An alternative disjunctive optimization model for heat integration with variable temperatures

This paper presents an alternative model to deal with the problem of optimal energy consumption minimization of non-isothermal systems with variable inlet and outlet temperatures. The model is based on an implicit temperature ordering and the “transshipment model” proposed by Papoulias and Grossmann (1983). It is supplemented with a set of logical relationships related to the relative position of the inlet temperatures of process streams and the dynamic temperature intervals. In the extreme situation of fixed inlet and outlet temperatures, the model reduces to the “transshipment model”. Several examples with fixed and variable temperatures are presented to illustrate the model's performance.

Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

MINLP Optimization Algorithm for the Synthesis of Heat and Work Exchange Networks

This paper introduces a new optimization model for the simultaneous synthesis of heat and work exchange networks. The work integration is performed in the work exchange network (WEN), while the heat integration is carried out in the heat exchanger network (HEN). In the WEN synthesis, streams at high-pressure (HP) and low-pressure (LP) are subjected to pressure manipulation stages, via turbines and compressors running on common shafts and stand-alone equipment. The model allows the use of several units of single-shaft-turbine-compressor (SSTC), as well as helper motors and generators to respond to any shortage and/or excess of energy, respectively, in the SSTC axes. The heat integration of the streams occurs in the HEN between each WEN stage. Thus, as the inlet and outlet streams temperatures in the HEN are dependent of the WEN design, they must be considered as optimization variables. The proposed multi-stage superstructure is formulated in mixed-integer nonlinear programming (MINLP), in order to minimize the total annualized cost composed by capital and operational expenses. A case study is conducted to verify the accuracy of the proposed approach. The results indicate that the heat integration between the WEN stages is essential to enhance the work integration, and to reduce the total cost of process due the need of a smaller amount of hot and cold utilities.

Logic-Based Outer-Approximation Algorithm for Solving Discrete-Continuous Dynamic Optimization Problems

We present an extension of the logic outer-approximation algorithm for dealing with disjunctive discrete-continuous optimal control problems whose dynamic behavior is modeled in terms of differential-algebraic equations. Although the proposed algorithm can be applied to a wide variety of discrete-continuous optimal control problems, we are mainly interested in problems where disjunctions are also present. Disjunctions are included to take into account only certain parts of the underlying model which become relevant under some processing conditions. By doing so the numerical robustness of the optimization algorithm improves since those parts of the model that are not active are discarded leading to a reduced size problem and avoiding potential model singularities. We test the proposed algorithm using three examples of different complex dynamic behavior. In all the case studies the number of iterations and the computational effort required to obtain the optimal solutions is modest and the solutions are relatively easy to find.

Primal Attainment in Convex Infinite Optimization Duality

This article provides results guarateeing that the optimal value of a given convex infinite optimization problem and its corresponding surrogate Lagrangian dual coincide and the primal optimal value is attainable. The conditions ensuring converse strong Lagrangian (in short, minsup) duality involve the weakly-inf-(locally) compactness of suitable functions and the linearity or relative closedness of some sets depending on the data. Applications are given to different areas of convex optimization, including an extension of the Clark-Duffin Theorem for ordinary convex programs.

New glimpses on convex infinite optimization duality

Given a convex optimization problem (P) in a locally convex topological vector space X with an arbitrary number of constraints, we consider three possible dual problems of (P), namely, the usual Lagrangian dual (D), the perturbational dual (Q), and the surrogate dual (Δ), the last one recently introduced in a previous paper of the authors (Goberna et al., J Convex Anal 21(4), 2014). As shown by simple examples, these dual problems may be all different. This paper provides conditions ensuring that inf(P)=max(D), inf(P)=max(Q), and inf(P)=max(Δ) (dual equality and existence of dual optimal solutions) in terms of the so-called closedness regarding to a set. Sufficient conditions guaranteeing min(P)=sup(Q) (dual equality and existence of primal optimal solutions) are also provided, for the nominal problems and also for their perturbational relatives. The particular cases of convex semi-infinite optimization problems (in which either the number of constraints or the dimension of X, but not both, is finite) and linear infinite optimization problems are analyzed. Finally, some applications to the feasibility of convex inequality systems are described.

Optimization of Chemical Processes Using Surrogate Models Based on a Kriging Interpolation

Superstructure approaches are the solution to the difficult problem which involves the rigorous economic design of a distillation column. These methods require complex initialization procedures and they are hard to solve. For this reason, these methods have not been extensively used. In this work, we present a methodology for the rigorous optimization of chemical processes implemented on a commercial simulator using surrogate models based on a kriging interpolation. Several examples were studied, but in this paper, we perform the optimization of a superstructure for a non-sharp separation to show the efficiency and effectiveness of the method. Noteworthy that it is possible to get surrogate models accurate enough with up to seven degrees of freedom.

