Batched First-Order Methods for Parallel LP Solving in MIP
This work addresses computational bottlenecks in mixed-integer programming for optimization practitioners, though it is incremental as it extends existing primal-dual hybrid gradient methods.
The authors tackled the problem of solving multiple linear programs in parallel for mixed-integer programming by developing a batched first-order method on GPUs, which leverages matrix-matrix operations to achieve significant computational advantages over traditional simplex-based solvers in certain problem sizes.
We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise in mixed-integer programming techniques such as strong branching and bound tightening. By leveraging matrix-matrix operations instead of repeated matrix-vector operations, we obtain significant computational advantages on GPU architectures. We demonstrate the effectiveness of our approach on various case studies and identify the problem sizes where first-order methods outperform traditional simplex-based solvers depending on the computational environment one can use. This is a significant step for the design and development of integer programming algorithms tightly exploiting GPU capabilities where we argue that some specific operations should be allocated to GPUs and performed in full instead of using light-weight heuristic approaches on CPUs.