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Reviewing the effectiveness of GPU power when used for water network optimization problems
Abstract
The computational effectiveness can be achieved with various well-known parallel technologies like clusters (distributed computing through a group of linked computers) and grids (loosely coupled and geographically dispersed computer network). Because of their expensive set-up costs, availability or universality to run the present code (distributed software license costs) it can not be used by various companies/institutions. Another possibility to parallelize the calculations and therefore to get faster results is to utilize a single PC's GPU (Graphical Processing Unit) card as those set-ups are already in use for several engineering tasks. Visual effects community has been employed the GPU (Graphical Processing Unit) power for various computationally expensive calculations for some years. GPU power as an alternative to mainstream CPU (Central Processing Unit) has been available quite a long time thanks to well-known graphics board manufactures (like NVIDIA, AMD) but just recently the curiosity to use it for everyday scientific calculations has been arisen. The capability to use for example single GPU's 128 processing cores instead just 4 or 8 CPU cores should make the point - we get faster results to our water network optimization problems even in a consumer desktop (or laptop) computer. The increase in calculations time does not come without recoding our algorithms. The scope of this article is to search the possibilities how the present optimization code can be transferred to use endorsed GPU power. For that purpose the NVIDIA GPU parallel language CUDA (Compute Unified Device Architecture) will be used that supports developers to program also on MATLAB (using some wrapper or add-on). Starting with simple engineering problems and test-procedures, the final goal is to enhance a global optimization code called SCEM-UA (Shuffled Complex Evolution Metropolis algorithm) such that it utilizes also GPU power during water network optimization run. All tests are carried out with NVIDIA Quadro FX 3700M graphics board which performance is compared to Intel Core 2 Duo T9400 processor.
... More recently, efforts by Puust et al. (2011) and Crous et al. (2012) to speed up hydraulic modeling have considered solving the system hydraulics on parallel architectures and using graphical processing units, both of which are now commonly found in personal computers. Not surprisingly, parallelization based on the GGA has been shown to speed up simulations for large networks (e.g., Guidolin et al. 2011;Wu and Lee 2011). ...
The forest core partitioning algorithm (FCPA) and the fast graph matrix partitioning algorithm (GMPA) have been used to improve efficiency in the determination of the steady-state heads and flows of water distribution systems that have large, complex network graphs. In this paper, a single framework for the FCPA and the GMPA is used to extend their application from demand dependent models to pressure dependent models (PDMs). The PDM topological minor (TM) is characterized, important properties of its key matrices are identified, and efficient evaluation schemes for the key matrices are presented. The TM captures the network's most important characteristics: It has exactly the same number of loops as the full network, and the flows and heads of those elements not in the TM depend linearly on those of the TM. The inverse of the TM's Schur complement is shown to be the top, left block of the inverse of the full system Jacobian's Schur complement, thereby providing information about the system's essential behavior more economically than is otherwise possible. The new results are applicable to other nonlinear network problems, such as in gas, district heating, and electrical distribution.
... GPUs are highly parallel and very e cient in solving matrix equations. [208] The downside with the approach is that it is time-consuming to move the matrices between the computer's main memory and GPU, so that any bene ts are lost if the network is not very large. ...
A novel, general framework for performing whole-cost optimization of water production and distribution in real-time was developed in this dissertation. Optimization enables significant savings in energy and chemical costs.
Optimization resulted in near optimal settings for all pump, valve and source stations, and optimal frequencies for all pumps in the water supply system as a function of time for the next 24 hours in near real-time.
This dissertation developed a novel way to formulate the design variables of the optimization problem in order to minimize the size of the search space, a novel way to pre-optimize operation of pump batteries, a novel way to model pressure or flow controlled variable-speed driven pumping and a novel method to model complex control strategies in the hydraulic simulator.
The optimization algorithm used is a modified version of greedy, meta-heuristic, single-solution Hybrid Discrete Dynamically Dimensioned Search (HD-DDS), that has not been applied in operational optimization of water supply systems before.
According to the author's review of previous studies, this research is the first where real-time operative optimization of a large-scale water supply system (WSS) is performed using a non-simplified and non-surrogate model covering all pipes in the system, and where the raw water production, conveyance and treatment are also included in the model and optimization.
In the case study (Tampere Water) the proposed optimization framework resulted in 20 % savings in the production and distribution costs, while ensuring better quality of service than before. Real-time aspect is ensured by the optimization run taking about two hours of computation time.
... Electrical energy is mainly consumed by the pump units [2]. Therefore, a number of solutions have been implemented to optimize the operation of pumping stations of different levels [3,4]. In addition to optimization of the pump unit selection, optimized systems for their control have been developed as well [5]. ...
... In addition, recent results show that the SC+NR method may be significantly improved for large systems using the nested dissection node reordering method (Giustolisi et al., 2011). Finally, in recent years (Puust et al., 2011;Crous et al., 2012) efforts to speed up hydraulic modelling have looked at solving the system hydraulics in parallel on the multiple processors now common in personal computers and graphical processing units (GPUs). Parallelisation based on Todini's global gradient algorithm (GGA) has been shown to speed up simulations for large networks (Guidolin et al. 2011;Wu and Lee 2011). ...
Hydraulic network software has to solve a set of linear equations repeatedly in an iterative process making them computationally intensive for large systems. The objective of this study was to restructure the Porteau hydraulic freeware by using parallel computational techniques. The method used consists of comparing two linear solver algorithms, a direct Cholesky kind method with nested dissection renumbering and an indirect preconditioned Conjugate Gradient. A message-passing interface C++ tool called from Java is used for the parallelism. Numerical tests and experimental performance curves on networks on medium and large sizes confirm the computational time decreases for systems with more than 4,500 nodes.
Keywords: Graphics Processing Units (GPUs) are in the process of becoming a major source of computational power for numerical applications. Originally designed for application of time-consuming graphics operations, GPUs are stream processors that implement the SIMD paradigm. The true degree of parallelism of GPUs is often hidden from the user, making programming even more flexible and convenient. In this chapter we survey Genetic Programming methods currently ported to GPUs. graphics processing units, parallel processing 1.