Optimization of test and maintenance of ageing components consisting of multiple items and addressing effectiveness

There are many models in the literature that have been proposed in the last decades aimed at assessing the reliability, availability and maintainability (RAM) of safety equipment, many of them with a focus on their use to assess the risk level of a technological system or to search for appropriate design and/or surveillance and maintenance policies in order to assure that an optimum level of RAM of safety systems is kept during all the plant operational life. This paper proposes a new approach for RAM modelling that accounts for equipment ageing and maintenance and testing effectiveness of equipment consisting of multiple items in an integrated manner. This model is then used to perform the simultaneous optimization of testing and maintenance for ageing equipment consisting of multiple items. An example of application is provided, which considers a simplified High Pressure Injection System (HPIS) of a typical Power Water Reactor (PWR). Basically, this system consists of motor driven pumps (MDP) and motor operated valves (MOV), where both types of components consists of two items each. These components present different failure and cause modes and behaviours, and they also undertake complex test and maintenance activities depending on the item involved. The results of the example of application demonstrate that the optimization algorithm provide the best solutions when the optimization problem is formulated and solved considering full flexibility in the implementation of testing and maintenance activities taking part of such an integrated RAM model.

Large scale optimization of a sour water stripping plant using surrogate models

In this work, we propose a new methodology for the large scale optimization and process integration of complex chemical processes that have been simulated using modular chemical process simulators. Units with significant numerical noise or large CPU times are substituted by surrogate models based on Kriging interpolation. Using a degree of freedom analysis, some of those units can be aggregated into a single unit to reduce the complexity of the resulting model. As a result, we solve a hybrid simulation-optimization model formed by units in the original flowsheet, Kriging models, and explicit equations. We present a case study of the optimization of a sour water stripping plant in which we simultaneously consider economics, heat integration and environmental impact using the ReCiPe indicator, which incorporates the recent advances made in Life Cycle Assessment (LCA). The optimization strategy guarantees the convergence to a local optimum inside the tolerance of the numerical noise.

Optimization of the Modular Educational Program Structure

Optimized structure of the educational program consisting of a set of the interconnected educational objects is offered by means of problem solution of optimum partition of the acyclic weighed graph. The condition of acyclicity preservation for subgraphs is formulated and the quantitative assessment of decision options is executed. The original algorithm of search of quasioptimum partition using the genetic algorithm scheme with coding chromosomes by permutation is offered. Object-oriented realization of algorithm in language C++ is described and results of numerical experiments are presented.

Dynamic, convex, and robust optimization with Bayesian learning for response-guided dosing

Thesis (Ph.D.)--University of Washington, 2016-08

Submodular Optimization and Data Processing

Thesis (Ph.D.)--University of Washington, 2016-06

Geometry and Optimization of Relative Arbitrage

Thesis (Ph.D.)--University of Washington, 2016-06

Design and implementation of a windows-based parallel computing environment for large scale optimization

A parallel computing environment to support optimization of large-scale engineering systems is designed and implemented on Windows-based personal computer networks, using the master-worker model and the Parallel Virtual Machine (PVM). It is involved in decomposition of a large engineering system into a number of smaller subsystems optimized in parallel on worker nodes and coordination of subsystem optimization results on the master node. The environment consists of six functional modules, i.e. the master control, the optimization model generator, the optimizer, the data manager, the monitor, and the post processor. Object-oriented design of these modules is presented. The environment supports steps from the generation of optimization models to the solution and the visualization on networks of computers. User-friendly graphical interfaces make it easy to define the problem, and monitor and steer the optimization process. It has been verified by an example of a large space truss optimization. (C) 2004 Elsevier Ltd. All rights reserved.

A theoretical comparison of two optimization methods for radiofrequency drive schemes in high frequency MRI resonators

In this paper, numerical simulations are used in an attempt to find optimal Source profiles for high frequency radiofrequency (RF) volume coils. Biologically loaded, shielded/unshielded circular and elliptical birdcage coils operating at 170 MHz, 300 MHz and 470 MHz are modelled using the FDTD method for both 2D and 3D cases. Taking advantage of the fact that some aspects of the electromagnetic system are linear, two approaches have been proposed for the determination of the drives for individual elements in the RF resonator. The first method is an iterative optimization technique with a kernel for the evaluation of RF fields inside an imaging plane of a human head model using pre-characterized sensitivity profiles of the individual rungs of a resonator; the second method is a regularization-based technique. In the second approach, a sensitivity matrix is explicitly constructed and a regularization procedure is employed to solve the ill-posed problem. Test simulations show that both methods can improve the B-1-field homogeneity in both focused and non-focused scenarios. While the regularization-based method is more efficient, the first optimization method is more flexible as it can take into account other issues such as controlling SAR or reshaping the resonator structures. It is hoped that these schemes and their extensions will be useful for the determination of multi-element RF drives in a variety of applications.