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Automatic sizing functions for unstructured mesh generation revisited

ENGINEERING COMPUTATIONS 2021年第10期38卷 3995-4023页

作者： Liu, Zhiwei Chen, Jianjun Xia, Yifan Zheng, Yao Ctr Engn & Sci Computat Hangzhou Peoples R China Zhejiang Univ Sch Aeronaut & Astronaut Hangzhou Peoples R China

Purpose Sizing functions are crucial inputs for unstructured mesh generation since they determine the element distributions of resulting meshes to a large extent. Meanwhile, automating the procedure of creating a sizing function is a prerequisite to set up a fully automatic mesh generation pipeline. In this paper, an automatic algorithm is proposed to create a high-quality sizing function for an unstructured surface and volume mesh generation by using a triangular mesh as the background mesh. Design/methodology/approach A practically efficient and effective solution is developed by using local operators carefully to re-mesh the tessellation of the input Computer Aided Design (CAD) models. A nonlinear programming (NLP) problem has been formulated to limit the gradient of the sizing function, while in this study, the object function of this NLP is replaced by an analytical equation that predicts the number of elements. For the query of the sizing value, an improved algorithm is developed by using the axis-aligned bounding box (AABB) tree structure. Findings The local operations of re-meshing could effectively and efficiently resolve the banding issue caused by using the default tessellation of the model to define a sizing function. Experiments show that the solution of the revised NLP, in most cases, could provide a better solution at the lower cost of computational time. With the help of the AABB tree, the sizing function defined at a surface background mesh can be also used as the input of volume mesh generation. Originality/value Theoretical analysis reveals that the construction of the initial sizing function could be reduced to the solution of an optimization problem. The definitions of the banding elements and surface proximity are also given. Under the guidance of this theoretical analysis, re-meshing and ray-casting technologies are well-designed to initial the sizing function. Smoothing with the revised NLP and querying by the AABB tree, the paper provides an

关键词： Mesh generation Mesh adaptation Sizing function non-linear programming Ray-casting Axis Aligned Bounding Box (AABB)

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Capacity selection under uncertainty with ratio objectives

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第1期143卷 138-147页

作者： Gerchak, Y Hassini, E Ray, S Univ Waterloo Dept Management Sci Waterloo ON N2L 3G1 Canada

Capacity choice or expansion, whether organic or via mergers and acquisitions, creates firms of widely varying scales. The ex-post profitability of such a transformed firm relative to its original size will typically be evaluated on ratio (rate) measures like earnings per share or profits to asset ratio, as such are the only meaningful ways to compare profitability of firms of substantially different sizes. It thus seems desirable that ex-ante capacity selection decisions will also be guided by a ratio objective. We explore capacity choice decisions under demand uncertainty through the ratio measures: (1) Expected "newsvendor" (i.e., single period) costs per unit capacity. (2) Expected (newsvendor) profit per unit of capacity. (3) Expected profit per costs of acquiring capacity. (4) A weighted average of a ratio and non-ratio objectives. We allow the capacity-acquisition costs and capacity's production capability to be general non-linear functions. Cost and profit objectives cease to be equivalent when ratio objectives are involved. We show that cost ratio optimizers will select a larger capacity than absolute cost optimizers, while profit ratio optimizers will select smaller capacities than absolute counterpart. We provide examples which show that the difference in optimal capacities, and the associated difference in objective value can be substantial. We also perform comparative statics analyses of the effect of change in item's shortage cost and of stochastic shifts in demand. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： uncertainty modelling capacity expansion ratio objectives non-linear programming

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non-linear global optimization via parameterization and inverse function approximation: An artificial neural networks approach

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INTERNATIONAL JOURNAL OF NEURAL SYSTEMS 2007年第5期17卷 353-368页

作者： Mayorga, Rene V. Arriaga, Mariano Univ Regina Fac Engn Regina SK S4S 0A2 Canada

In this article, a novel technique for non-linear global optimization is presented. The main goal is to find the optimal global solution of non-linear problems avoiding sub-optimal local solutions or inflection points. The proposed technique is based on a two steps concept: properly keep decreasing the value of the objective function, and calculating the corresponding independent variables by approximating its inverse function. The decreasing process can continue even after reaching local minima and, in general, the algorithm stops when converging to solutions near the global minimum. The implementation of the proposed technique by conventional numerical methods may require a considerable computational effort on the approximation of the inverse function. Thus, here a novel Artificial Neural Network (ANN) approach is implemented to reduce the computational requirements of the proposed optimization technique. This approach is successfully tested on some highly non-linear functions possessing several local minima. The results obtained demonstrate that the proposed approach compares favorably over some current conventional numerical (Matlab functions) methods, and other non-conventional (Evolutionary Algorithms, Simulated Annealing) optimization methods.

