Sequential Optimization Approach Research Articles

Stochastic closed-loop model predictive control of continuous nonlinear chemical processes

A new predictive control framework for chemical processes is presented, that has a number of fundamental differences to classical MPC. Both future disturbances and future process measurements are explicitly introduced in the model prediction, while back-off prevents violation of the inequality constraints. A feedforward trajectory, used for constraint pushing, is optimized simultaneously with a linear time-varying feedback controller, used to minimize the back-off. No feedback is generated by the receding horizon implementation itself. Via several transformations, the resulting optimization problem is rendered convex. For nonlinear processes, this applies to the sub-problem in a sequential conic optimization approach. A two stage LQG approach reduces the complexity even further for large scale systems. The method is illustrated on a HDPE reactor example and compared to a LTV-MPC.

Delay-Dependent γ-Suboptimal H∞ Model Reduction for Neutral Systems With Time-Varying Delays

Abstract In this paper, the model reduction problem of neutral systems with time-varying delays is studied with γ suboptimality under the H∞ measure. A delay-dependent bounded realness condition of the H∞ norm is given via linear matrix inequalities (LMIs). Based on such a condition, a sufficient condition to characterize the existence of the reduced-order models is given in terms of LMIs with inverse constraints. By employing a sequential convex optimization approach, a reduced-order model can be computed with H∞ error less than some prescribed scalar γ.

On-line dynamic optimization and control strategy for improving the performance of batch reactors

Since batch reactors are generally applied to produce a wide variety of specialty products, there is a great deal of interest to enhance batch operation to achieve high quality and purity product while minimizing the conversion of undesired by-product. The use of process optimization in the control of batch reactors presents a useful tool for operating batch reactors efficiently and optimally. In this work, we develop an approach, based on an on-line dynamic optimization strategy, to modify optimal temperature set point profile for batch reactors. Two different optimization problems concerning batch operation: maximization of product concentration and minimization of batch time, are formulated and solved using a sequential optimization approach. An Extended Kalman Filter (EKF) is incorporated into the proposed approach in order to update current states from their delayed measurement and to estimate unmeasurable state variables. A nonlinear model-based controller: generic model control algorithm (GMC) is applied to drive the temperature of the batch reactor to follow the desired profile. A batch reactor with complex exothermic reaction scheme is used to demonstrate the effectiveness of the proposed approach. The simulation results indicate that with the proposed strategy, large improvement in batch reactor performance, in term of the amount of a desired product and batch operation time, can be achieved compared to the method where the optimal temperature set point is pre-determined. This paper gathers and integrates efficient well-known methodologies such as EKF, GMC and on-line optimization together, resulting in an applicable, reliable and robust control technique for batch reactors.

Sequential optimization approach for the multi‐class user equilibrium problem in a continuous transportation system

AbstractWe consider a city region with several facilities that are competing for customers of different classes. Within the city region, the road network is dense, and can be represented as a continuum. Customers are continuously distributed over space, and they choose a facility by considering both the transportation cost and market externalities. More importantly, the model takes into account the different transportation cost functions and market externalities to which different customer classes are subjected. A logit‐type distribution of demand is specified to model the decision‐making process of users' facility choice. We develop a sequential optimization approach to decompose the complex multi‐class and multi‐facility problem into a series of smaller single‐class and single‐facility sub‐problems. An efficient solution algorithm is then proposed to solve the resultant problem. A numerical example is given to demonstrate the effectiveness and potential applicability of the proposed methodology.

Uncertainty quantification using evidence theory in multidisciplinary design optimization

Abstract Advances in computational performance have led to the development of large-scale simulation tools for design. Systems generated using such simulation tools can fail in service if the uncertainty of the simulation tool's performance predictions is not accounted for. In this research an investigation of how uncertainty can be quantified in multidisciplinary systems analysis subject to epistemic uncertainty associated with the disciplinary design tools and input parameters is undertaken. Evidence theory is used to quantify uncertainty in terms of the uncertain measures of belief and plausibility. To illustrate the methodology, multidisciplinary analysis problems are introduced as an extension to the epistemic uncertainty challenge problems identified by Sandia National Laboratories. After uncertainty has been characterized mathematically the designer seeks the optimum design under uncertainty. The measures of uncertainty provided by evidence theory are discontinuous functions. Such non-smooth functions cannot be used in traditional gradient-based optimizers because the sensitivities of the uncertain measures are not properly defined. In this research surrogate models are used to represent the uncertain measures as continuous functions. A sequential approximate optimization approach is used to drive the optimization process. The methodology is illustrated in application to multidisciplinary example problems.

