A decomposition algorithm for the optimisation of hybrid dynamic processes

This paper presents a decomposition algorithm for the dynamic optimisation of hybrid processes described by general state-transition networks (Pantelides, 1995). In each state, the transient system behaviour is described by a different set of differential and algebraic equations (DAEs). Transitions occur from one state to another whenever certain logical conditions are satisfied. A complete discretisation procedure is employed to convert the original infinite dimensional dynamic optimisation problem into a large mixed integer nonlinear programming (MINLP) problem. We then utilise a novel outer approximation/augmented penalty/equality relaxation algorithm, comprising a continuous nonlinear programming (NLP) subproblem and a mixed integer linear programming (MILP) master problem. The MILP master problem determines the sequence of state transitions the system goes through and the NLP subproblem solves the dynamic optimization problem for the given sequence. In contrast to our previous work (Avraam et al., 1998), here we describe a much more efficient approach based on a reduced NLP containing only the active state-period combinations determined by the MILP master problem. The computational efficiency of this approach is illustrated.