This paper describes an extension to the optimal power use surface (OPUS) methodology, which consists of applying a metaheuristic post-optimization process after a network has been designed through the OPUS algorithm. Four different types of metaheuristics were tested in this study. The OPUS methodology focuses on the setting up of efficient ways in which energy is dissipated and flow is distributed, thereby obtaining deterministic design after a few iterations. On the other hand, the stochastic techniques used for the post-optimization step mimic different phenomena, usually requiring several iterations. The proposed methodology is tested on four networks; three of these are benchmark problems. When compared to the results obtained through other methodologies, this algorithm stands out for allowing designs with constructive costs very close to the lowest found in other investigations. However, when compared to the results obtained through the OPUS algorithm alone, this approach reduces the capital cost of the network by a very small percentage while increasing the number of iterations required. This extension to the OPUS methodology proves that following hydraulic principles allows near-optimal results to be obtained, whose improvement demands a considerable number of iterations, providing minimum benefit as the reduction in cost is only 1% at most.
In this paper we show that Diophantine problem in solvable Baumslag-Solitar groups BS(1, k) and in wreath products A ≀ Z, where A is a finitely generated abelian group and Z is an infinite cyclic group, is decidable.
In recent years, iterative computational techniques have been considered as the most effective methods to tackle the problem of Water Distribution System (WDS) minimum-cost design. Given their stochastic nature, these approaches involve a large number of hydraulic simulations in order to obtain suitable results. Herein, a WDS design methodology based entirely on hydraulic principles is presented. This methodology, named Optimal Power Use Surface (OPUS), focuses on both reaching low-cost designs and diminishing the number of hydraulic executions (iterations), by establishing efficient ways in which energy is dissipated and flow is distributed throughout the system. The algorithm was tested in four well known benchmark networks, previously reported in the literature. OPUS proved that following hydraulic principles is a fair choice to design WDS, showing plenty of potential in other water distribution mathematical modeling applications and offering an alternative for the extensive search process undertaken by metaheuristics.
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