Differences between barrier and simplex optimizers
Contrasts barrier optimizer with simplex optimizers.
The barrier optimizer and the simplex optimizers (primal and dual) are fundamentally different approaches to solving linear programming problems. The key differences between them have these implications:
Simplex and barrier optimizers differ with respect to the nature of solutions. Barrier solutions tend to be midface solutions. In cases where multiple optima exist, barrier solutions tend to place the variables at values between their bounds, whereas in basic solutions from a simplex technique, the values of the variables are more likely to be at either their upper or their lower bound. While objective values will be the same, the nature of the solutions can be very different.
By default, the barrier optimizer uses crossover to produce a basis. However, you may choose to run the barrier optimizer without crossover. In such a case, the fact that barrier without crossover does not produce a basic solution has consequences. Without a basis, you will not be able to optimize the same or similar problems repeatedly using advanced start information. You will also not be able to obtain range information for performing sensitivity analysis.
Simplex and barrier optimizers have different numeric properties, sensitivity, and behavior. For example, the barrier optimizer is sensitive to the presence of unbounded optimal faces, whereas the simplex optimizers are not. As a result, problems that are numerically difficult for one method may be easier to solve by the other. In these cases, concurrent optimization, as documented in Concurrent optimizer in parallel, may be helpful.
Simplex and barrier optimizers have different memory requirements. Depending on the size of the Cholesky factor, the barrier optimizer can require significantly more memory than the simplex optimizers.
Simplex and barrier optimizers work well on different types of problems. The barrier optimizer works well on problems where the AAT remains sparse. Also, highly degenerate problems that pose difficulties for the primal or dual simplex optimizers may be solved quickly by the barrier optimizer. In contrast, the simplex optimizers will probably perform better on problems where the AAT and the resulting Cholesky factor are relatively dense, though it is sometimes difficult to predict from the dimensions of the model when this will be the case. Again, concurrent optimization, as documented in Concurrent optimizer in parallel, may be helpful.