CIM PROGRAMS AND ACTIVITIES

Fields Industrial Optimization Seminar
2010-11

Kim B. McAuley (Queen's University)
Optimization for Development of Reliable Fundamental Models

Fundamental models are used to design, debottleneck and optimize chemical processes to ensure safe and economical manufacture of high-quality chemicals, petroleum, plastics and pharmaceuticals. Reliable optimization results require reliable models. This talk will focus on some optimization tools and statistical concepts that can be used during model building. One common problem that arises when modeling chemical processes is the large number of parameters that can appear in equations that describe the rates of chemical reactions. Often, there is insufficient information in the available data to reliably estimate all of the model parameters. Parameter estimability analysis techniques and model-selection criteria will be presented that can help modellers to estimate parameters, simplify model equations and design additional experiments to ensure good model predictions. These methods will be illustrated using models and data from several different laboratory-scale and industrial processes.

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Keith Marchildon (Keith Marchildon Chemical Process Design Inc.)
Modeling Successes in a Polymer Production Process

Mathematical modeling of chemical processes is an expensive business, requiring skilled personnel to create the models and to secure the supporting data, and requiring long-term commitment by management. If the models are to be fundamental rather than statistical then they additionally require persons with the ability to interpret a process according to principles of chemistry, physics and engineering. These conditions came together in support of a particular polymer production process. The work has been more than justified over the years by a variety of profitable benefits, many of them only vaguely foreseen: the very existence of the model was the catalyst for new methods and entirely new ideas. We present an account of the architecture of the model, an early major project to gather and interpret supporting data, some applications in process optimization and expansion, solution of a complex problem in process control, and the use of the model in building an on-line process monitor. Along the way we comment on some issues in model building such as language, input and output, maintenance, and use of commercial simulators.

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Norm Hann (Hydro One)
Closing the Crevice: Achieving Valuable Maintenance Analyses by Linking Corporate Data with Maintenance Analysis Software

There is currently a gap or crevice between corporate databases and powerful maintenance analysis software, such as Exakt. This crevice has impeded the development of usable maintenance decision models. The CMMS has not ventured into this area, and general-purpose data warehouses are ill-equipped to handle the analysis and the complex requirements of maintenance and reliability. This presentation describes a flexible technique developed with the needs of reliability analysts in mind. It enables the automated filtering of large volumes of work and monitoring data in order to produce the "Events" and "Inspections" tables of the quality and form required for analysis, modeling and processing by an Exakt decision agent. The process will be described using examples from Hydro One’s experience in the challenging area of data management and decision making.

Boris Mordukhovich (Wayne State University)
GENERALIZED NEWTON'S METHOD BASED ON GRAPHICAL DERIVATIVES

This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations. Based on advanced techniques of variational analysis and generalized differentiation, we establish the well-posedness of the algorithm, its local superlinear convergence, and its global convergence of the Kantorovich type. Our convergence results hold with no semismoothness assumption, which is illustrated by examples. The algorithm and main results obtained in the paper are compared with well-recognized semismooth and B-differentiable versions of Newton's method for nonsmooth Lipschitzian equations.

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San Yip (Suncor Energy)
Challenges of Integrating Planning and Scheduling in Oil Industry

Decision making hierarchy in process industry is typically broken down into several layers: Planning, Scheduling, Real-time Operations Optimization (RTO) and Process Control. Each layer executes the optimization problem at a different frequency. Planning and scheduling layers consider a horizon of weeks to months and their calculations are performed monthly and weekly, respectively. The RTO calculation is executed every few hours or minutes, depending on the dynamics of the processes, to reject disturbances with frequencies higher than those considered in the planning and scheduling layers. The lowest process control layer executes its calculations every minute or second to maintain the controlled variables at the setpoints.

Each layer optimizes its objective based on the decision from the layer above. Planning layer determines the monthly average production targets by maximizing long-term economics. Scheduling layer calculates daily operating targets by minimizing deviations from the monthly optimum targets determined from the planning layer. The daily operating targets are then passed to the RTO layer which optimizes the operating conditions of process units. Finally, process control layer keeps the units running at the optimum operating conditions.

This presentation will focus on planning and scheduling layers. By reviewing current industrial practice, challenges of integrating planning and scheduling layers will be discussed, and a strategy to interface commercial planning and scheduling tools for gasoline blending will be presented.

