Optimization of multistage cyclic and braching systems by serial procedures

Abstract

Abstract The calculus of variations, dynamic programing, and Pontryagin's maximum principle all are methods for optimzing serial decision processes, the kind associated with multistage operations having no recycle or bypass. Addition of recycle to a serial process makes it cyclic, and branching structures can be built up by connecting serial ones. The concept of cut state makes possible the decomposition of cyclic and branched systems into serial ones solvable by serial procedures. Under favorable circumstances cut states can be directed to their optimum values by efficient optimum seeking methods, which is not possible for ordinary state variables. These method are worthwhile only for loops having at least three stages, and the treatment of converging branches is more complicated than for diverging ones. Visualization of the various system structures is aided by functional diagrams. Definitions and nomenclature are developed for continued research on optimization of macrosystems by serial techniques.