Theoretical Framework for Comparing Several Stochastic Optimization Approaches

Spall, James C.; Hill, S.D.; Stark, D.

doi:10.1007/1-84628-095-8_3

Cited by 30 publications

(23 citation statements)

References 25 publications

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“…The approach developed in our model is based on stochastic optimization (Spall et al 2006) with application to variable rainfall measurement errors and relevant evacuation thresholds, which has barely been applied to landslide problems so far. In landslide research, it is therefore rather uncommon to link measured environmental parameters such as rainfall with landslide consequences and damage in one integrated model.…”

Section: Discussion and Implications For Landslide Ewsmentioning

confidence: 99%

Implementation and integrated numerical modeling of a landslide early warning system: a pilot study in Colombia

et al. 2009

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Landslide early warning systems (EWS) are an important tool to reduce landslide risks, especially where the potential for structural protection measures is limited. However, design, implementation, and successful operation of a landslide EWS is complex and has not been achieved in many cases. Critical problems are uncertainties related to landslide triggering conditions, successful implementation of emergency protocols, and the response of the local population. We describe here the recent implementation of a landslide EWS for the Combeima valley in Colombia, a region particularly affected by landslide hazards. As in many other cases, an insufficient basis of data (rainfall, soil measurements, landslide event record) and related uncertainties represent a difficult complication. To be able to better assess the influence of the different EWS components, we developed a numerical model that simulates the EWS in a simplified yet integrated way. The results show that the expected landslide-induced losses depend nearly exponentially on the errors in precipitation measurements. Stochastic optimization furthermore suggests an increasing adjustment of the rainfall landslide-triggering threshold for an increasing observation error. These modeling studies are a first step toward a more generic and integrated approach that bears important potential for substantial improvements in design and operation of a landslide EWS.

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Section: Discussion and Implications For Landslide Ewsmentioning

confidence: 99%

Implementation and integrated numerical modeling of a landslide early warning system: a pilot study in Colombia

et al. 2009

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“…. , kp = { ki } i=1: p from a distribution with bounded inverse expectation [11,19,23] (for example, a Bernoulli random number) in the search space at each iteration and (2) finding an ascent direction (using an approximate gradient estimate) by computing a two-sided simultaneous perturbation using the selected random direction. Given the random choice of direction k , it is natural to expect that a step in the selected direction does not necessarily result in an improvement of the objective function; meaningful computational saving over the finite-difference perturbation would only be achieved if very few random directions (relative to number of decision variables) are needed to yield marked improvements in the objective function.…”

Section: Objective Functionmentioning

confidence: 99%

“…In [16], a coordinate descent approach was developed for large-scale optimization with SPSA algorithm. The SPSA algorithm has also been compared with other stochastic search methods [23]. An important result is that [19,22,23] for a pdimensional problem under reasonably general conditions, the SPSA algorithm reaches the same level of accuracy as the finite-difference stochastic approximation method for a given number of iterations; however, SPSA uses p times fewer function evaluations at each iteration.…”

Section: Introductionmentioning

confidence: 99%

“…This implies that, overall, a properly generated random perturbation of all p variables is as effective as approximating the p partial derivatives one at a time. In [22,23], SPSA is compared with several state-of-theart optimization methods such as simulated annealing and genetic algorithm, where it is shown to be quite competitive (and possibly more efficient) in terms of computational time for the same solution accuracy.…”

Section: Introductionmentioning

confidence: 99%

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A simultaneous perturbation stochastic approximation algorithm for coupled well placement and control optimization under geologic uncertainty

2012

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Development of subsurface energy and environmental resources can be improved by tuning important decision variables such as well locations and operating rates to optimize a desired performance metric. Optimal well locations in a discretized reservoir model are typically identified by solving an integer programming problem while identification of optimal well settings (controls) is formulated as a continuous optimization problem. In general, however, the decision variables in field development optimization can include many design parameters such as the number, type, location, short-term and long-term operational settings (controls), and drilling schedule of the wells. In addition to the large number of decision variables, field optimization problems are further complicated by the existing technical and physical constraints as well as the uncertainty in describing heterogeneous properties of geologic formations. In this paper, we consider simultaneous optimization of well locations and dynamic rate allocations under geologic uncertainty using a variant of the simultaneous perturbation and stochastic approximation (SPSA). In addition, by taking advantage of the robustness of SPSA against errors in calculating the cost function, we develop an efficient field development optimization under geologic uncertainty, where an ensemble of models are used to describe important flow and transport reservoir properties (e.g., permeability and porosity). We use several numerical experiments, including a channel layer of the SPE10 model and the three-dimensional PUNQ-S3 reservoir, to illustrate the performance improvement that can be achieved by solving a combined well placement and control optimization using the SPSA algorithm under known and uncertain reservoir model assumptions.

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“…Simultaneous Perturbation Stochastic Approximation (SPSA) is an attractive choice for the optimiser: it is capable of evading local minima due to its stochastic nature and, when adapted for our framework, is orders of magnitude more efficient [13] than the traditional stochastic algorithms. Moreover, while in traditional gradient-based methods the number of function evaluations required to estimate the gradient at a point grows linearly with the dimensionality of the space, SPSA offers independence of the number of function evaluations at each iteration on the dimensionality of the space.…”

Section: Stochastic Optimisationmentioning

confidence: 99%

An efficient stochastic approach to groupwise non-rigid image registration

Sidorov

Richmond

Marshall

2009

2009 IEEE Conference on Computer Vision and Pattern Recognition

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The groupwise approach to non-rigid image registration, solving the dense correspondence problem, has recently been shown to be a useful tool in many applications, including medical imaging, automatic construction of statistical models of appearance and analysis of facial dynamics. Such an approach overcomes limitations of traditional pairwise methods but at a cost of having to search for the solution (optimal registration) in a space of much higher dimensionality which grows rapidly with the number of examples (images) being registered. Techniques to overcome this dimensionality problem have not been addressed sufficiently in the groupwise registration literature.In this paper, we propose a novel, fast and reliable, fully unsupervised stochastic algorithm to search for optimal groupwise dense correspondence in large sets of unmarked images. The efficiency of our approach stems from novel dimensionality reduction techniques specific to the problem of groupwise image registration and from comparative insensitivity of the adopted optimisation scheme (Simultaneous Perturbation Stochastic Approximation (SPSA)) to the high dimensionality of the search space. Additionally, our algorithm is formulated in way readily suited to implementation on graphics processing units (GPU).In evaluation of our method we show a high robustness and success rate, fast convergence on various types of test data, including facial images featuring large degrees of both inter-and intra-person variation, and show considerable improvement in terms of accuracy of solution and speed compared to traditional methods.

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Theoretical Framework for Comparing Several Stochastic Optimization Approaches

Cited by 30 publications

References 25 publications

Implementation and integrated numerical modeling of a landslide early warning system: a pilot study in Colombia

Implementation and integrated numerical modeling of a landslide early warning system: a pilot study in Colombia

A simultaneous perturbation stochastic approximation algorithm for coupled well placement and control optimization under geologic uncertainty

An efficient stochastic approach to groupwise non-rigid image registration

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