A direct approach to optimization of a complex system

Abstract

Recently Adelman and Stevens (1972) applied a constrained simplex method to optimize the design of a chemical plant which consisted of a continuous stirred tank reactor, a heat exchanger, a decanter, and a distillation column. The operation of the plant is described by 9 equations in 1 3 variables-FA, FB, FD, FG, FP, FRA, FRB, FRC, FRE, FRP, F R , V , and T . The authors fixed one variable F p at the value 4763 and then considered the optimization of the plant as a nonlinear programming problem. The objective function to be maximized is percent return from the plant.The purpose of this communication is to point out that the mass balance equations are not all independent and that the equations can be rearranged to provide a simple means of solution. Also, we wish to show that the optimal performance index does not change if F P is allowed to change, provided that the other variables are allowed to take on new optimal values. In order that the reader may

PGS-COM: A hybrid method for constrained non-smooth black-box optimization problems

“…Friedman and Pinder (1972), and Gaines and Gaddy (1976) consider as case study a gasoline polymerization process and optimize the plant net earnings with different direct-search methods, namely the Complex of Box (1965), the Pattern Search of Hooke and Jeeves (1961) and a Random Search algorithm. Luus and Jaakola (1973a, 1973b, 1974 apply their "LJ Random Search" algorithm to the design of a variety of chemical processes. In all these works the attention is focused on directsearch methods instead of the more efficient gradient/Hessian based methods, such as the very efficient sequential quadratic programming method, for multiple reasons.…”

“…For example, the objective function value could be the result of a process simulation, a finite element method study, a computational fluid-dynamic analysis, or the value returned by the solver of a lower level optimization problem (i.e., in bilevel programming, the lower level optimization problem is solved multiple times for fixed values of the upper level variables). Non-smooth black-box problems with non-differentiable and/or discontinuous objective functions typically arise in chemical and energy engineering when the process is simulated by means of a sequential flowsheet solver, as in Luus and Jaakola (1973a), Gaines and Gaddy (1976), Banga and Seider (1996), Gross and Roosen (1998), and Morin, Wahl, and Molnvik (2011). On the other hand, Gassner and Marechal (2009) have shown that total site optimization problems, in which the process is optimized together with the heat exchanger network and the utility systems, can be successfully decomposed into bilevel programs with a non-smooth black-box problem at the upper level, and a Mixed Integer Linear Problem (MILP) at the lower level.…”

Empirical strategies for open‐loop on‐line optimization

“…The CSTR is part of a larger system introduced by Williams and Otto (1960) as a test system for process control studies. However, it has been used in the literature (e.g., Rangaiah, 1985;Luus and Jaakola, 1973) primarily for testing and comparison of (off-line steady state) optimization methods.…”

Adaptive optimizing control of multivariable constrained chemical processes. 2. Application studies

“…The CSTR model is part of a larger test system introduced by Williams and Otto (1960). The Williams and Otto model has been used frequently in the literature for simulation testing of control and optimization systems (e.g., Di Bella and Stevens, 1965; Jung et al, 1971; Adelmann and Stevens, 1972; Davison and Chadha, 1972; Luus and Jaakola, 1973;; Rangaiah, 1985).…”