Vasilios Manousiouthakis

Automatic synthesis of mass-exchange networks with single-component targets

This paper addresses the problem of automatically synthesizing mass-exchange networks in which the mass of a single (key) component is exchanged between a set of rich streams and a set of lean streams. In the first part of this paper we present a two-stage synthesis procedure that employs one minimum allowable composition difference for all possible rich-lean stream pairs. In the first stage, a linear programming problem is solved to determine the minimum cost of mass-separating agents and to locate thermodynamic bottlenecks (pinch points) which restrict the exchange of mass between the rich and the lean streams. This formulation can also preclude (preassign) any specified forbidden (compulsory) matches between streams. In the second stage, a mixed-integer linear program is solved to yield minimum-utility cost networks in which the number of mass-exchanger units is minimized. In the second part of this paper we present a more general, yet computationally intensive, procedure that employs one minimum allowable composition difference for each possible rich-lean stream pair. These degrees of freedom are then used to minimize the annualized total cost of the network. An additional merit of the latter methodology is its potential as an improved approach for the synthesis of optimal heat-exchange networks. Several examples with industrial relevance are solved to demonstrate the usefulness of the notion of synthesizing mass-exchange networks and to illustrate the computational effectiveness of the proposed synthesis strategy.

Strict detailed balance is unnecessary in Monte Carlo simulation

Detailed balance is an overly strict condition to ensure a valid Monte Carlo simulation. We show that, under fairly general assumptions, a Monte Carlo simulation need satisfy only the weaker balance condition. Not only does our proof show that sequential updating schemes are correct, but also it establishes the correctness of a whole class of new methods that simply leave the Boltzmann distribution invariant.

Best achievable decentralized performance

In this paper, a novel parameterization of all decentralized stabilizing controllers is employed in mathematically formulating the best achievable decentralized performance problem as an infinite dimensional optimization problem, Finite dimensional optimization problems are then constructed that have values arbitrarily close to this infinite dimensional problem. An algorithm which identifies the best achievable performance over all linear time-invariant decentralized controllers is then presented. It employs a global optimization approach to the solution of these finite dimensional approximating problems. >

On the state space approach to mass/heat exchanger network design

In this paper, the conceptual framework and applications of the State Space Approach to Process Synthesis are presented. It is shown that the State Space Approach contains the concept of a Network Superstructure as a special case. Additionally, through various operators, it is shown to provide increased flexibility in formulating process network synthesis problems. As an example, it is demonstrated that an Assignment Operator can be used to facilitate the solution of large-scale problems. Pinch Operators are also employed in solving combined heat and mass exchange network synthesis problems. To demonstrate the usefulness of this new approach, two important problems are discussed. First, a one-step procedure is developed that minimizes the total annualized cost (TAC) of heat/mass exchange networks. Next, a novel problem, namely the pinch-based calculation of Minimum Utility Cost for a separable heat and mass exchange network, is solved.

Kinetic model reduction using genetic algorithms

Large reaction networks pose difficulties in simulation and control when computation time is restricted. We present a novel approach to simplification of reaction networks that formulates the model reduction problem as an optimization problem and solves it using a genetic algorithm (GA). Two formulations of kinetic model reduction and their encodings are considered, one involving the elimination of reactions and the other the elimination of species. The GA approach is applied to reduce an 18-reaction, 10-species network, and the quality of solutions returned is evaluated by comparison with global solutions found using complete enumeration. The two formulations are also solved for a 32-reaction, 18-species network.

A GLOBAL OPTIMIZATION APPROACH TO RATIONALLY CONSTRAINED RATIONAL PROGRAMMING

Abstract The rationally constrained rational programming (RCR) problem is shown, for the first time, to be equivalent to the quadratically constrained quadratic programming problem with convex objective function and constraints that are all convex except for one that is concave and separable. This equivalence is then used in developing a novel implementation of the Generalized Benders Decomposition (GBDA) which, unlike all earlier implementations, is guaranteed to identify the global optimum of the RCRP problem. It is also shown, that the critical step in the proposed GBDA implementation is the solution of the master problem which is a quadratically constrained, separable, reverse convex programming problem that must be solved globally. Algorithmic approaches to the solution of such problems are discussed and illustrative examples are presented.