An integrated model for facility location and technology acquisition

This paper presents an analytical approach for simultaneous optimization of the facility location, capacity acquisition and technology selection decisions. The proposed approach can be useful when there is considerable interaction between these structural decisions, e.g., in global manufacturing companies. In these cases, a sequential optimization approach is bound to produce sub-optimal facility designs, and hence an integrated model is needed. We present a formal definition of the facility location and technology acquisition problem, and provide a basic model. We describe the analytical properties of the model, which led to the development of a solution procedure. We report on a set of experiments, and conclude that the computational performance of the proposed algorithm is quite satisfactory.

Sequential optimization of integrated climate change models

A sequential optimization approach is applied to optimize the behavior of a complex dynamical system. It sequentially solves a large set of mathematical equations and next optimizes the behavior of a reduced-system, fixing certain variables of the larger original problem. These two steps are repeated till convergence occurs. The approach is applied to the problem of identifying response strategies for climate change caused by antropogenic emissions of different trace gases. The convergence properties are analyzed for this example.

An optimum design for 3-D fixture synthesis in a point set domain

Addresses the problem of fixture synthesis for 3-D workpieces with a set of discrete locations on the workpiece surface as a point set of candidates for locator and clamp placement. A sequential optimization approach is presented in order to reduce the complexity associated with an exhaustive search. The approach is based on a concept of optimum experimental design, while the optimization focuses on the fixture performance of workpiece localization accuracy. In using the D-optimality criterion to minimize the workpiece positioning errors, two different greedy algorithms are developed for force-closure fixturing in the point set domain. Both 2-D and 3-D examples are presented to illustrate the effectiveness of the synthesis approach.

On-line scheduling in metal removal processing using variable routings and control strategies

In this paper, a simulation program for the analysis of operations in a manufacturing system is presented. The simulation program is integrated using a control algorithm and a relational data model implemented on the ORACLE RDBMS into a scheduling control system. The control algorithm considers the on-line use of alternative machines tools and/or alternative control strategies in order to optimize a given criterion, which in the present case corresponds to the total delay of jobs in the shop. A series of variables, such as the average machine utilization, were chosen to be the output. A sequential optimization approach, where the dynamically calculated average delay per job is assumed to represent the system state up to the current decision stage, is used for the control algorithm. An application of the scheduling control system to the manufacturing of a piston pump is also presented. The on-line utilization of variable routings and strategies was investigated, demonstrating the overall performance of the algorithm, namely a reduction of the total processing time up to 30%.

Structural topology and shape optimization for a frequency response problem

A topology and shape optimization technique using the homogenization method was developed for stiffness of a linearly elastic structure by Bendsøe and Kikuchi (1988), Suzuki and Kikuchi (1990, 1991), and others. This method has also been extended to deal with an optimal reinforcement problem for a free vibration structure by Diaz and Kikuchi (1992). In this paper, we consider a frequency response optimization problem for both the optimal layout and the reinforcement of an elastic structure. First, the structural optimization problem is transformed to an Optimal Material Distribution problem (OMD) introducing microscale voids, and then the homogenization method is employed to determine and equivalent “averaged” structural analysis model. A new optimization algorithm, which is derived from a Sequential Approximate Optimization approach (SAO) with the dual method, is presented to solve the present optimization problem. This optimization algorithm is different from the CONLIN (Fleury 1986) and MMA (Svanderg 1987), and it is based on a simpler idea that employs a shifted Lagrangian function to make a convex approximation. The new algorithm is called “Modified Optimality Criteria method (MOC)” because it can be reduced to the traditional OC method by using a zero value for the shift parameter. Two sensitivity analysis methods, the Direct Frequency Response method (DFR) and the Modal Frequency Response method (MFR), are employed to calculate the sensitivities of the object functions. Finally, three examples are given to show the feasibility of the present approach.

