1,683 research outputs found
Water network operational optimization: Utilizing symmetries in combinatorial problems by dynamic programming
This paper introduces a dynamic programming (DP) approach for solving deterministic combinatorial operational optimization problem of water distribution networks. The implementation of dynamic programming over control domain using permutational symmetries is suggested to replace the state space based DP procedures. To enhance the understanding an application on a ub-network of the water supply and distribution network of the city of Sopron (Hungary) is presented which is sufficiently small to track the (pseudo) state space and approach related quantities
Price decomposition in large-scale stochastic optimal control
We are interested in optimally driving a dynamical system that can be
influenced by exogenous noises. This is generally called a Stochastic Optimal
Control (SOC) problem and the Dynamic Programming (DP) principle is the natural
way of solving it. Unfortunately, DP faces the so-called curse of
dimensionality: the complexity of solving DP equations grows exponentially with
the dimension of the information variable that is sufficient to take optimal
decisions (the state variable). For a large class of SOC problems, which
includes important practical problems, we propose an original way of obtaining
strategies to drive the system. The algorithm we introduce is based on
Lagrangian relaxation, of which the application to decomposition is well-known
in the deterministic framework. However, its application to such closed-loop
problems is not straightforward and an additional statistical approximation
concerning the dual process is needed. We give a convergence proof, that
derives directly from classical results concerning duality in optimization, and
enlghten the error made by our approximation. Numerical results are also
provided, on a large-scale SOC problem. This idea extends the original DADP
algorithm that was presented by Barty, Carpentier and Girardeau (2010)
Modeling water resources management at the basin level: review and future directions
Water quality / Water resources development / Agricultural production / River basin development / Mathematical models / Simulation models / Water allocation / Policy / Economic aspects / Hydrology / Reservoir operation / Groundwater management / Drainage / Conjunctive use / Surface water / GIS / Decision support systems / Optimization methods / Water supply
Representation Of Uncertainty And Corridor Dp For Hydropower Optimization
This thesis focuses on optimization techniques for multi-reservoir hydropower systems operation, with a particular concern with the representation and impact of uncertainty. The thesis reports on three research investigations: 1) examination of the impact of uncertainty representations, 2) efficient solution methods for multi-reservoir stochastic dynamic programming (SDP) models, and 3) diagnostic analyses for hydropower system operation. The first investigation explores the value of sophistication in the representation of forecast and inflow uncertainty in stochastic hydropower optimization models using a sampling SDP (SSDP) model framework. SSDP models with different uncertainty representation ranging in sophistication from simple deterministic to complex dynamic stochastic models are employed when optimize a single reservoir systems [similar to Faber and Stedinger, 2001]. The effect of uncertainty representation on simulated system performance is examined with varying storage and powerhouse capacity, and with random or mean energy prices. In many cases very simple uncertainty models perform as well as more complex ones, but not always. The second investigation develops a new and efficient algorithm for solving multi-reservoir SDP models: Corridor SDP. Rather than employing a uniform grid across the entire state space, Corridor SDP efficiently concentrates points in where the system is likely to visit, as determined by historical operations or simulation. Radial basis functions (RBFs) are used for interpolation. A greedy algorithm places points where they are needed to achieve a good approximation. In a four-reservoir test case, Corridor DP achieves the same accuracy as spline-DP and linear-DP with approximately 1/10 and 1/1100 the number of discrete points, respectively. When local curvature is more pronounced (due to minimum-flow constraints), Corridor DP achieves the same accuracy as spline-DP and linear-DP with approximately 1/30 and 1/215 the number of points, respectively. The third investigation explores three diagnostic approaches for analyzing hydropower system operation. First, several simple diagnostic statistics describe reservoir volume and powerhouse capacity in units of time, allowing scale-invariant comparisons and classification of different reservoir systems and their operation. Second, a regression analysis using optimal storage/release sequences identifies the most useful hydrologic state variables . Finally spectral density estimation identifies critical time scales for operation for several single-reservoir systems considering mean and random energy prices. Deregulation of energy markets has made optimization of hydropower operations an active concern. Another development is publication of Extended Streamflow Forecasts (ESP) by the National Weather Service (NWS) and others to describe flow forecasts and their precision; the multivariate Sampling SDP models employed here are appropriately structured to incorporate such information in operational hydropower decisions. This research contributes to our ability to structure and build effective hydropower optimization models
Research and Education in Computational Science and Engineering
Over the past two decades the field of computational science and engineering
(CSE) has penetrated both basic and applied research in academia, industry, and
laboratories to advance discovery, optimize systems, support decision-makers,
and educate the scientific and engineering workforce. Informed by centuries of
theory and experiment, CSE performs computational experiments to answer
questions that neither theory nor experiment alone is equipped to answer. CSE
provides scientists and engineers of all persuasions with algorithmic
inventions and software systems that transcend disciplines and scales. Carried
on a wave of digital technology, CSE brings the power of parallelism to bear on
troves of data. Mathematics-based advanced computing has become a prevalent
means of discovery and innovation in essentially all areas of science,
engineering, technology, and society; and the CSE community is at the core of
this transformation. However, a combination of disruptive
developments---including the architectural complexity of extreme-scale
computing, the data revolution that engulfs the planet, and the specialization
required to follow the applications to new frontiers---is redefining the scope
and reach of the CSE endeavor. This report describes the rapid expansion of CSE
and the challenges to sustaining its bold advances. The report also presents
strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie
Approximate stochastic dynamic programming for hydroelectric production planning
This paper presents a novel approach for approximate stochastic dynamic programming (ASDP) over a continuous state space when the optimization phase has a near-convex structure. The approach entails a simplicial partitioning of the state space. Bounds on the true value function are used to refine the partition. We also provide analytic formulae for the computation of the expectation of the value function in the “uni-basin” case where natural inflows are strongly correlated. The approach is experimented on several configurations of hydro-energy systems. It is also tested against actual industrial data
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