Rigorous Optimization Problem Research Articles

Perspectives on Clustering and Declustering of Earthquakes

Abstract Clustering is a fundamental feature of earthquakes that impacts basic and applied analyses of seismicity. Events included in the existing short-duration instrumental catalogs are concentrated strongly within a very small fraction of the space–time volume, which is highly amplified by activity associated with the largest recorded events. The earthquakes that are included in instrumental catalogs are unlikely to be fully representative of the long-term behavior of regional seismicity. We illustrate this and other aspects of space–time earthquake clustering, and propose a quantitative clustering measure based on the receiver operating characteristic diagram. The proposed approach allows eliminating effects of marginal space and time inhomogeneities related to the geometry of the fault network and regionwide changes in earthquake rates, and quantifying coupled space–time variations that include aftershocks, swarms, and other forms of clusters. The proposed measure is used to quantify and compare earthquake clustering in southern California, western United States, central and eastern United States, Alaska, Japan, and epidemic-type aftershock sequence model results. All examined cases show a high degree of coupled space–time clustering, with the marginal space clustering dominating the marginal time clustering. Declustering earthquake catalogs can help clarify long-term aspects of regional seismicity and increase the signal-to-noise ratio of effects that are subtler than the strong clustering signatures. We illustrate how the high coupled space–time clustering can be decreased or removed using a data-adaptive parsimonious nearest-neighbor declustering approach, and emphasize basic unresolved issues on the proper outcome and quality metrics of declustering. At present, declustering remains an exploratory tool, rather than a rigorous optimization problem, and selecting an appropriate declustering method should depend on the data and problem at hand.

An optimization scheme for routing and scheduling of concurrent user requests in wireless mesh networks

Multiple-radio multiple-channel (MRMC) wireless mesh networks (WMNs) have been increasingly used to construct the wireless backbone infrastructure for ubiquitous Internet access. These networks often face a challenge to satisfy multiple concurrent user requests for data transfers between different source-destination pairs with various performance requirements.We construct analytical network models and formulate such multi-pair data transfers as a rigorous optimization problem. We propose an optimization scheme for cooperative routing and scheduling together with channel assignment to establish a network path for each request through the selection of appropriate link patterns. The performance superiority of the proposed optimization scheme over existing methods is illustrated by simulation-based experiments in various types of mesh networks.

Modeling and geometry optimization of photochemical reactors: Single- and multi-lamp reactors for UV–H2O2 AOP systems

This paper deals with the modeling and optimization of a photochemical reactor for the production of hydroxyl radicals. These radicals can be used in advanced oxidation processes for water purification. The UV-lamps used in the photochemical reactor lead to a relatively high energy and operating cost. Minimization of these costs is possible via a model-based optimization of the reactor geometry. First, a model is built taking into account the reaction kinetics, the reactor geometry and the radiation intensity distribution in the reactor. Afterwards, two different configurations of photochemical reactors are optimized. The first modeled reactor configuration is a single-lamp reactor and consists of a cylindrical UV-lamp that is present inside a quartz sleeve, outside of which the water flows between it and the external reactor wall (annular channel reactor). A rigorous optimization problem is formulated consisting of the calculation of the optimal reactor geometry (length and radius) in such a way that, for a given reactor volume and a given flow rate of the water to be treated, the mean outlet concentration of an organic pollutant is minimized. By solving this optimization problem, it has been shown that an optimal reactor length exists. If the absorption coefficient of the water or the reaction rate constant increases, the optimal reactor length increases as well. The second modeled reactor configuration is similar to the first one but now contains multiple lamps positioned symmetrically in a circular pattern (i.e. multi-lamp reactor). The optimization problem consists of the calculation of the optimal lamp position inside the reactor in such a way that the mean outlet concentration of an organic pollutant is minimized. The lamp position is given by the radial distance between the centers of the reactor and a lamp. Again a well-posed optimization problem is obtained and an optimal lamp position exists. If the number of lamps or the reaction rate constant increases or the absorption coefficient of the water decreases, the optimal distance between the centers of the reactor and the lamp increases.

