2009 Presentations

Date	Speaker	Presentation Title & File Link
11/18/09	Andrew Conn	A Framework for Mixed-Integer Nonlinear Programs - An Introduction
A.R. Conn, IBM Thomas J. Watson Research Center Mixed integer nonlinear programming is an area of ever increasing importance and is nevertheless significantly under researched - no doubt because it presents many difficult challenges. I will present a basic hybrid framework for mixed-integer nonlinear programming. In one extreme case, the method becomes the branch-and-bound approach, where a nonlinear optimization problem is solved in each node of the enumeration tree, and in the other extreme it reduces to an outer approximation algorithm, which alternates between the solution of a nonlinear optimization problem and a mixed-integer linear program. In the last part of the talk, I will present numerical results for some of the methods introduced before. This work results from an on-going research collaboration between IBM and Carnegie Mellon University.
10/15/09	Reidar Bratvold	Bayesian Decision Networks - A Powerful Tool for Supporting and Valuing Decision-Making in Integrated Operations
R. Bratvold, University of Stavanger Today's decision makers in the oil and gas industry are faced with remarkable new technologies, huge amounts of information to help them make high-quality decisions, and the ability to share information at unprecedented speeds and quantities. In this talk we will cover two related topics. 1. The use of Bayesian Decision Networks (BDN) to structure drilling decision problems, show the relevance between the key uncertainties and decisions, and consistently update information with the arrival of new data. The BDN provides a methodology for robust (in both the conceptual framework and algorithm performance) decision support in drilling operations. 2. The use of a decision analytic approach to assess the value of Integrated operations (IO), and/or Smart Fields applications. A central element in the valuation is the capturing of the interplay between information revelation and decision making over time and the approach will not only provide a value of IO for the specific decision at hand but will also include a policy map indicating the value add of each IO component.
09/23/09	Honggang Wang	Retrospective Optimization for Discrete Stochastic Systems
H. Wang, Stanford University Optimizing a stochastic system with a set of discrete design variables x is an important and difficult problem arising widely in various fields of operations research and the management sciences. Much research has originated methods for discrete stochastic optimization problems in which the objective function g is defined by a Monte Carlo simulation oracle. The function g is implicit in the oracle, i.e., for any design point x the objective value g(x) can be obtained only asymptotically by averaging over many calls to the oracle. Our interest is in integer decision variables x when the objective function g is smooth, in the sense that if "viewed from a distance" the discreteness is negligible. Such applications arise, for example, when the decision variables are inventory reorder points and quantities, numbers of machines, numbers of stock options, or staffing levels. Such smoothness implies that a local search on g can be successful in finding a good solution. Many global random search methods also could be used for such problems, but their generality makes them inefficient compared to local-search approaches. We propose a family of simulation-based retrospective optimization algorithms for large-scale discrete stochastic systems via piecewise-linear interpolation. With a simplicial linear interpolation we create a continuous response surface for a discrete feasible region. A retrospective framework generates a sequence of deterministic sample-path problems that can be solved using deterministic nonlinear optimization techniques. Numerical experiments show that our method finds good estimates of optimal solutions for inventory control and transportation and scheduling systems, significantly faster than other state-of-the-art schemes. Some examples, including well placement optimization problems, are discussed in the talk.
7/30/09	Oliver Kramer	Advanced Evolutionary Computation for Global Optimization
O. Kramer, TU Dortmund Evolutionary computation comprises stochastic methods for global optimization, i.e., optimization problems with multiple local optima. They are biologically inspired and imitate principles that can be observed in natural evolution like mutation, crossover and selection. Evolutionary methods are direct search methods, i.e., they can be applied in solution spaces where no derivatives are available. The advanced methods are designed for special solution space conditions such as multimodal, constrained and multi-objective fitness landscapes. The talk puts the focus on covariance matrix self-adaptation evolution strategies that are based on the automatic control of step sizes to adapt to local solution space conditions. Many problems are subject to constraints that make a hard problem even harder. A constraint handling method for covariance matrix self-adaptation is presented that is based on estimating meta-models of the constraint boundary with machine learning methods. If multiple conflictive objectives have to be optimized at the same time, evolutionary multi-objective optimization methods deliver the Pareto set of balanced solutions. The talk introduces rake selection, a new method that approximates uniformly distributed solutions on the Pareto-front. Perspectives are shown where these stochastic methods can solve optimization problems in the oil and gas industry.
