J. Alberto Bandoni

Interaction between process design and process operability of chemical processes: an eigenvalue optimization approach

An increasing effort is being devoted to consider controllability issues (or in a wider sense operability issues) at the process design stage. Controllability has mainly to do with dynamics in the face of disturbances. One philosophy for the integration of design and controllability is to explicitly consider dynamic elements within the process design formulation. An outstanding feature of dynamics is stability, which is related with the spectrum (set of eigenvalues) of the dynamic system Jacobian matrix. Dynamic convergence speed may also be analyzed in terms of the eigenvalues of the matrix from a Lyapunov function related to the Jacobian of the system. It is the purpose of this contribution to formulate and solve the chemical process design problem, considering process dynamics from an eigenvalue optimization approach.

Estimation of domains of attraction: A global optimization approach

In this paper a methodology for the estimation of domains of attraction of stable equilibriums based on maximal Lyapunov functions is proposed. The basic idea consists in finding the best level set of a Lyapunov function which is fully contained in the region of negative definiteness of its time derivative. An optimization problem is formulated, which includes a tangency requirement between the level sets and constraints on the sign of the numerator and denominator of the Lyapunov function. Such constraints help in avoiding a large number of potential dummy solutions of the nonlinear optimization model. Moreover, since global optimality is also required for proper estimation, a deterministic global optimization solver of the branch and bound type is adopted. The methodology is applied to several examples to illustrate different aspects of the approach.

Nonlinear dynamic systems design based on the optimization of the domain of attraction

In this paper an optimization-based methodology for the design of the operating equilibrium of a nonlinear dynamic system based on a measure of the extension of its domain of attraction is proposed. The approach consists in maximizing the radius of a ball in the state space contained in the region of negative definiteness of the time derivative of a quadratic Lyapunov function, using a two level optimization strategy. A deterministic global optimization problem is solved at the inner level to ensure proper estimation of the domain of attraction for each feasible realization of the design variables which are optimized at the outer level. In order to cope with the non-differentiable nature of the inner problem, a stochastic algorithm is applied to manipulate the design variables at the outer level. The methodology is applied to several examples to illustrate different aspects of the approach.

Estimation of domains of attraction in epidemiological models with constant removal rates of infected individuals

The spread of infections is commonly represented through the so-called Susceptible - Infectious - Recovered models (SIR). Treatment based on isolation of infected individuals is often applied to decrease the spread of certain diseases. Such situation is considered in the SIR model through a constant removal rate term. It has been shown that in such cases, the outcome of the disease spread may depend on the position of the initial states for certain range of the model parameters. The estimation of the domains of attraction of the equilibrium points may therefore be useful to understand the dynamic behavior of the infection spread as a function of the initial population distribution. In this contribution, a Lyapunov based approach to estimate the domain of attraction of the endemic steady state point in SIR models is proposed.

Simultaneous re-design and scheduling of multiple effect evaporator systems

Evaporation is a key operation in many industries and its optimization is required for the efficient management of water and energy within the process. During the operation, dissolved solids settle on the heat exchange surfaces with the consequent increase in the heat transfer resistance. Therefore, periodic shutdowns of the trains of evaporators are required for the cleaning of the units in order to restore acceptable performance. In this work the simultaneous re-design and scheduling of multiple effect evaporation systems is addressed. A mixed integer nonlinear programming model based on a discrete time representation is proposed and applied to a typical evaporation system in the sugar industry with several multiple effect parallel lines and time decaying performance. Highlights? Fouling reduces heat exchange efficiency in evaporation processes. ? Evaporation lines have to be periodically shut down for cleaning. ? Improved evaporation networks and cleaning schedules reduce steam consumption.

Determination of storage tanks location for optimal short-term scheduling in multipurpose/multiproduct batch-continuous plants under uncertainties

A multipurpose/multiproduct plant has to deal with many combinations of tasks sequences and operation rates that lead to accumulation problems. These problems can be handled using storage tanks, but usually their location within the flowsheet is predetermined and not subject to optimization, missing the opportunity to better satisfy the customers. In this work we will determinate the optimal location of storage tanks for the short-term scheduling under uncertainty. A hybrid simulation-based optimization (SBO) strategy was developed and implemented to solve the problems combining stochastic and deterministic solution algorithms.

A Global Optimization Approach for the Estimation of Domains of Attraction

Abstract In order to completely characterize an asymptotically stable equilibrium point, some information about the size and shape of its Domain of Attraction is required. In this contribution a global optimization approach is proposed to estimate domains of attraction of general nonlinear dynamic systems. The technique is illustrated by a two states system that presents a very rich nonlinear behavior and is then applied to a typical continuous stirred tank reactor.

A bi-objective optimization model for tactical planning in the pome fruit industry supply chain

Abstract In this work, a multi-period mixed integer linear programming formulation for the medium-term planning of the apples and pears supply chain is presented. Given the supply chain structure, demand data, and harvesting dates, the proposed approach integrates production, processing, distribution, and inventory decisions considering two conflicting objectives: profit and product supply shortage. The mathematical model is solved by using the lexicographic method to deal with the multi-objective optimization. The system is analyzed in the face of changes in storage, processing and transportation capacities. Major results indicate that in order to minimize supply shortage (leading objective) in the second part of the season, beneficial trade opportunities have to be missed along the year with the consequent reduction in the total profit (subordinated objective). To illustrate the approach, a pome fruit industry located in the “Alto Valle de Rio Negro y Neuquen” Argentine region is considered as a case study.

Optimal drug infusion profiles using a Particle Swarm Optimization algorithm

Abstract The dynamic optimization of the administration of therapeutic drugs in simulated patients is proposed. The approach is based on a non-linear discontinuous cardiorespiratory model, which has been conceived to simulate the effect of inotropic and vasoactive drugs as well as anesthetic agents. A stochastic technique (Particle Swarm Optimization), within the context of the control vector parameterization approach, is adopted to identify the infusion profiles of various drugs in order to track, as close as possible, the set-points on several variables of medical interest. Two different medical procedures are investigated in order to test the efficiency and robustness of the algorithm: a congestive heart failure and the unclamping of an aortic vessel. Due to the conflicting nature of the different objectives, compromise solutions are obtained in all cases.

Supply chain optimisation in a petrochemical complex

Abstract This paper addresses the supply chain optimisation of a petrochemical complex as a multiperiod model over a short time horizon. In order to coordinate responses to demands while maximising profit, simultaneous planning of production and each plant production distribution has been undertaken. The model is optimised along a short-term planning horizon spanning multiple periods and supports the decision-making process of supply, production, intermediate and final product storage and distribution. Intermittent deliveries and demand satisfaction have been considered. Nonconvexities arise from blending and storage of multicomponent streams. The resulting nonconvex large scale mixed integer nonlinear model has been solved with GAMS using as initial point a linear model where bilinerities have been reformulated into linear equations.