A two-layer architecture for economically optimal process control and operation

A two-layer architecture for dynamic real-time optimization (or nonlinear modelpredictive control (NMPC) with an economic objective) is presented, where the solution of the dynamic optimization problem is computed on two time-scales. On the upper layer, a rigorous optimization problem is solved with an economic objective function at a slow time-scale, which captures slow trends in process uncertainties. On the lower layer, a fast neighboring-extremal controller is tracking the trajectory in order to deal with fast disturbances acting on the process. Compared to a single-layer architecture, the two-layer architecture is able to address control systems with complex models leading to high computational load, since the rigorous optimization problem can be solved at a slower rate than the process sampling time. Furthermore, solving a new rigorous optimization problem is not necessary at each sampling time if the process has rather slow dynamics compared to the disturbance dynamics. The two-layer control strategy is illustrated with a simulated case study of an industrial polymerization process.

Neighboring-extremal updates for nonlinear model-predictive control and dynamic real-time optimization

Nonlinear model-predictive control (NMPC) and dynamic real-time optimization (DRTO) lead to a substantial improvement of the operation of complex nonlinear processes. Whereas the focus in NMPC is primarily on control performance by minimizing the deviation from a given set-point, the objective in DRTO is to achieve a profitable and flexible operation adapted to changing market conditions and process uncertainties by employing an economic optimization criterion. A method for solving dynamic optimization problems based on neighboring-extremal updates suitable for applications in NMPC and DRTO is presented in this paper. If process operation is affected by small perturbations, efficient techniques for updating the nominal trajectories based on parametric sensitivities can be applied [J. Kadam, W. Marquardt, Sensitivity-based solution updates in closed-loop dynamic optimization, in: Proceedings of the DYCOPS 7 Conference, Cambridge, USA, 2004]; these updates do not require the solution of the rigorous optimization problem but rely on first and second-order sensitivities computed by composite adjoints. However for larger perturbations and strong nonlinearities, the fast updates obtained by the neighboring-extremal solutions are not sufficiently accurate, and the solution of the nonlinear optimization problem requires further iterations with updated sensitivities to give a feasible and optimal solution. The application of the method to a simulated semi-batch reactor demonstrates its capabilities. The presented method is discussed in comparison to other methods in the literature.

An Efficient Strategy for Real-Time Dynamic Optimization based on Parametric Sensitivities

The optimal operation of chemical processes is challenged by frequent transitions and by the influence of process or model uncertainties. Under uncertainties, it is necessary to quickly update the optimal trajectories in order to avoid the violation of constraints and the deterioration of the economic performance of the process. Although an economically optimal operation can be ensured by online dynamic optimization, the high computational load of dynamic optimization associated with nonlinear and complex models is often prohibitive in real-time applications. To reduce the computational time required for online computation of the optimal trajectories in the neighborhood of the optimal solution under uncertainty, different strategies have been explored recently. If the operation is affected by small perturbations, efficient techniques for updating the nominal trajectories based on parametric sensitivities are applied, which do not require the solution of the rigorous optimization problem. However for larger perturbations, the linear updates obtained by the neighboring extremal solutions are not sufficiently accurate, and the solution of the nonlinear optimization problem requires further iterations with updated sensitivities to give a feasible and optimal solution. In this work, the sensitivity-based approach of Kadam and Marquardt (2004) is extended with a fast computational method for second-order derivatives based on composite adjoints. The application of the method to a simulated semi-batch reactor demonstrates that fast and optimal trajectory updates can be obtained.

Budget constrained planning to optimize power system reliability

De-regulation and re-regulation are forcing electric utilities to become more cost conscious. At some utilities, this has manifested itself in drastically reduced capital budgets. At the same time, utilities are under great pressure to maintain (and even improve) system reliability. With reduced budgets, it becomes necessary to establish accept/reject criteria that best allocates the budget while obtaining the highest possible system reliability. This paper presents a Budget Constrained Planning method to handle this situation. This method formulates project approvals as a rigorous optimization problem and uses a marginal cost/benefit approach similar to economic dispatch. Budget Constrained Planning is applied to the 1999 discretionary projects fund at Ameren Corporation and results are discussed.