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Choosing the right algorithm

Gurobi Optimizer provides two main algorithms to solve continuous models and the continuous relaxations of mixed-integer models: barrier and simplex.

The barrier algorithm is usually fastest for large, difficult models. However, it is also more numerically sensitive. And even when the barrier algorithm converges, the crossover algorithm that usually follows can stall due to numerical issues.

The simplex method is often a good alternative, since it is generally less sensitive to numerical issues. To use dual simplex or primal simplex, set the Method parameter to 1 or 0, respectively.

Note that, in many optimization applications, not all problem instances have numerical issues. Thus, choosing simplex exclusively may prevent you from taking advantage of the performance advantages of the barrier algorithm on numerically well-behaved instances. In such cases, you should use the concurrent optimizer, which uses multiple algorithms simultaneously and returns the solution from the first one to finish. The concurrent optimizer is the default for LP models, and can be selected for MIP by setting the Method parameter to 3 or 4.

For detailed control over the concurrent optimizer, you can create concurrent environments, where you can set specific algorithmic parameters for each concurrent solve. For example, you can create one concurrent environment with Method=0 and another with Method=1 to use primal and dual simplex simultaneously. Finally, you can use concurrent optimization with multiple distinct computers using distributed optimization. On a single computer, the different algorithms run on multiple threads, each using different processor cores. With distributed optimization, independent computers run the separate algorithms, which can be faster since the computers do not compete for access to memory.