关键词： artificial neural networks global optimization inverse functions non-linear programming

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Modelling the economic trade-offs of irrigation pipeline investments for improved energy management

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WATER SA 2016年第4期42卷 542-550页

作者： Venter, Marcill Grove, Bennie Univ Free State Dept Agr Econ POB 339 ZA-9300 Bloemfontein South Africa

Higher electricity tariffs have accentuated the importance of the trade-off between lowering investment cost by buying pipes with smaller diameters and the higher operating costs that result from the increased power requirement to overcome the higher friction losses of the thinner pipes. The Soil Water Irrigation Planning and Energy Management (SWIP-E) mathematical programming model was developed and applied in this paper to provide decision support regarding the optimal mainline pipe diameter, irrigation system delivery capacity and size of the irrigation system. SWIP-E unifies the interrelated linkages between mainline pipe diameter choice and the timing of irrigation events in conjunction with time-of-use electricity tariffs. The results showed that the large centre pivot resulted in higher net present values than the smaller centre pivot and the lower delivery capacities were more profitable than higher delivery capacities. More intense management is, however, necessary for delivery capacities lower than 12 mm.d(-1) to minimise irrigation during peak timeslots. Variable electricity costs are highly dependent on the interaction between kilowatt requirement and irrigation hours. For the large centre pivot the interaction is dominated by changes in kilowatt whereas the effect of irrigation hours in relation to kilowatts is more important for smaller pivots. Optimised friction loss expressed as a percentage of the length of the pipeline was below 0.6%, which is much lower than the design norm of 1.5% that is endorsed by the South African Irrigation Institute. The main conclusion is that care should be taken when applying the friction loss norm when sizing irrigation mainlines because the norm will result in pipe diameters that are too small, consequently resulting in increased lifecycle operating costs. A clear need for the revision of the friction loss design norm was identified by this research.

关键词： non-linear programming economic trade-off electricity costs irrigation system investment costs water management net present value

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A systematic core design method for reduction of critical boron concentration in APR 1400 with gadolinia-bearing assembly

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ANNALS OF NUCLEAR ENERGY 2014年 72卷 421-427页

作者： Hah, Chang Joo Kahar, Wan Shakirah Wan Abdul Chang, Do Ik Seong, Ki Bong KEPCO Int Nucl Grad Sch Dept Nucl Power Plant Engn Ulsan 689882 South Korea Korea Nucl Fuel Co Ltd Technol & Engn Div Taejon 305303 South Korea

A systematic core design method is developed to design Gd-bearing fuel assembly having two types of Gd rods, low-wt%-Gd rod and high-wt%-Gd rod. The purpose of the method is to lower the critical boron concentration (CBC) of a preliminary core loading pattern, and consequently to achieve more negative or less positive moderator temperature coefficient (MTC). The proposed core design method is a process of solving a non-linear programming problem stated with a system of equations. In this method, both the ratio of the number of low-wt%-Gd rod to the number of high-wt%-Gd rod (r) and the assembly average Gd wt% (w) are the solution variables of the system of equations. The target function is the amount of soluble boron concentration reduction, Delta CBC, which is correlated with the reactivity change, Delta k(FA), per Gd-bearing fuel assembly by a quadratic reactivity equation. The coefficients of the quadratic equations are calculated prior to the determination of Gd-bearing fuel assembly pattern, using the least square method. The constraints required to determine (r, w) are physically realizable Gd rods pattern, Delta k(i) close to Delta k(FA) derived from Delta CBC, etc. An objective function, min [f(Sigma(i)(Delta k(FA) - Delta k(i)))], enables a final loading pattern to reach a target CBC. This design methodology is applied to APR 1400. Total six cases with various target CBCs are investigated to validate the proposed method. CASMO-3/MASTER calculations with new design assemblies produce lower CBCs at BOC than target CBCs keeping maximum pin power below the safety limit, and thus show more negative MTC. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Critical boron concentration reduction Core design Gadolinium rod non-linear programming

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A spring-embedding approach for the facility layout problem

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2004年第1期55卷 73-81页

作者： Castillo, I Sim, T Univ Alberta Sch Business Dept Finance & Management Sci Edmonton AB T6G 2R6 Canada

The facility layout problem is concerned with finding the most efficient arrangement of a given number of departments with unequal area requirements within a facility. The facility layout problem is a hard problem, and therefore, exact solution methods are only feasible for small or greatly restricted problems. In this paper, we propose a spring-embedding approach that unlike previous approaches results in a model that is convex. Numerical results demonstrating the potential of our model and the efficiency of our solution procedure are presented.