Fully integrated aerodynamic/dynamic optimization of helicopter rotor blades

This paper describes a fully integrated aerodynamic/dynamic optimization procedure for helicopter rotor blades. The procedure combines performance and dynamics analyses with a general purpose optimizer. The procedure minimizes a linear combination of power required (in hover, forward flight, and maneuver) and vibratory hub shear. The design variables include pretwist, taper initiation, taper ratio, root chord, blade stiffnesses, tuning masses, and tuning mass locations. Performance constraints consist of limits on power required in hover, forward flight, maneuver, airfoil section stall, drag-divergence Mach number, minimum tip chord, and trim. Dynamic constraints are on blade natural frequencies, minimum autorotational inertia, and maximum blade weight. The procedure is demonstrated for two cases. In the first case, the objective function involves power required (in hover, forward flight, and maneuver) and vibratory hub shear. In the second case, the objective function involves power required in hover and vibratory hub shear. For both cases, the designs from the integrated procedure are compared with designs from a sequential optimization approach. In the sequential optimization approach, the blade is optimized first for performance (minimum power) using only aerodynamic design variables and performance constraints. Then these optimized aerodynamic design variables are held fixed, and the blade is optimized for minimum vibratory hub shear, using only dynamic design variables and dynamic constraints. In both cases, the integrated approach is superior to the sequential approach.

A feasibility study for the fabrication of planar silicon multichip modules using electron beam lithography for precise location and interconnection of chips : Andy Hopperet al. IEEE Trans. Compon. Hybrids mfg Technol.15, 97 (1992)

The study attempts to seek the optimal thermal design of planar multichip module (MCMs) under natural convection through optimal chip placement design. To attain the goal, a sequential metamodeling-based optimization approach is introduced. This approach incorporates a response surface methodology (RSM)-based design of experiment (DOE), three-dimensional (3D) thermal finite element analysis (FEA) and an updating scheme. Essentially, the RSM is used to construct, via quadratic polynomial approximation, the global RS of the chip junction temperature in terms of design variables. For speeding up the DOE and the solution of the optimization, several dynamic experimental design strategies using move limits and different proposed sampling techniques are introduced. The feasibility of the strategies is demonstrated, and their solution accuracy and efficiency are also compared with each other. By the explicit RS-based performance function together with geometry constraints, a constrained thermal optimization subproblem is formed. The optimum of the subspace optimization is sought, which is considered as the nominal starting point of next iteration. The iterative process continues with a new defined design subspace and factorial design plan until convergence is attained. The applicability of the proposed design optimization technique is demonstrated through several design case studies involving various planar MCMs.

Simultaneous optimization of variables influencing selectivity and elution strength in micellar liquid chromatography : Effect of organic modifier and micelle concentration

Previously, the simultaneous enhancement of separation with elution strength was reported in micellar liquid chromatography (MLC) using the hybrid eluents of water—organic solvent—micelles The practical implication of this phenomenon is that better separations can be achieved in shorter analysis times by using the hybrid eluents. Since both micelle concentration and volume fraction of organic modifier influence selectivity and solvent strength, only an investigation of the effects of a simultaneous variation of these parameters will disclose the full separation capability of the method, i.e. the commonly used sequential solvent optimization approach of adjusting the solvent strength first and then improving selectivity in reversed-phase liquid chromatography is inefficient for the case of MLC with the hybrid eluents. This is illustrated in this paper with two examples: the optimization of the selectivity in the separation of a mixture of phenols and the optimization of a resolution-based criterion determined for the separation of a number of amino acids and small peptides.The large number of variables involved in the separation process in MLC necessitates a structured approach in the development of practical applications of this technique. A regular change in retention behavior is observed with the variation of the surfactant concentration and the concentration of organic modifier, which enables a successful prediction of retention times. Consequently interpretive optimization strategies such as the iterative regression method are applicable.

A sequential linear optimization approach for controller design

A linear optimization approach with a simple, real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first-order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam, finite element model for the optimal sizing and placement of active/passive structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to the initial conditions of the linear optimization approach is also demonstrated.

Information structures in deterministic decentralized control problems

The information structures associated with deterministic decentralized control are examined. Conditions are derived under which such structures are partially nested. The tuning regulator approach and the sequential optimization approach are used as examples to examine these conditions in the context of concrete decentralized controller design philosophies.

A sequential algorithmic approach to synthesizing minimum cost solar collector fields

A sequential optimization approach to finding minimum cost solar collector fields is presented. Minimum cost fields are found for various values of useful thermal power as measured by the fluid mass flow rate and temperatures in and out of the field. The optimum piping arrangements, field geometries, mixes of collector types, pipe diameters and insulation thicknesses are determined for each minimum cost field. Examples of the application of the optimization approach are also presented.

On Solving Nonlinear Equations with a One-Parameter Operator Imbedding

One parameter operator imbedding to modify Newton method for solution of nonlinear equations

On a sequential optimization approach in nonlinear control

On a sequential optimization approach in nonlinear control