Xpress-MP Software Overview
The Xpress-Optimizer
The Xpress-Optimizer features three optimization algorithms which enable the user to solve linear programming problems (LP), mixed integer programming problems (MIP), quadratic programming problems (QP), and mixed integer quadratic programming problems (MIQP).

The simplex optimizer, which includes primal and dual methods, solves LP problems, and is also used within a branch-and-bound framework to solve MIP and MIQP problems. The Newton barrier optimizer is an interior point method for solving LP and QP problems. Xpress-MP uses ultra-efficient sparse matrix handling to allow it to solve the largest problems in record time. A presolve procedure reduces the size of the problem before it is solved, sometimes by an order of magnitude. Xpress-MP is also noted for its ability to solve numerically hard or unstable problems, which is one of the reasons Xpress-MP is the clear market leader in the process industries.

The MIP optimizer uses a sophisticated branch-and-bound algorithm to solve MIP and MIQP problems, and is particularly known for its ability to find high quality solutions fast. MIP problems can have an exponential number of possible solutions, and the essential property of the Xpress MIP optimizer is its ability to cut down the number of solutions to a manageable size, and then to navigate through them so it can find good ones quickly.

Some of the more sophisticated techniques include various classes of cutting planes, which are generated automatically during the optimization to improve the quality of bounds and reduce the size of the search (so the MIP algorithm is really called "branch-cut-cut"). The presolve is particularly effective on MIP problems, as it is able to tighten the formulation, which improves the quality of initial solutions and enables better cutting planes to be generated.

The Hyper32 edition of Xpress-MP has no internal limits on problem size, allowing the user to solve any problem which can physically be accommodated within the limits of 32-bit memory on their computer. And if that isn't big enough, Hyper64 unleashes the power of 64-bit computing. Two restricted size editions, Extended and Professional, are also available.

When it is important to solve MIP problems in the shortest possible time, or to obtain solutions for the hardest MIP problems, Xpress-Parallel is the ideal solution. Operating on multi-processor machines or across a network of computers, it enables the user to harness all of the computing power at their disposal to solve MIP problems in parallel.