| |
Powerful LINGO Solvers
LINGO
includes a set of built-in solvers to tackle a
wide variety of
problems. Unlike many modeling packages, all of
the LINGO solvers are
directly linked to the modeling environment.
This seamless integration
allows LINGO to pass the problem to the
appropriate solver directly in
memory rather than through more sluggish
intermediate files. This
direct link also minimizes compatibility
problems between the modeling
language component and the solver components.
Linear Solvers
LINGO is available with three state of the art
solvers for linear models.
Primal and
Dual Simplex Solvers
The
base version includes the Primal and Dual
Simplex solvers, which
incorporate numerous enhancements for maximum
speed and robustness.
Pricing options, for instance, include partial
pricing and Devex. The
solver dynamically chooses the best pricing
option based upon problem
characteristics.
Barrier
Solver
The
optional Barrier solver provides an alternative
means of solving linear
models. The Barrier option utilizes a barrier or
interior point method
to solve linear models. Unlike the Simplex
solvers that move along the
exterior of the feasible region, the Barrier
solver moves through the
interior space to find the optimum. Depending
upon the size and
structure of a particular model, the Barrier
solver may be
significantly faster than the Simplex solvers
and can provide
exceptional speed on large linear models --
particularly on sparse
models with more than 5,000 constraints or
highly degenerate models.
The Barrier license option is required to
utilize the Barrier solver.
Integer
Solver
For
models with general and binary integer
restrictions, LINGO includes an
integer solver that works in conjunction with the
linear, nonlinear,
and quadratic solvers. For linear models, the
integer solver includes
preprocessing and dozens of constraint "cut"
generation routines that
can greatly improve solution times on large
classes of integer models.
Nonlinear Solver
LINGO includes a number of ways
to find locally or globally optimal solutions to
nonlinear models.
General Nonlinear Solver
For
nonlinear programming models, the primary
underlying technique used by
LINGO's optional nonlinear solver is based upon
a Generalized Reduced
Gradient (GRG) algorithm. However, to help get
to a good feasible
solution quickly, LINGO also incorporates
Successive Linear Programming
(SLP). The nonlinear solver takes advantage of
sparsity for improved
speed and more efficient memory usage. The
Nonlinear license option is
required to solve nonlinear models.
Global
Solver
Local
search solvers are generally designed to search
only until they have
identified a local optimum. If the model is
non-convex, other local
optima may exist that yield significantly better
solutions. Rather than
stopping after the first local optimum is found,
the Global solver will
search until the global optimum is confirmed. The
Global solver
converts the original non-convex, nonlinear
problem into several
convex, linear subproblems. Then, it uses the
branch-and-bound
technique to exhaustively search over these
subproblems for the global
solution. The Nonlinear and Global license options
are required to
utilize the global optimization capabilities.
Multistart
Solver
When
limited time makes searching for the global
optimum prohibitive, the
Multistart solver can be a powerful tool for
finding good solutions
more quickly. This intelligently generates a set
of candidate starting
points in the solution space. Then, the general
nonlinear solver
intelligently selects a subset of these to
initialize a series of local
optimizations. For non-convex nonlinear models,
the quality of the
solution returned by the multistart solver will
be superior to that of
the general nonlinear solver. The Nonlinear and
Global license options
are required to utilize the multistart
capabilties.
Quadratic
Solver
In
addition to solving linear and mixed integer
models, with the Barrier
option LINGO can automatically detect and solve
models in which the
objective function and/or some constraints
include quadratic terms. By
taking advantage of the quadratic structure,
LINGO can solve these
models much more quickly than using the general
nonlinear solver. LINGO
can even handle quadratic models with binary and
general integer
restrictions. These quadratic capabilities make
LINGO suitable for
applications such as portfolio optimization
problems, constrained
regression problems, and certain classes of
difficult logistics
problems (e.g., layout problems,
fixed-charge-network problems with
quadratic objectives). The Quadratic solver is
included in the Barrier
license option.
Conic
Solver
The Barrier option for LINGO includes a
Conic solver
to efficiently solve Second Order Cone Problems
(SOCP). By expressing
certain nonlinear models as SOCPs, the Conic
solver can be used to
solve the model substantially faster than the
general nonlinear solver.
The Barrier and Global options are required to
utilize the Conic option
capabilities.
Stochastic Programming Solver
Incorporate
risk into multi-stage optimization models,
maximize expected profit,
and summarize results in histograms showing the
distribution of
possible profit, etc. This new option allows
modeling and optimization
for models with uncertain elements via
multistage stochastic linear,
nonlinear and integer stochastic programming
(SP). Benders
decomposition is used for solving large linear
SP models. Deterministic
equivalent method is used for solving nonlinear
and integer SP models.
Support is available for over 20 distribution
types (discrete or
continuous). The Stochastic Programming solver
is included in the
Stochastic Programming option.
Preprocessing
Preprocessing
routines are included in all solvers. The Linear
and Nonlinear solvers
include scaling and model reduction techniques.
Scaling procedures can
improve speed and robustness on numerically
difficult models. Model
reduction techniques can often make models solve
faster by analyzing
the original formulation and mathematically
condensing it into a
smaller problem. The Integer solver includes
extensive preprocessing
and cut generation routines.
LINGO is designed, so
the process of solving the model requires as
little input from the user
as possible. When the Solve command is
initiated, LINGO analyzes the
problem and, when possible, reduces the problem
and even substitutes
out variables. Based upon the models structure,
LINGO automatically
selects the appropriate solver and intelligently
adjusts internal
parameters.
Linearization
LINGO's
Linearization capabilities can dramatically
improve performance on
models with common nonsmooth functions. The
feature can automatically
convert many nonsmooth functions and operators
(e.g., @IF, @MAX and
@ABS) to a series of linear, mathematically
equivalent expressions.
Similarly, the product of a continuous and
binary variable can also be
linearized. Many nonsmooth models may be
entirely linearized. This
allows the linear solver to quickly find a
global solution to what
would have otherwise been an intractable
problem.
© Copyright 2015 Lindo
Systems Inc.
|
|
