Optimization of nonhierarchically decomposed problems

Abstract

The increasing computational power available to practitioners leads to challenging applications of optimization approaches to large scale systems. To address such problems, decomposition of the original or “all-in-one” (AiO) problem into smaller and simpler subproblems is the approach taken by engineers. Analytical target cascading (ATC), a hierarchical decomposition and coordination approach, is extended to model and coordinate problems with nonhierarchical interactions among the subproblems. Convergence results for ATC based on Lagrangian duality theory are extended for the new approach. Under certain conditions, the optimal solution of the AiO problem can be achieved by independently solving the nonhierarchically interacting subproblems. A mathematical example with several subproblems interacting in a network is included and new applications in engineering design are highlighted.