry out
transformations that serve to reduce problem size, convert piecewise-linearities
to linear terms, and substitute out selected variables.
AMPL is further distinguished by its continuing development to serve users'
needs. Recent additions include
looping and testing constructs for writing executable scripts in the AMPL
command language, and facilities for defining and working with several
interrelated subproblems. Numerous commands have also been added for producing
diagnostic reports and custom-formatted tables.
There are also many optimization modeling systems based on representations
other than algebraic modeling languages. Popular alternative forms include:
- block-schematic diagrams, which depict a linear constraint matrix as a
collection of structured submatrices (or blocks).
- activity specifications, which describe a model in terms of activities
(variables) and their effects (constraints) on inputs and outputs.
- netforms, which use graph or network diagrams to depict models involving
flows and allocations.
Each of these has special advantages for
certain classes of problems. In contrast, an algebraic modeling language such as
AMPL is more general. It is the most natural form for many classes of problems,
and is one of the most natural forms for an even broader variety of problem
classes.
The Excel, 1-2-3 and Quattro spreadsheet packages come with solvers for
linear, nonlinear, and integer programming; they accept enhanced add-in solvers
as well. Their principal advantage lies in allowing all aspects of optimization
-- including formulation, solution, and analysis of results -- to be performed
within the spreadsheet environment. In particular, variables and constraints can
be defined directly in terms of ranges of spreadsheet cells.
AMPL incorporates a far richer language than spreadsheet optimizers for
describing optimization problems. As a result, AMPL is much more natural and
reliable for developing and maintaining complex models. The difference is
particularly pronounced when many model components have more than two dimensions
(or more than two subscripts or indices, in AMPL terms).
By avoiding much of the spreadsheet overhead, AMPL also generates model
instances faster than spreadsheet optimizers. AMPL's speed advantage is
significant for a few thousand model components, and becomes relatively greater
as problem size increases.
AMPL is available with a greater variety of solvers than spreadsheet
optimizers.
AMPL models can use data stored in spreadsheet ranges, but only through the
exchange of appropriately formatted text files. AMPL's read command facilitates this
exchange.
Certain low-cost versions of AMPL have built-in limits on problem size. The
student
edition bundled with the AMPL
book is limited to 300 variables and a total of 300 objectives and
constraints, for example, and several packages having higher limits are offered
to registered users. The professional
edition of AMPL has no intrinsic limit on problem size, however; it is
limited only by the resources available to the computer that is running AMPL.
In practice, memory is most often the limiting resource. The amount of memory
used by AMPL necessarily depends on the numbers of variables and constraints,
and on the number and complexity of the terms in the constraints -- or in the
case of linear programs, on the number of nonzero coefficients in the
constraints. Memory use also depends on the size and complexity of the model's
sets and parameters. AMPL's presolve phase may require additional memory to
execute (though it may accomplish problem reductions that allow savings of
memory later).
AMPL's memory use for a linear program can be estimated crudely as 1000000 +
260 (m + n) + 50 nz bytes, where m is the number of
constraints, n the number of variables, and nz the number of
nonzeroes. Allowing for memory occupied by DOS, this suggests that the following
sizes of problems might be accommodated on a PC:
m = 1200, n = 4800, nz = 14400 on a 4MB machine,
m = 3600, n = 14400, nz = 43200 on an 8MB machine,
m = 8000, n = 24000, nz = 96000 on a 16MB machine.
Memory required for a solver must be added, if the solver is to be run while
AMPL remains active. See also our advice elsewhere in this FAQ for further
comments on what to do (including running the solver separately) if
you suspect a problem with insufficient memory.
Especially difficult problems may cause your solver to encounter its own
resource limitations. Solvers that accept binary and integer
variables, in particular, can consume impractical amounts of time and disk space
as well as memory, even for problems of apparently modest size. Nonlinear
problems can also be very time-consuming compared to linear programs in the same
numbers of variables and constraints.
As a practical matter, there is no substitute for experimentation to
determine the resource requirements of your particular problem. The best
approach is usually to try out your model on progressively larger collections of
data, so that you can record the trend in resource requirements as problem size
increases.
Currently AMPL is not configured as a subroutine library
whose individual pieces can be called as needed from a user's program. A "batch"
session of AMPL can be executed from a C program, however. This feature can be
used as a high-level "call" to AMPL that is sufficient for some applications.
Under Unix, MS-DOS or Microsoft Windows, you would execute AMPL by use of the
system procedure, as in these examples:
system("ampl <cut.run");
system("ampl <cut.run >cut.out");
The argument to system can be anything one would type on a command
line. Most commonly, an input file (cut.run above) contains a series of
AMPL commands that read model and data input, invoke solvers, and write results
to files. This arrangement does not provide for results to be passed back
directly to your program; following the call to system, your program
must get the results by reading a file that AMPL has written.
The AMPL book is the most
comprehensive source of information on AMPL. It is written in the form of a
textbook with an appendix for reference, in contrast to the more common format
of a reference manual with some tutorial material at the front. Virtually all
language features are illustrated by continuing, meaningful examples, and
additional exercises are provided. A student
edition of the AMPL software and the MINOS and CPLEX solvers are included.
See also the news section
for features added since the book was published.
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