A Numerical Study on the Parallelization of Dual Decomposition-based Distributed Mixed-Integer Programming

The shift from centralized to decentralized systems is increasing the complexity of many problems in control and optimization. However, it also presents the opportunity to exploit parallelized computational schemes. This paper shows how the solution process of mixed-integer problems, which often arise in areas like production scheduling or logistics, can be supported by employing parallel computations. To this end, dual variables are introduced that enable the decomposition of these complex problems into subproblems that can then be solved in parallel. The presented dual decomposition-based approach provides a lower bound for the optimal solution of the original problem, which can support the overall solution process. The focus of this paper is on the parallelizability of the computation of this lower bound. The bounds from three different dual decomposition- based distributed optimization algorithms are compared to the lower bounds provided by several commercial solvers within their branch-&-cut framework.