Efficient Combinatorial Optimization Under Uncertainty. 1

This paper presents hierarchical improvements to the combinatorial stochastic annealing algorithm using a new and efficient sampling technique. The Hammersley sequence sampling technique is used for updating discrete combinations, reducing the Markov chain length, determining the number of samples automatically, and embedding better confidence intervals of the samples. The improved algorithm, Hammersley stochastic annealing, can significantly improve computational efficiency over traditional stochastic programming methods. Three distinctive example functions considered proved the efficiency improvement of Hammersley stochastic annealing to be up to 99.3% better than the traditional counterparts. Thus, this new method can be a useful tool for large-scale combinatorial stochastic programming problems. Application of this new algorithm to a real world problem of solvent selection under uncertainty is presented in part 2 of this series

Multiobjective Optimal Controlled Variable Selection for a Gas Turbine–Solid Oxide Fuel Cell System Using a Multiagent Optimization Platform

Hybrid gas turbine–fuel cell systems have immense potential for high efficiency in electrical power generation with cleaner emissions compared with fossil-fueled power generation. A systematic controlled variable (CV) selection method is deployed for a hybrid gas turbine–fuel cell system in the HyPer (hybrid performance) facility at the U.S. Department of Energy’s National Energy Technology Laboratory (NETL) for maximizing its economic and control performance. A three-stage approach is used for the CV selection comprising a priori analysis, multiobjective optimization, and a posteriori analysis. The a priori analysis helps to screen off several candidate CVs, thus reducing the size of the combinatorial optimization problem for multiobjective CV selection. For optimal CV selection, a transfer function model of the HyPer facility is identified. By considering several candidate models, the final transfer function model is selected using Akaike’s Final Prediction Error criterion. Experimental data from the HyPer facility are used to estimate the noise in the measurement data. For solving the combinatorial multiobjective optimization problem for CV selection, a multiagent optimization platform comprising simulated annealing, genetic algorithm, and efficient ant colony optimization algorithms is used. Pareto-optimal CV sets exhibit a high trade-off between the economic and control objective. The a posteriori analysis is undertaken for several top Pareto-optimal CV sets. An optimal CV set is selected that shows the best compromise between process economics and controllability under both nominal and off-design conditions

Introduction to applied optimization

Intended for advanced undergraduate/graduate students as well as scientists and engineers, this textbook presents a multi-disciplinary view of optimization, providing a thorough examination of algorithms, methods, techniques, and tools from diverse areas of optimization. Linear programming, nonlinear programming, discrete optimization, global optimization, optimization under uncertainty, multi-objective optimization, optimal control, and stochastic optimal control are introduced in each self-contained chapter, with exercises, examples, and case studies, the true gems of this text. This third edition includes additional content in each chapter designed to clarify or enhance the exposition, and update methodologies and solutions. A new real-world case study related to sustainability is added in Chapters 2—7. GAMS, AIMMS, and MATLAB® files of case studies for Chapters 2, 3, 4, 5, and 7 are freely accessible electronically as extra source materials. A solutions manual is available to instructors who adopt the textbook for their course. From the reviews: This work is definitely a welcome addition to the existing optimization literature, given its emphasis on modeling and solution practice, as well as its ‘user-friendly’ style of exposition. — János D. Pintér, European Journal of Operations Research, Vol. 177, 2007 Urmila Diwekar’s book on applied optimization is one of the few books on the subject that combines impressive breadth of coverage with delightful readability. In her exposition of concepts and algorithms in the major areas of optimization, she always goes to the heart of the matter and illustrates her explanations with simple diagrams and numerical examples. Graduate and undergraduate students, who constitute part of the target audience, should find this a very useful book. — Jamshed A. Modi, Interfaces, Vol. 36 (1), 2006 Optimization is a rich field with a strong history; this book nicely introduces both, moving from very introductory material to challenging techniques toward the end … Examples range from quite simplistic through realistic difficult scheduling problems. Some examples resurface in different chapter with twists to demonstrate how different techniques are required for differing data and constraints. — CHOICE, September 2004

Optimization Under Uncertainty in Chemical Engineering

This article presents an overview of optimization under uncertainty with application to chemical manufacturing. The article introduces the basic algorithms and methods, and presents applications related to all stages of design starting from chemical synthesis, process synthesis, to manufacturing, planning, and management

Thermodynamic uncertainties in batch processing and optimal control

Abstract Batch distillation is an important separation process for small-scale production especially in pharmaceutical, specialty chemical and biochemical industries. Although batch distillation units require lower capital cost than continuous units, the unsteady state nature of the process, results in higher operating costs. Optimal control in batch distillation is a mode of operation which allows us to optimize the column operating policy by selecting a trajectory for reflux ratio. Due to the uncertainties in thermodynamic models the reflux ratio profile obtained is often suboptimal. Recently a new method was proposed by Rico-Ramirez et al. [Comput. Chem. Eng. 27 (2003) 1867] to include time-dependent uncertainties in current formulations of batch distillation optimal control for ideal systems. In this paper, a general approach is proposed to handle both dynamic and static uncertainties in thermodynamics for more complex non-ideal systems. The static uncertainties result from the inaccuracies associated with predicting vapor-liquid equilibrium using group contribution methods such as UNIFAC. The unsteady state nature of batch distillation translates these static uncertainties into time-dependent uncertainties. A new Ito process representation is proposed for the dynamic behavior of relative volatility for non-ideal mixtures. Numerical case studies are presented to demonstrate the usefulness of this approach for batch as well as bio-processing

Optimizing TEG Dehydration Process under Metamodel Uncertainty

Natural gas processing requires the removal of acidic gases and dehydration using absorption, mainly conducted in tri-ethylene glycol (TEG). The dehydration process is accompanied by the emission of volatile organic compounds, including BTEX. In our previous work, multi-objective optimization was undertaken to determine the optimal operating conditions in terms of the process parameters that can mitigate BTEX emission using data-driven metamodeling and metaheuristic optimization. Data obtained from a process simulation conducted using the ProMax® process simulator were used to develop a metamodel with machine learning techniques to reduce the computational time of the iterations in a robust process simulation. The metamodels were created using limited samples and some underlying phenomena must therefore be excluded. This introduces the so-called metamodeling uncertainty. Thus, the performance of the resulting optimized process variables may be compromised by the lack of adequately accounting for the uncertainty introduced by the metamodel. In the present work, the bias of the metamodel uncertainty was addressed for parameter optimization. An algorithmic framework was developed for parameter optimization, given these uncertainties. In this framework, metamodel uncertainties are quantified using real model data to generate distribution functions. We then use the novel Better Optimization of Nonlinear Uncertain Systems (BONUS) algorithm to solve the problem. BTEX mitigation is used as the objective of the optimization. Our algorithm allows the determination of the optimal process condition for BTEX emission mitigation from the TEG dehydration process under metamodel uncertainty. The BONUS algorithm determines optimal process conditions compared to those from the metaheuristic method, resulting in BTEX emission mitigation up to 405.25 ton/yr

Multi-objective integrated solvent selection and solvent recycling under uncertainty using a new genetic algorithm

Abstract: The optimal design of waste treatment processes always involves several objectives to be considered like cost and Environmental Impact (EI). Hence a multi-objective optimisation framework is required whose solution is not a single value but a Pareto set, which includes the alternatives representing potential compromise solutions among the objectives. Further, uncertainties are inherent in EI assessment, these uncertainties need to be propagated and analysed. In this paper, a multi-objective optimisation algorithm called MOEGA is developed. This new and efficient algorithm identifies more tradeoff solutions (with and without uncertainties in EI) than before