04/15/09	David Cameron	Optimization of Carbon Dioxide Sequestration in Deep Brine Aquifers
D.A. Cameron and L.J. Durlofsky, Stanford University One way to reduce anthropogenic carbon emissions may be to capture carbon dioxide produced in power plants and store it in geological structures. This research treats the injection of CO2 in deep brine aquifers as an optimal control problem, for which, the injection parameters are controlled with respect to maximizing safety and minimizing cost. The optimizations are carried out on a 3D, synthetic, heterogeneous model. Two possible objective functions are considered: 1) the fraction of mobile CO2 after equilibration; and 2) the fraction of CO2 stored immediately underneath the cap-rock after equilibration. We compare several low-level optimization algorithms including general pattern search (GPS), mesh-adaptive pattern search (MADS) and some simple gradient methods. Preliminary results indicate that optimized solutions perform significantly better than if one were to inject an equal volume into each well. Furthermore, we have found that GPS is the best method tested, and that large improvements can be made to the optimal solution if more than one update to the control is used.
04/08/09	Jerome Onwunalu	Application of a Particle Swarm Optimization Algorithm for Determining Optimum Well Location and Type
J.E. Onwunalu and L.J. Durlofsky, Stanford University Determining the optimum type and location of new wells is an essential component in the efficient development of oil and gas fields. The optimization problem is, however, demanding due to the potentially high dimension of the search space and the computational requirements associated with function evaluations, which in this case entail full reservoir simulations. In this talk the Particle Swarm Optimization (PSO) algorithm is applied for the determination of optimal well type and location. The PSO algorithm is a stochastic procedure that uses a population of solutions, called particles, which move in the search space. Particle positions are updated iteratively according to particle fitness (objective function value) and position relative to other particles. The general PSO procedure is first discussed, and then the particular variant implemented for well optimization is described. Some examples are shown. These involve vertical, deviated and dual-lateral wells and optimization over single and multiple reservoir realizations. For each case, both the PSO algorithm and the widely used genetic algorithm (GA) are applied to maximize net present value. Multiple runs of both algorithms are performed and the results are averaged in order to achieve meaningful comparisons. It is observed that, on average, PSO outperforms GA in all cases considered, though the relative advantages of PSO vary from case to case. Taken in total these findings are very promising and demonstrate the applicability of PSO for this challenging problem.
03/11/09	Abeeb Awotunde	A Multiresolution Analysis of the Relationship between Spatial Distribution of Reservoir Parameters and Time Distribution of Data Measurements
A. Awotunde and R.N. Horne, Stanford University An important issue in reservoir parameter estimation is to develop computationally efficient and reliable nonlinear regression procedures. We present a multiresolution wavelet approach to estimate spatial distribution of reservoir parameters. By performing the nonlinear least squares procedure completely in the wavelet domain we achieve proper data integration. Wavelet transforms have the ability to reveal important events in any signal or image. Thus we transformed the model space and the data time into spatial wavelet and time wavelet domains and used a thresholding to select a subset of wavelet coefficients from each of the transformed domains. These subsets were subsequently used in the nonlinear regression procedure to estimate the appropriate set of reservoir parameters. We applied the procedure to a radial composite reservoir system to demonstrate the reliability of the approach. The test case reservoir was composed of unknown permeability values distributed in the radial field. The inverse problem was solved to estimate the distributed permeability values by performing the nonlinear least square regression in the wavelet domains (time and space). Results obtained were compared to those obtained from conventional nonlinear regression approach. The time-space wavelet approach proves to be computationally more efficient compared to the conventional approach. By reducing the dimensions of the model and data spaces the model stabilizes the algorithm and gives faster convergence. Significantly, the approach reveals the true number of reservoir parameters that can be appropriately estimated from a given data set.
01/23/09	Juan Luis Fernández Martínez	Particle Swarm: A Powerful Family Of Optimizers For Inversion (Applications in Hydrogeophysics)
J.L. Fernández Martínez, University of Oviedo Geophysical inverse problems are ill-posed: in geoelectrical inverse problems the error function has its minimum in a flat elongated valley or surrounded by many local minima. Local optimization methods give unpredictable results if no prior information is available. Traditionally this has generated mistrust in the use of geophysical inverse methods (equivalence problem in Vertical Electrical Soundings). Stochastic approach of inverse problems consists in shifting attention to the probability of existence of certain interesting subsurface structures instead of "looking for the true model". Also, inverse problems are ill-conditioned and observed data are noisy. Thus, with no regularization methods (priors) these uncertainties are transmitted to the model parameters by the optimization algorithm. Global optimization methods had become a good alternative to sample efficiently the model space. They are very robust since they do not solve the optimization problem. In this seminar I will talk about our research on Particle Swarm Optimization (PSO) to solve efficiently geophysical inverse problems. The PSO algorithm can be physically interpreted as a stochastic damped mass-spring system. This analogy served us to introduce the PSO continuous model and to deduce a whole family of PSO algorithms arising from different discretizations of the PSO continuous model. The performance of these methods can be checked using synthetic functions showing a degree of ill-posedness similar to that found in real problems. Finally, I will be focused on two different low-cost methods in hydrogeophysics: 1) a water intrusion study using Vertical Electrical Soundings (VES), 2) the inversion of SP data in hydrogeophysics.

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