Markov modelling and parameterisation of genetic evolutionary test generations

Genetic evolutionary algorithms are effective and optimal test generation methods. However, the methods to select the algorithm parameters are often ad hoc, relying on empirical data. We used a Markov-based method to model the genetic evolutionary test generation process, parameterise the process characteristics, and derive analytical solutions for selecting the optimisation parameters. The method eliminates preliminary test generation calibration and experimentation effort needed to select these parameters, which are used in current practice.     

The effect of radial diffusion on current generation by electron-cyclotron waves in tokamak plasma

The effect of radial diffusion of electrons on current generation by electron-cyclotron waves in a tokamak plasma is studied in the framework of the three-dimensional kinetic model. A numerical solution of the problem is obtained. The results suggest that electron diffusion in the radial direction has a significant effect on the energy spectrum of the excited current. The lower diffusion bound in the velocity space plays an important role in this context.Translated from Matematicheskie Modeli Estestvoznaniya, Published by Moscow University, Moscow, 1995, pp. 27–31.     

Integrated lot-sizing and one-dimensional cutting stock problem with usable leftovers

This paper addresses the integration of the lot-sizing problem and the one-dimensional cutting stock problem with usable leftovers (LSP-CSPUL). This integration aims to minimize the cost of cutting items from objects available in stock, allowing the bringing forward production of items that have known demands in a future planning horizon. The generation of leftovers, that will be used to cut future items, is also allowed and these leftovers are not considered waste in the current period. Inventory costs for items and leftovers are also considered. A mathematical model for the LSP-CSPUL is proposed to represent this problem and an approach, using the simplex method with column generation, is proposed to solve the linear relaxation of this model. A heuristic procedure, based on a relax-and-fix strategy, was also proposed to find integer solutions. Computational tests were performed and the results show the contributions of the proposed mathematical model, as well as, the quality of the solutions obtained using the proposed method.

     

Developing concurrent investment plans for power generation and transmission

Decisions on electric power generation and transmission investments may have crucial effects on the development of industrial and residential areas. Decisions made on the infrastructure should have economically beneficial consequences for producers and consumers. The aim of this paper is to propose a model that considers transmission and generation investments simultaneously. The proposed model fills in the gap between models for developing long-term power generation policies and instantaneous power flow models. Unlike other investment models, it explicitly takes the high voltage transmission network into account and the selection of new generation plants located on the interconnected network is made in a more realistic manner considering transmission bottlenecks.The problem subsumes the capacitated network location problem and the network design problem, the former being related to decisions on generation expansion and the latter to decisions on transmission network expansion. The integrated model becomes NP in both feasibility and optimality, because of the sub-problems it contains. Here, a practical procedure is proposed to achieve overall feasibility and also to improve investment decisions when the solution is feasible. The model is tested on the dense interconnected network of an industrialized region in Turkey. The implementation shows how future infeasibilities in the transmission network are highlighted by the model and how generation investment decisions are affected by network expansion alternatives.     

Simulation of direct chill casting under the influence of a low-frequency electromagnetic field

A comprehensive, multiphysics, meshless, numerical model is developed for the simulation of direct chill casting under the influence of a low-frequency electromagnetic field. The model uses mixture-continuum-mass, momentum and energy-conservation equations to simulate the solidification of axisymmetric aluminium-alloy billets. The electromagnetic-induction equation is coupled with the fluid flow and used to calculate the Lorentz force. The involved partial-differential equations are solved with the meshless-diffuse-approximate method by employing second-order polynomial shape functions and a 13-noded local support. An explicit time-stepping scheme is used. The boundary conditions for the heat transfer involve the effects of hot-top, mould chill and direct chill. The use of a meshless method and the automatic node-arrangement generation made it possible to investigate the complicated flow structures in geometrically complex inflow conditions, including sharp and curved edges, in a straightforward way. A time-dependent adaptive computational node arrangement is used to decrease the calculation time. The model is demonstrated by casting an Al-5.25wt%Cu aluminium alloy billet with a radius of 120 mm. Results on simplified and realistic inflow geometry are considered and compared. The effect of the low-frequency electromagnetic force on the temperature, liquid fraction and fluid flow are investigated under different current densities and frequencies.     