关键词： facility layout non-linear programming optimisation augmented Lagrangian multiplier method

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Computation of weighted sums of rewards for concurrent MDPs

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2019年第1期89卷 1-42页

作者： Buchholz, Peter Scheftelowitsch, Dimitri TU Dortmund Informat 4 Dortmund Germany

We consider sets of Markov decision processes (MDPs) with shared state and action spaces and assume that the individual MDPs in such a set represent different scenarios for a system's operation. In this setting, we solve the problem of finding a single policy that performs well under each of these scenarios by considering the weighted sum of value vectors for each of the scenarios. Several solution approaches as well as the general complexity of the problem are discussed and algorithms that are based on these solution approaches are presented. Finally, we compare the derived algorithms on a set of benchmark problems.

关键词： Markov decision processes Optimization Multi-objective optimization non-linear programming

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Planning and managing intermodal transportation of hazardous materials with capacity selection and congestion

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2015年 76卷 45-57页

作者： Assadipour, Ghazal Ke, Ginger Y. Verma, Manish Mem Univ Fac Business Adm St John NF Canada McMaster Univ DeGroote Sch Business Hamilton ON L8S 4L8 Canada

The current literature in the rail truck intermodal transportation of hazardous materials (hazmat) domain ignores congestion at intermodal yards. We attempt to close that gap by proposing a bi-objective optimization framework for managing hazmat freight that not only considers congestion at intermodal yards, but also determines the appropriate equipment capacity. The proposed framework, i.e., a non-linear MIP and a multi-objective genetic algorithm based solution methodology, is applied to a realistic size problem instance from existing literature. Our analysis indicates that terminal congestion risk is a significant portion of the network risk;and, that policies and tools involving number of cranes, shorter maximum waiting times, and tighter delivery times could have a positive bearing on risk. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Rail-truck transportation Congestion Hazardous materials Capacity planning non-linear programming Metaheuristics

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Applying multiple objective tabu search to continuous optimization problems with a simple neighbourhood strategy

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2006年第3期65卷 406-424页

作者： Baykasoglu, A Gaziantep Univ Dept Ind Engn TR-27310 Gaziantep Turkey

One of the first multiple objective versions of the tabu search (TS) algorithm is proposed by the author. The idea of applying TS to multiple objective optimization is inspired from its solution structure. TS works with more than one solution (neighbourhood solutions) at a time and this situation gives the opportunity to evaluate multiple objectives simultaneously in one run. The selection and updating stages are modified to enable the original TS algorithm to work with more than one objective. In this paper, the multiple objective tabu search (MOTS) algorithm is applied to multiple objective non-linear optimization problems with continuous variables using a simple neighbourhood strategy. The algorithm is applied to four mechanical components design problems. The results are compared with several other solution techniques including multiple objective genetic algorithms. It is observed that MOTS is able to find better and much wider spread of solutions than the reported ones. Copyright (c) 2005 John Wiley & Sons, Ltd.

关键词： multiple objective optimization tabu search non-linear programming design optimization

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Modeling and parameters fitting of chemical and phase equilibria in reactive systems for biodiesel production

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BIOMASS & BIOENERGY 2015年 81卷 544-555页

作者： Yancy-Caballero, Daison M. Guirardello, Reginaldo Univ Campinas UNICAMP Sch Chem Engn BR-13083852 Campinas SP Brazil

Biodiesel, a non-toxic biodegradable fuel from renewable sources such as vegetable oils, has been developed in order to reduce dependence on crude oil and enable sustainable development. The knowledge of phase equilibrium in systems containing compounds for biodiesel production is valuable, especially in the purification stage of the biodiesel. nonetheless, the refining process of biodiesel and byproducts can be difficult and can elevate the production costs considerably unless it has an appropriate knowledge about the phase separation behavior. In addition, the transesterification reaction yield for producing biodiesel depends upon several operation parameters e.g. the feed molar ratio oil-to-alcohol and the temperature. These parameters were analyzed through a thermodynamic analysis by direct Gibbs energy minimization method in this paper, with the purpose of calculating the chemical and phase equilibrium of some mixtures containing compounds found in biodiesel production. For this, optimization techniques associated with the GAMS 2.5 software were utilized and the UNIQUAC and NRTL models were applied to represent the non-idealities of the liquid phases. Also, binary interaction parameters of studied compounds were correlated for NRTL and UNIQUAC models by using the least squares principle. The results showed that the use of optimization techniques associated with the GAMS software are useful and efficient tools to calculate the chemical and phase equilibrium by minimizing the Gibbs energy. Moreover, a good agreement was observed in cases in which calculated data were compared with experimental data. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Biodiesel Optimization Gibbs energy minimization Chemical and phase equilibrium non-linear programming

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