Many systems in chemical engineering are difficult to optimize using gradient-based algorithms. These include process models with multimodalobjective functions and discontinuities. Herein, a stochastic algorithm is applied for the optimal design of a fermentation process, to determine multiphase equilibria, for the optimal control of a penicillin reactor, for the optimal control of a non-differentiable system, and for the optimization of a catalyst blend in a tubular reactor. The advantages of the algorithm for the efficient and reliable location of global optima are examined. The properties of these algorithms, as applied to chemical processes, are considered, with emphasis on the ease of handling constraints and the ease of implementation and interpretation of results. For the five processes, the efficiency of computation is improved compared with selected stochastic and deterministic algorithms. Results closer to the global optimum are reported for the optimal control of the penicillin reactor and the non-differentiable system.

Introduction and Problem Statement Interest in dynamic simulation and optimization of chemical processes has increased significantly during the last two decades. Common problems include control and scheduling of batch processes; startup, upset, shutdown and transient analysis; safety studies and the evaluation of control schemes. Chemical processes are modeled dynamically using differentialalgebraic equations (DAEs). The DAE formulation consists of differential equations that describe the dynamic behavior of the system, such as mass and energy balances, and algebraic equations that ensure physical and thermodynamic relations. The general dynamic optimization problem can be stated as follows: min z(t);y(t);u(t);t f ;p '(z(t f ); y(t f ); u(t<F8

The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements of the process. A general framework is presented for the synthesis of optimal chemical reactor networks via an optimization approach. The possible design alternatives are represented via a process superstructure which includes continuous stirred tank reactors and cross flow reactors along with mixers and splitters that connect the units. The superstructure is mathematically modeled using differential and algebraic constraints and the resulting problem is formulated as an optimal control problem. The solution methodology for addressing the optimal control formulation involves the application of a control parameterization approach where the selected control variables are discretized in terms of time invariant parameters. The dynamic system is decoupled from the optimization and solved as a func...

. In this paper we consider a model for a fed-batch fermentation process which describes the biosynthesis of penicillin. Firstly, we solve the problem numerically by using a direct method. By discretization of the control variable, we transform the basic optimal control problem to a finite dimensional nonlinear programming problem, which is solved numerically by a standard SQP-method. Contrary to an earlier paper by Luus (1993) we consider the problem as a free final time problem, thus obtaining an improved value of the penicillin output. The results indicate that the assumption of a continuous control which underlies the discretization scheme seems not to be valid. In a second step, we apply classical optimal control theory to the fed-batch fermentation problem. We derive a boundary-value problem (bvp) with switching conditions, which can be solved numerically by multiple shooting technique. It turns out, however, that this bvp is sensitive, which is due to the rigid behaviour of the ...