A Multigenerational Game Model to Analyze Sustainable Development

This paper deals with a multigeneration game that provides a new rationale for representing time preference in very long term cost benefit analysis, as it happens typically in the economics of global climate change. One defines an intergenerational game where each generation has a random life duration and transfers the control of the economic system to the next generation at the end of its life. The payoff to a generation is a discounted sum of the expected consumption by the whole infinite sequence of generations, starting with the current one. The equilibrium is characterized by a dynamic programming equation; a unique solution is proved to exist; a numerical technique is proposed and implemented on a continuous time simplified version of the model DICE94. The results show the influence of this form of altruism on the asymptotic steady states of the economy subject to a global climate change effect. This research has been supported by an SNSF grant in the NCCR-Climate research program.     

A stochastic multiscale model for electricity generation capacity expansion

Long-term planning for electric power systems, or capacity expansion, has traditionally been modeled using simplified models or heuristics to approximate the short-term dynamics. However, current trends such as increasing penetration of intermittent renewable generation and increased demand response requires a coupling of both the long and short term dynamics. We present an efficient method for coupling multiple temporal scales using the framework of singular perturbation theory for the control of Markov processes in continuous time. We show that the uncertainties that exist in many energy planning problems, in particular load demand uncertainty and uncertainties in generation availability, can be captured with a multiscale model. We then use a dimensionality reduction technique, which is valid if the scale separation present in the model is large enough, to derive a computationally tractable model. We show that both wind data and electricity demand data do exhibit sufficient scale separation. A numerical example using real data and a finite difference approximation of the Hamilton–Jacobi–Bellman equation is used to illustrate the proposed method. We compare the results of our approximate model with those of the exact model. We also show that the proposed approximation outperforms a commonly used heuristic used in capacity expansion models.     

Structural properties of the one-dimensional drift-diffusion models for semiconductors

This paper is devoted to the analysis of the one-dimensional current and voltage drift-diffusion models for arbitrary types of semiconductor devices and under the assumption of vanishing generation recombination. We show in the course of this paper, that these models satisfy structural properties, which are due to the particular form of the coupling of the involved systems. These structural properties allow us to prove an existence and uniqueness result for the solutions of the current driven model together with monotonicity properties with respect to the total current , of the electron and hole current densities and of the electric field at the contacts. We also prove analytic dependence of the solutions on . These results allow us to establish several qualitative properties of the current voltage characteristic. In particular, we give the nature of the (possible) bifurcation points of this curve, we show that the voltage function is an analytic function of the total current and we characterize the asymptotic behavior of the currents for large voltages. As a consequence, we show that the currents never saturate as the voltage goes to , contrary to what was predicted by numerical simulations by M. S. Mock (Compel. 1 (1982), pp. 165--174). We also analyze the drift-diffusion models under the assumption of quasi-neutral approximation. We show, in particular, that the reduced current driven model has at most one solution, but that it does not always have a solution. Then, we compare the full and the reduced voltage driven models and we show that, in general, the quasi-neutral approximation is not accurate for large voltages, even if no saturation phenomenon occurs. Finally, we prove a local existence and uniqueness result for the current driven model in the case of small generation recombination terms.

     

单水库在线发电调度策略设计与分析

考察单水库电站的多时段发电调度问题,决策者在每个时段初决策该时段的发电量,目标是使得在整个调度期内总发电量最大。针对在每个时段决策时缺乏当前及后续时段来水信息的情形,运用在线理论建立在线发电调度模型,设计给出了竞争比为2/(2-β(1-Ф))的在线发电调度策略,其中,β∈(0,1)表示每个时段最大来水导致的水头最大增幅与水库有效水头最大落差的比值,Ф∈(0,1)表示最低与最高有效水头数值之比。针对各时段可获知当前时段来水信息的情形,给出了在线调度策略,并证明了其竞争比为1+(1-Ф)/(1+Ф)。     

