Bb-atc: Analytical Target Cascading Using Branch and Bound for Mixed-integer Nonlinear Programming

The analytical target cascading (ATC) methodology for optimizing hierarchical systems has demonstrated convergence properties for continuous, convex formulations. However, many practical problems involve both continuous and discrete design variables, resulting in mixed integer nonlinear programming (MINLP) formulations. While current ATC methods have been used to solve such MINLP formulations in practice, convergence properties have yet to be formally addressed, and optimality is uncertain. This paper describes properties of ATC for working with MINLP formulations and poses a solution method applying branch and bound as an outer loop to the ATC hierarchy in order to generate optimal solutions. The approach is practical for large hierarchically decomposed problems with relatively few discrete variables.