The Method box on the Linear Solver tab:

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is used to control the algorithm LINGO’s linear solver employs.

The current choices are:

•Solver Decides — LINGO selects the algorithm it determines is most appropriate.
•Primal Simplex — LINGO uses a primal simplex algorithm.
•Dual Simplex — LINGO uses a dual simplex algorithm.
•Barrier — LINGO uses a barrier algorithm (i.e., interior point.)

The simplex algorithm moves around the exterior of the feasible region to the optimal solution, while the interior point algorithm, or barrier solver, moves through the interior of the feasible region. In general, it is difficult to say which algorithm will be fastest for a particular model. A rough guideline is primal simplex tends to do better on sparse models with fewer rows than columns. Dual simplex does well on sparse models with fewer columns than rows. And the barrier solver works best on densely structured models or very large models.

The barrier solver is available only as an additional option to the LINGO package. Furthermore, if the model has any integer variables, the barrier solver will be used for solving the LP at the initial root node of the branch-and-bound tree, but may or may not be used on subsequent nodes. From a performance point-of-view, the barrier solver’s impact will be reduced on integer models.

LINGO defaults to the Solver Decides option.