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Premium Solver for Excel - Linear and Integer Programming

Linear and Integer Programming

The Premium Solver includes an LP Simplex Solver -- greatly improved over the Simplex method included with the standard Excel Solver -- and capable of solving linear programming problems up to 2,000 variables.

To handle LP problems with integer constraints -- especially those with 0-1 or binary integer variables -- the Premium Solver uses a variety of preprocessing and probing techniques to preset values for some binary integer variables based on the settings of others.  It automatically recognizes, and takes advantage of "cliques" (also called Special Ordered Sets). Other advanced strategies are used to select the next node or subproblem to be explored, and the next variable to branch upon.

LP/Quadratic Integer Options dialog (29206 bytes)

Integer Options dialog

Cut Generation Methods

In Version 8.0, the Premium Solver uses cut generation methods to create new constraints, or cuts, that reduce the size of the LP feasible region without eliminating any potential integer solutions.  Gomory cuts are generated for all integer variables, based on the LP ending basis of the parent problem.  Knapsack cuts, also known as lifted cover inequalities, are generated for sets of 0-1 integer variables.  Options on the Integer Options tab for the Simplex LP Solver allow you to control the frequency of application of these cut generation methods.   

Dual Simplex Method with Bound Swapping

The Premium Solver uses the Dual Simplex method (by default) to solve the LP subproblems created in the Branch & Bound search, starting from the ending basis of a parent problem.  Since these subproblems are always dual feasible, it is often possible to reach a dual optimal (and primal feasible) solution in just a few Dual Simplex iterations. 

In Version 8.0, the Premium Solver uses an advanced Dual Simplex method with "bound-swapping" for variables that have both upper and lower bounds (such as 0-1 integer variables), which becomes faster as the Branch & Bound search progresses and the bounds become tighter.

Controlling Solution Time on Integer Problems

The Premium Solver provides new ways to control the solution time of problems with integer constraints. You can limit the number of subproblems explored and/or the number of integer solutions found, as well as the maximum time in seconds. The limits you specify can be as large as you like, whereas they have an upper bound of 32767 in the standard Excel Solver.

If you have a known integer solution value for a problem from a previous Solver run, you can enter it as an integer cutoff value, which the Solver can use to speed up the solution process on new runs, by eliminating branches whose objective must be worse than the "cutoff" value.

And you can easily solve the relaxation of the problem (temporarily ignoring the integer constraints) by selecting an option in the new Integer Options dialog (pictured above), or -- even more convenient -- on a "one-time-only" basis in the Solver Results dialog.

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