Mathematical decomposition strategies for large-scale infrastructure optimization with distributed decision variables

Abstract

Large-scale infrastructure systems comprise highly interdependent parts, decision variables, and operational constraints making it difficult to optimize such systems via traditional central optimization methods. The need for decomposable optimization methods results from an increase in the size of the system, computational restrictions, communication costs, and the necessity to coordinate distributed entities efficiently. In this research, will develop the methodology of mathematical decomposition of large-scale infrastructure systems optimization by turning complicated optimization problems into cooperative subproblems without losing the quality and convergence of the resulting solution. Study proposes to formulate the problem of infrastructure optimization via block angular formulation and apply three decomposition algorithms, namely, Dantzig-Wolfe decomposition, Bender’s decomposition, and consensus-based ADMM. Theoretical analyses are conducted in order to prove strong duality, convergence, and sublinear convergence properties of the distributed optimization procedure. Experiments carried out using a large-scale synthetic model of the infrastructure extension have proved that the consensus ADMM method offers better scalability than centralized and conventional decomposition algorithms. The presented framework saves about 71% computational time when compared to centralized optimization and consumes considerably less memory resources, although the difference in the optimality gap is negligible. The obtained results prove that the mathematical decomposition technique is an efficient way to handle large-scale infrastructure systems in terms of increasing computational efficiency and distributed decision-making capabilities.