Branch and bound method for multiobjective control structure design

Control structure design deals with the selection of controlled and manipulated variables, and the pairings interconnecting these variables. The available criteria for these tasks require enumeration of every alternative, which can be computationally forbidding for large-scale process. Owing to the computational complexity, variables and pairings are often selected sequentially, which may result in sub-optimal control structures. In this paper, an efficient branch and bound (BAB) method is proposed to select the variables and pairings together in a multiobjective optimization framework. As an illustration of the proposed multiobjective BAB framework, the minimum singular value rule and the mu-interaction measure are used as the criteria for selection of controlled variables and pairings, respectively. Numerical tests using randomly generated matrices and large-scale case study of HDA process show that the BAB method is able to reduce the solution time by several orders of magnitude in comparison with exhaustive search.