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Nondeterminism |
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The parallel optimizers are nondeterministic: repeated solutions of a model using exactly the same settings can produce different solution paths and, in the case of the parallel MIP optimizer, very different solution times and results.
The basic algorithm in the ILOG CPLEX Parallel MIP Optimizer is branch & cut. The primary source of parallelism in branch & cut is the solution of the continuous relaxations at the individual nodes of the search tree. These subproblems can be distributed over available processors to be carried out in parallel. The individual solution paths for these subproblems will, in fact, be deterministic, but the speed at which their solutions occur can vary slightly. These variations lead to nodes being taken from and replaced in the branch & cut tree in different order, and this reordering leads to nondeterminism about many other quantities that control the optimization. This nondeterminism is unavoidable in such a context, and its effects can result in some cases in very different solution paths.
The ILOG CPLEX Barrier Optimizer is also not deterministic, but in practice the differences between runs will be minor in comparison to the case of MIP, and should usually amount to a change (if any) of at most a few iterations. The difference is due to uncertainty in the parallel order of arithmetical operations, in conjunction with numerical roundoff.
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