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Jose M. Pinto, Praxair R&D
Risk Management in the Industrial Gas Supply Chain
(co-authored by Atul Rangarajan)

The capital intensive industrial gases business involves the production, distribution and sale of atmospheric gases (argon, nitrogen and oxygen), carbon dioxide, hydrogen, helium and specialty gases. Atmospheric gases are produced though cryogenic processes in air separation plants. There are three basic distribution methods for industrial gases: (i) via pipelines (“on-site”); (ii) as cryogenic liquids via trucks (“merchant liquid”); and (iii) as gas in cylinders (“packaged gases”). These distribution methods are often integrated, with products from multiple supply modes coming from the same plant. The method of supply is generally determined by the lowest cost means of meeting the customer’s needs, depending upon factors such as volume requirements, purity, pattern of usage, and the form in which the product is used (as a gas or as a cryogenic liquid). A typical business model is the so called “sale-of-gas” in which the industrial gas company owns and operates the plants. These capital investments are characterized by long payback periods and long term contracts with customers. Due to the complexity and expanding geographic reach of the company’s operations, a wide range of factors, many of which are outside of the company’s control, could materially affect its future operations and financial performance. For example, the following risks may significantly impact the company:
• Project execution including construction, supplier risk, new technology
• Operations including reliability, maintainability, performance
• Commercial and Market including onsite demand, liquid demand, energy and raw material availability and costs, contracting
• Financial like currency, inflation rates, country/regulatory
• Others like general economic conditions, global financial markets conditions, competitor actions; catastrophic events, international events and circumstances
The objective of the talk is to discuss the several risk factors and their impact on the industrial gas supply chain. In addition we will present work that considers the simultaneous capacity allocation and distribution planning under demand risk for an industrial gas supply chain. A stochastic inventory approach is proposed and it is incorporated into a multi-period two-stage stochastic mixed-integer nonlinear programming (MINLP) model to handle uncertainty of demand and loss or addition of customers. This nonconvex MINLP formulation takes into account customer synergies and simultaneously predicts the optimal sizes of customers’ storage tanks, the safety stock levels and the estimated delivery cost for replenishments. Three case studies including instances with up to 200 customers are presented to demonstrate the effectiveness of the proposed stochastic models and solution algorithms.

We consider a two-dimensional isothermal model of gases in cathode channel and gas diffusive layer (GDL) of HFC, given by a system of PDEs. This system involves the velocity, pressure and concentration of oxygen
and water vapor. The objective is to minimize, with respect to the channel shape, a certain energy functional which ``measures`` the oxygen at the contact of GDL with the catalyst layer, the water vapor on channel outlet and the pressure drop.

The shape of the cathode channel which minimizes this energy functional enhances the performance of HFC.

Under some assumptions we prove that this PDE system has a solution, and that there exists a channel shape, in the class of Lipschitz channel shapes, minimizing the energy functional. Using classical shape optimization techniques we prove the shape differentiability of state variables and of the energy functional, and we give an explicit expression of the energy functional shape gradient.

By using an appropriate adjoint problem we transform the shape derivative of the energy functional in a form appropriate for numerical computations. Furthermore, we prove that the adjoint problem is well-posed.

We will conclude with the presentation of several numerical solutions of optimal channel shape

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Jeff Renfro, Honeywell Process Solutions
Overview of a Nonlinear Model Predictive Optimal Control Technology used in Industrial Process Control Applications

Linear Model Predictive Control (MPC) has been successfully used to address difficult process control problems in the chemical and refining industries since the 1970s. It use in new application areas continues to expand today. The linear and/or quadratic programming components of this MPC technology are highly reliable and can provide computed solutions to large control problems in the required cycle time. However, there are limitations to the class of control problems this linear MPC approach can address due to the linear dynamic models used in the technology. In particular, control of processes that require changes in operating conditions to regions with widely different process sensitivities and dynamics are difficult to manage by linear MPC approaches, due to the dramatic model/process mismatches that develop.

In the mid 1990s some commercial approaches to using nonlinear dynamic models in MPC algorithms were developed in the chemical industry to address the process control challenges that could not be addressed by linear MPC. Some of these approaches for nonlinear model predictive control algorithms required the solution of nonlinear programming problems at each control cycle. This presented challenges for obtaining predictable solution times, reliable convergence and insuring physically meaningful solutions not experienced with linear MPC. In addition, the combination of prioritized control and optimization (optimal control) objectives presents a challenging nonlinearly constrained optimization problem formulation. These issues were addressed to yield a practical nonlinear MPOC (Model Predictive Optimal Control) technology that was productized and has successfully solved a class of difficult process control problems in industry.

This seminar will present an overview of the theoretical formulation, solution strategies, implementation experience and benefits of a nonlinear model predictive optimal control system that has been used in industry since 1994.

In this talk we present the main directions of research in Structural Convex Optimization. In this field, we use additional information on the structure of specific problem instances for accelerating standard Black-Box methods. We show that the proper use of problem structure can provably accelerate these methods by the order of magnitudes. As examples, we consider polynomial-time interior-point methods, smoothing technique, minimization of composite functions and some other approaches.
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Ivan Miletic, ProSensus, Inc.
Data-Driven Models in Industrial Applications of Optimization Methods

Industrial uses of optimization methods cover a wide variety of engineering applications ranging from process control, feedstock and product blending, plant operations optimization, real-time optimization, scheduling, and others.

