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The Xpress-Optimizer
The Xpress-Optimizer features sophisticated, robust multi-threaded algorithms to quickly and accurately solve industry`s most demanding problems. The proven optimization technology is employed by a huge variety of commercial installations throughout the world to provide fast, reliable solutions to problems with millions of variables and constraints. The shared memory, deterministic parallelism can exploit as many CPU cores as are available for fast execution times. Xpress-Optimizer uses ultra efficient sparse matrix handling and on-the-fly data compression to solve the largest problems that industry has to offer
The Xpress-Optimizer is noted for its ability to solve numerically difficult or unstable problems which is one of the reasons why it is the clear market leader in the process industries.
Cutting-edge Algorithms
The Xpress-Optimizer algorithms enable you to solve:
- LP - Linear problems
- MIP - Mixed integer problems
- QP - Quadratic problems
- MIQP - Mixed integer quadratic problems
- QCQP - Quadratically constrained quadratic problems
- MIQCQP - Quadratically constrained mixed integer problems
- NLP - Convex non-linear problems
And if your problem is non-linear and non-convex then the Xpress-SLP solver, which uses successive linear approximation techniques, can solve non-linear and mixed integer non-linear problems with many thousands of variables.
Flexible Deployment
The Xpress-Optimizer is available as a command-line tool with a simple yet powerful interactive user interface and as a callable library with C, C++, Java, Fortran, VB6 and .NET programming interfaces. It is fully compatible with the industry-standard LP and MPS file formats and has extensive support for logging, binary save/basis files and ASCII/binary solution files.
The callable library provides both a low-level matrix orientated API and an object orientated model construction interface called BCL. As an integrated component of the Xpress product, the advanced model development environment of Xpress-Moselcan be used to interact with the raw power and performance of the Xpress-Optimizer engine.
Cross-Platform
The Xpress-Optimizer is available for a wide variety of architectures and operating systems and is enhanced to take advantage of individual platform characteristics.
The Simplex Optimizer
The Xpress-Optimizer provides fast, reliable implementations of the primal and dual simplex methods for solving LP problems.
- Integrated presolve algorithm to reduce problem size and solve time
- Automatic settings for best performance and an extensive range of user-configurable parameters for advanced control of the optimization process.
- Fast restarts from an existing advanced basis. Problems can be modified and then resolved in a fraction of the original solution time
- Infeasibility detection and diagnostics for tracing problem infeasibilities
- Effective degeneracy resolution techniques
The Barrier Optimizer
The Xpress-Optimizer Barrier algorithm provides an alternative to the simplex algorithms and uses interior point methods to solve both linear programming and quadratic programming problems.
- Integrated presolve algorithm to reduce problem size and solve time
- Cutting edge Cholesky factorization algorithms
- Fast primal and dual crossover to basic solutions
- Dense column handling
- Solutions available without crossover
- Available as Parallel Barrier for multi-processor machines on specific platforms
The MIP Optimizer
The Xpress-Optimizer uses a sophisticated branch and bound algorithm to solve MIP and MIQP problems and is well known for its ability to quickly find high quality solutions.
- MIP presolve algorithm pre-processes the problem to reduce problem size and solve time
- Advanced cutting-plane strategies to automatically improve the quality of bounds and reduce the size of the global search
- Flow covers
- GUB covers
- Lift and Project
- Clique cuts
- Flow paths
- Mixed integer rounding
- Gomory fractional cuts
- Binary, integer and semi-continuous variables, and special ordered sets
- Breadth-first, best-first or depth-first search. Customizable node and variable selection strategies. User callbacks allow complete control over the node and variable selection
- Multiple LP algorithms for initial LP relaxation and node solution
- User-defined branching priority and branch direction directives
- Heuristics
- Available as Parallel-MIP for multi-processor machines on specific platforms
The Tuner
Xpress-Optimizer is designed for out-of-the-box high performance on a wide range of model types. It also features a number of customisable parameters. The Tuner tools allows the user to find values for the algorithm parameters which improve on the solver default values for their models, often leading to significant performance gains. The Tuner uses multi-threaded genetic algorithms to find the best parameter settings for a model or set of models, and presents the results of the search using a clear graphical interface.
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