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

Bonus algorithm for large scale stochastic nonlinear programming problems

This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these methods assume that there are a small number of scenarios to be evaluated for calculation of the probabilistic objective function and constraints. This book begins to tackle these issues by describing a generalized method for stochastic nonlinear programming problems. This title is best suited for practitioners, researchers and students in engineering, operations research, and management science who desire a complete understanding of the BONUS algorithm and its applications to the real world