Large-Scale and Big Optimization Based on Hadoop

Abstract

Integer Linear Programming (ILP) is among the most popular optimization techniques found in practical applications, however, it often faces computational issues in modeling real-world problems. Computation can easily outgrow the computing power of standalone computers as the size of problem increases. The modern distributed computing releases the computing power constraints by providing scalable computing resources to match application needs, which boosts large-scale optimization. This chapter presents a paradigm that leverages Hadoop, an open-source distributed computing framework, to solve a large-scale ILP problem that is abstracted from real-world air traffic flow management. The ILP involves millions of decision variables, which is intractable even with existing state-of-the-art optimization software package. Dual decomposition method is used to separate variables into a set of dual subproblems that are smaller ILPs with lower dimensions, the computation complexity is downsized. As a result, the subproblems are solvable with optimization tools. It is shown that the iterative update on Lagrangian multipliers in dual decomposition method can fit into the Hadoop’s MapReduce programming model, which is designed to allocate computations to cluster for parallel processing and collect results from each node to report aggregate results. Thanks to the scalability of the distributed computing, parallelism can be improved by assigning more working nodes to the Hadoop cluster. As a result, the computational efficiency for solving the whole ILP problem is not impacted by the input size.