One key aspect in all of these diverse cases is the need for data and suitable modelling methods in order to develop and drive robust optimization solutions. This important aspect of using data and effective modelling methods to support optimization is examined in this talk by looking at the application of multivariate analysis methods that lead to working empirical models, design of experiments, and improved knowledge and insight into processes.

The examples examined in this talk include commercial applications of optimization-based closed-loop batch control in the food industry, and optimal product design and development. In both cases, the successful use of optimization methods is tied to the effective use of the information in process data through empirical model building.

In this talk we will discuss how the power of semidefinite relaxation can be harnessed to yield a computationally-efficient approximate MIMO soft demodulator. Semidefinite relaxation techniques have previously been proposed for "hard" demodulation problems for which the output is a vector of binary symbols. Rather than making a "hard" decision on each bit, soft demodulators seek to provide more information to the decoder by providing an approximation of the posterior log likelihood ratio of each encoded bit. A key step in the development of the proposed soft demodulator is the use of an approximation of the randomization step in the semidefinite relaxation technique to generate a list of candidate bit vectors over which the likelihoods can be approximated.

The talk will include comparisons with the key competing approaches to MIMO soft demodulation, including the "minimum mean square error soft interference canceller", and the various "soft sphere decoders", which have their roots in tree-search methods for finding the closest point on a lattice. The computational properties of these algorithms have some distinct features, and present some interesting choices to system designers.

This talk is based on work with Mehran Nekuii, who is now with Wavesat, Montreal; Mikalai Kisialiou, who is now with Intel, Portland; and Zhi-Quan (Tom) Luo at the University of Minnesota.

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Ramy Gohary, RIM-Carleton Research Project, Manager

Jointly Optimal Design of The Transmit Covariance and The Relay Precoder in Amplify-and-Forward Relay Channels

The use of relays in wireless communication networks enhances the coverage area of these networks and enables them to operate at higher data rates. The extraction of these gains require the employment of effective signal processing techniques, which in many cases are too complex for practical implementation. Amplify-and-forward is a
computationally efficient scheme that, in some cases, was shown to provide better performance than more sophisticated decode-and-forward and compress-and-forward techniques.

In this work we consider designing a rate-optimal amplify-and-forward relay-assisted communication system in which the relay is assumed to be capable of sending and receiving at the same time and the same frequency. In addition to the transmitter-relay and relay-receiver links, we assume that there is a direct transmitter-receiver link. In this case a rate-optimal design of the system involves the joint optimization of the input signal covariance matrix and the relay precoder; a non-convex problem with potentially high dimensionality.

To solve this problem, we note that the design problem of the input covariance is convex for any given relay precoder. Using this observation, we obtain closed form solutions of the corresponding Karush-Kuhn-Tucker (KKT) system of equations. For each of these solutions, we study the corresponding optimization of the relay precoder. We show that for some of the KKT solutions, a closed form expression for the optimal precoder can be obtained. However, for other solutions, we find necessary conditions that the optimal precoder must satisfy. Finally, for the latter case, we identify a class of precoders that meet the necessary conditions. For each case, an efficient algorithm is developed for obtaining the final pair of input covariance and relay precoder.

This is joint work with Professor Halim Yanikomeroglu, of Carleton University, and is funded by Research In Motion (RIM).

Pietro Belotti, Clemson University
Couenne, an Open-Source solver for non-convex Mixed Integer Nonlinear Optimization

Mixed integer nonlinear programming (MINLP) problems are among the most general and difficult in Optimization, especially if the nonlinear functions expressing the objective or the constraints are also non-convex. Because of their non-convexity, an optimal solution is in general sought using branch-and-bound techniques. These methods recursively partition the feasible set and obtain a lower bound on the optimal solution value by generating convex relaxation of the original problem.

The talk focuses on Couenne (Convex Over- and Under-ENvelopes for Nonlinear Estimation), an Open-Source software package whose development started within a collaboration between Carnegie Mellon University and IBM, and that is part of the Coin-OR initiative. Couenne is a branch-and-bound method which implements several techniques for obtaining tight lower bounds, heuristics for feasible solutions, and procedures for reducing variable bounds. We describe its main features and show how it can be used, extended, and adapted to solve several classes of MINLP problems.

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Alkis Vazacopoulos, FICO
Using Mixed Integer Programming to Solve Sequencing, Scheduling and Packing Problems

Recent advancements in Mixed Integer Programming solvers give us the ability to solve larger and more complex sequencing , scheduling and packing problems. We will demonstrate this fact by showing examples from tournament scheduling, space retail optimization, production scheduling and sequencing in energy applications.