Mathematical functions describe virtual 'n' dimensional worlds exhibiting the most strange topology one can imagine. To find optimum points means to climb the highest mountains of these fantasy realms, taking ...
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Mathematical functions describe virtual 'n' dimensional worlds exhibiting the most strange topology one can imagine. To find optimum points means to climb the highest mountains of these fantasy realms, taking care by not being deceived by false maximums. Usually, inside these kingdoms, there are forbidden zones places that must be avoided. Most of the times one become lost inside these prohibited territories, even without noting it. The search for good and fast algorithms to guide the traveler in his journey toward the pot of gold hidden in these heights tells a never ending story where, everyday, a new record is established. Like in a Olympic game, the yesterday impossible is inevitably beaten by some ignominious ignorant that doesn't know that such a record could not be overthrown. This paper tells the story of this search and suggests some approaches to enhance the performance of nowadays optimization algorithms.
For settle the divergence problem of ill-condition system, traditional power flow calculation in polar coordinates can be transformed into a nonlinear programming model. It is a convenient way to judge whether the gen...
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ISBN:
(纸本)9781424419050
For settle the divergence problem of ill-condition system, traditional power flow calculation in polar coordinates can be transformed into a nonlinear programming model. It is a convenient way to judge whether the general power flow equations have feasible solutions or not according to the value of target function. Getting the correction equations by Newton method, LDCT decomposition method is used to solve it. And the coefficient matrix of correct equation is reordered by using AMD reordering algorithm, thus the fill-in elements in LDLT decomposition is reduced significantly, which improves the calculating speed considerably. Proposed module and algorithm possess simplifying structure and can be implement or program easily with a novel vectorization expression. The adaptability and maintainability are also improved in this mode. Numerical simulations on test systems ranging in size from 118 to 1047 buses validate the correctness of the proposed model and method.
In this paper, a heap-based optimizer algorithm with chaotic search has been presented for the global solution of nonlinear programming problems. Heap-based optimizer (HBO) is a modern human social behavior-influenced...
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In this paper, a heap-based optimizer algorithm with chaotic search has been presented for the global solution of nonlinear programming problems. Heap-based optimizer (HBO) is a modern human social behavior-influenced algorithm that has been presented as an effective method to solve nonlinear programming problems. One of the difficulties that faces HBO is that it falls into locally optimal solutions and does not reach the global solution. To recompense the disadvantages of such modern algorithm, we integrate a heap-based optimizer with a chaotic search to reach the global optimization for nonlinear programming problems. The proposed algorithm displays the advantages of both modern techniques. The robustness of the proposed algorithm is inspected on a wide scale of different 42 problems including unimodal, multi-modal test problems, and CEC-C06 2019 benchmark problems. The comprehensive results have shown that the proposed algorithm effectively deals with nonlinear programming problems compared with 11 highly cited algorithms in addressing the tasks of optimization. As well as the rapid performance of the proposed algorithm in treating nonlinear programming problems has been proved as the proposed algorithm has taken less time to find the global solution.
Quadratic programming sequences must be solved to obtain a search direction by recursive quadratic algorithm for general nonlinear programming. Then the search can be one dimensional along the direction. The objective...
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Quadratic programming sequences must be solved to obtain a search direction by recursive quadratic algorithm for general nonlinear programming. Then the search can be one dimensional along the direction. The objective function of the one-dimensional search given in reference [1] is only suitable for equality constrains. The authors presented a new objective function for the one-dimensional search in the iterative quardratic programming, which is suitable for both equality and inequality constraints. After described how to construct such an objective function and the steps to realize the algorithm, the authors also proved the global convergence property of the algorithm and its local superlinear convergence rate under certain conditions, which theoretically ensure the realization of the algorithm on a computer.
In this paper, we consider the optimal operations of a thermal system for heat source and air conditioning system with a thermal storage tank using nonlinear programming. Firstly, we develop the mathematical model of ...
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In this paper, we consider the optimal operations of a thermal system for heat source and air conditioning system with a thermal storage tank using nonlinear programming. Firstly, we develop the mathematical model of the system components by applying the energy and mass balance principles. Secondly, the static balance of the system model is validated by the operational data. Thirdly, by applying the nonlinear programming method, IPOPT (Interior Point OPTimizer), to the mathematical model, we show the optimal operations of a thermal system under variable conditions of chilled water temperature, such as the number of person, heat generating equipment, outdoor and indoor air conditions. Finally, dynamic simulation results showed that, the variable set points of the chilled water temperature for thermal storage tank have an effect on reducing the running cost of a day. ? 2021 Elsevier Ltd. All rights reserved.
Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlin...
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Numerical simulation of latent heat thermal energy storage (LHTES) systems plays a fundamental role in studying the physical process and guiding the engineering design. Discretization of the PDEs describing the nonlinear solidification/melting process of phase change materials (PCMs) leads to a large-scale complex dynamics system, where the system behavior depends on a set of parameters. In a design setting, repeated model evaluations are required over the set of parameters results in significant computational burden. In this paper, an explicit analytic solution was built for the propagation of the solidification front in a cylindrical coordinate. The analytic solution approach is further employed to develop a low computational reduced model (RM) as a module for a shell-and-tube based LHTES heat exchanger. The levelized Cost of Energy (LCOE) is used as a design metric and the RM model is used to apply system-level constraints in the nonlinear programming formulation that facilitates efficient global optimal design of the PCM properties, flow conditions and tube geometries. The use of LCOE as the design metric prevents over design of the heat transfer rate and also establishes a fair ground for evaluation of different thermal storage technologies and their integrated applications with other systems. Optimal results showed that a higher effectiveness results in a higher LCOE;the velocity of the HTF and the length of the channel are highly correlated with each other;both larger PCM latent energy and conductivity result in lower LCOE. (C) 2021 Elsevier Ltd. All rights reserved.
As the development of the electronic information industry, the application range of the integrated circuit becomes wider and advances in its precision have been made gradually. With higher demands for functional requi...
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As the development of the electronic information industry, the application range of the integrated circuit becomes wider and advances in its precision have been made gradually. With higher demands for functional requirements, it is hard for the traditional integrated circuit to meet the actual use demands, therefore the stereoscopic integrated circuit is born. Different distributions of stereoscopic integrated circuit have different capabilities. Based on the perspective of the mathematical nonlinear programming, this paper carries out its research into the distribution of stereoscopic integrated circuit from three aspects, such as the performance prediction of three-dimensional circuits, power consumption distribution and thermal analysis and distribution adjustment, which provides theory references for the development of the stereoscopic integrated circuit.
A constrained nonlinear programming method is proposed for designing orthogonal waveforms applied to multiple input multiple output (MIMO) radar systems. The designed orthogonal waveforms are phase-coded signals with ...
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A constrained nonlinear programming method is proposed for designing orthogonal waveforms applied to multiple input multiple output (MIMO) radar systems. The designed orthogonal waveforms are phase-coded signals with a uniform amplitude and arbitrary phases. The optimal orthogonal waveforms have lower auto-correlation peak sidelobe levels (APSL) and lower peak cross-correlation levels (PCCL), compared with those of other methods. Additionally, the relationships among APSL, PCCL and the size of the orthogonal waveforms are studied via numerical experiments.
Disassembly sequence planning at the early conceptual stage of design leads to enormous benefits including simplification of products, lower assembly and disassembly costs, and design modifications which result in inc...
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Disassembly sequence planning at the early conceptual stage of design leads to enormous benefits including simplification of products, lower assembly and disassembly costs, and design modifications which result in increased potential profitability of end-of-life salvaging operations. However, in the early design stage, determining the best disassembly sequence is challenging. First, the required information is not readily available and very time-consuming to gather. In addition, the best solution is sometimes counterintuitive, even to those with experience and expertise in disassembly procedures. Integrating analytical models with immersive computing technology (ICT) can help designers overcome these issues. A two-stage procedure for doing so is introduced in this paper. In the first stage, a stochastic programming model together with the information obtained through immersive simulation is applied to determine the optimal disassembly sequence, while considering uncertain outcomes, such as time, cost, and the probability of causing damage. In the second stage, ICT is applied as a tool to explore alternative disassembly sequence solutions in an intuitive way. The benefit of using this procedure is to determine the best disassembly sequence, not only by solving the analytic model but also by capturing human expertise. The designer can apply the obtained results from these two stages to analyze and modify the product design. An example of a Burr puzzle is used to illustrate the application of the method.
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