On the Generalized Benders Decomposition

Abstract Generalized Benders Decomposition is a procedure to solve certain types of NLP and MINLP problems. The use of this procedure has been recently suggested as a tool for solving process design problems. This paper analyzes the solution of nonconvex problems through different implementations of the Generalized Benders Decomposition. It is demonstrated that in certain cases only local minima may be found, whereas in other cases not even convergence to local optima can be achieved. A criterion to identify whether the converged value is a candidate for being a local minimum is provided. It is also shown that in the presence of a dual gap, a particular implementation of the Generalized Benders Decomposition may provide upper and lower bounds on the global optimum. The conceptual steps undertaken in establishing the various implementations of GBD are summarized as follows: • -Convexity of X and of F ( x , y ) and G ( x , y ) in x , implies that (1) is equivalent to (4). When these conditions do not apply a gap between v ( y ) and its dual may exist (Remark 2.1). • -Problem (4) is replaced by a sequence of relaxed master problems (Remark 2.3). • -Convexity of X and of F ( x , y ) and G ( x , y ) in x (as well as satisfaction of certain other conditions) guarantees ϵ-convergence of the GBD iterations (Geoffrion, 1972, Theorem 2.5). It is implicitly understood, that for these results to hold, both the primal and the relaxed master problem must be solved globally. • -Global solution of the primal stems readily from convexity of X and of F ( x , y ) and G ( x , y ) in x . Global solution of the relaxed master may come either through the use of special algorithms or by the establishment of convexity of L *( y , u ) and L * ( y , λ) in y . One case for which convexity of these functions can be established is when F ( x , y ) and G ( x , y ) are jointly convex in x and y (Geoffrion, 1972, Section 4.2). • -Prior to the solution of the relaxed master problem, the evaluation of L *( y , u *) and L * ( y , λ*) is first required through (5) and (6). • -One case for which L *( y , u *) and L * ( y , λ*) can be obtained in explicit form is when the global minimum (over x ) of (5) and (6) can be obtained independently of y [ Property ( P )]. In this case one can construct the Benders iterations by selecting x to be the solution of the primal and u (or λ) the corresponding Lagrange multiplier. • -When the Benders iterations are built based on the primal solution, i.e. assuming that the solution of the minimization problem (5) or (6) is equal to the solution of the primal x *, [irrespective of the satisfaction of Property ( P )], the NP-GBD algorithm is obtained. When x * is indeed the solution of the minimization problem, it is said that Property ( P ′) holds. • -When the Benders iterations are built through the introduction of additional constraints as in (11), and through global solutions of (5) and (6) (problems R and S ), then the PL-GBD is obtained.

Euclidean condition and block relative gain: Connections, conjectures, and clarifications

Given an arbitrary nonsingular complex matrix, certain quantitative relationships between its Euclidean condition number and its associated block relative gains are established. In addition, an as yet unproven relation of this type is conjectured. The control theoretic implications of the established relations are briefly discussed, clarifying the role of the block relative gain concept in control theory.

Infinite DimEnsionAl State-space approach to reactor network synthesis: application to attainable region construction

In this work, we present a methodology for the construction of the attainable region (AR) and for the synthesis of globally optimal reactor networks employing isothermal, steady-state, plug flow reactors (PFR), continuous-stirred tank reactors (CSTR) as well as mixing. The problem is solved using the novel Infinite DimEnsionAl State-space (IDEAS) approach. Within the IDEAS framework, reactor network synthesis is formulated as an infinite dimensional convex (linear) optimization problem. Pointwise identification of the reactor networks attainable region is shown to be equivalent to the solution of an infinite dimensional linear program. A finite dimensional approximation strategy is presented and illustrated on an example from the literature.

On constrained infinite-time linear quadratic optimal control

This work presents a solution to the infinite-time linear quadratic optimal control (ITLQOC) problem with state and control constraints. It is shown that a single, finite dimensional, convex program of known size can yield this solution. Properties of the resulting value function, with respect to initial conditions, are also established and are shown to be useful in determining the aforementioned problem size. An example illustrating the method is finally presented.