政府-企业-居民多维演化博弈下城市垃圾绿色发电的政府财政策略优化研究

城市垃圾发电技术趋于成熟,但是部分企业并没有选择绿色技术进行清洁焚烧绿色发电,引发公众抗议。针对现行财政策略对企业绿色发电行为引导的不足,建立政府-企业-居民多维演化博弈模型,分析财政决策变量对企业绿色发电行为策略的影响,提出命题并推导证明电价补贴、垃圾处理费支付、税收退税和设备采购抵税这四个财政决策变量能够有效引导企业绿色发电行为的参数值域,并基于现实数据进行Matlab仿真,分析各财政决策变量对企业绿色发电行为策略的收敛性和敏感性作用,最后提出财政策略优化建议。结果表明通过财政间接扶持方式引导企业绿色技术行为,能使电价补贴处于更低阈值,减少财政直接支出成本,不可过度依赖电价补贴,需改善垃圾处理费支付水平,丰富税收扶持手段。     

Lie group analysis of unsteady MHD three dimensional by natural convection from an inclined stretching surface saturated porous medium

Lie group method is investigated for solving the problem of heat transfer in an unsteady, three-dimensional, laminar, boundary-layer flow of a viscous, incompressible and electrically conducting fluid over inclined permeable surface embedded in porous medium in the presence of a uniform magnetic field and heat generation/absorption effects. A uniform magnetic field is applied in the y-direction and a generalized flow model is presented to include the effects of the macroscopic viscous term and the microscopic permeability of porous medium. The infinitesimal generators accepted by the equations are calculated and the extension of the Lie algebra for the problem is also presented. The restrictions imposed by the boundary conditions on the generators are calculated. The investigation of the three-independent-variable partial differential equations is converted into a two-independent-variable system by using one subgroup of the general group. The resulting equations are solved numerically with the perturbation solution for various times. Velocity, temperature and pressure profiles, surface shear stresses, and wall-heat transfer rate are discussed for various values of Prandtl number, Hartmann number, Darcy number, heat generation/absorption coefficient, and surface mass-transfer coefficient.     

Plasmon resonance and heat generation in nanostructures

In this paper, the photothermal effects of plasmon resonance are investigated. Metal nanoparticles efficiently generate heat in the presence of electromagnetic radiation. The process is strongly enhanced when a fixed frequency of the incident wave illuminates on nanoparticles such that plasmon resonance happens. We introduce the electromagnetic radiation model and show exactly how and when the plasmon resonance happens. We then construct the heat generation and transfer theory and derive the heat effect induced by plasmon resonance. Finally, the heat generation under plasmon resonance in a concentric nanoshell structure is considered specially, and excited result is obtained. Copyright © 2015 John Wiley & Sons, Ltd.     

Automatic mesh-healing technique for model repair and finite element model generation

It has been accepted by many researchers that modification of a model is often a necessity as a precursor to effective mesh generation. However, editing the geometry directly is often found to be cumbersome, tedious and expensive. In preparing a CAD model for numerical simulation, one of the critical issues involves the rectification of geometrical and topological errors. Though visually insignificant, these errors hinder the creation of a valid finite element model with a good mesh quality. Most current state-of-the-art works have been trying to heal geometric models directly. The novelty of the method proposed in this paper is that the mesh-healing process includes both model repair and mesh generation in one black box. The mesh-healing algorithm essentially simplifies the problems of the imperfect models and allows one to deal with simple polygons rather than complex surface representations. This paper addresses errors such as gaps, overlaps, T-joints and simple holes.     

On the convergence of a factorized distribution algorithm with truncation selection

We investigate the global convergence of a factorized distribution algorithm (FDA) with truncation selection. Like conventional genetic algorithms, FDAs maintain and successively improve a population of solutions. In FDAs, a distribution model is built based on the statistical information extracted from a set of selected solutions in the current population, and then the model thus built is used to generate new solutions for the next generation. The variable‐dependence structure of the distribution model in FDAs is determined by the variable‐interaction structure of the objective function. We prove that the FDA with truncation selection converges globally for optimization of a class of additively decomposable functions (ADF). Our results imply that the utilization of appropriately selected dependence relationships is sufficient to guarantee the global convergence of estimation of distribution algorithms (EDAs) for optimization of ADFs. © 2004 Wiley Periodicals, Inc. Complexity 9: 17–23, 2004     

Stresses of a rotating circular disk of variable thickness carrying a current and bearing a coaxial viscoelastic coating

In the present work we consider a circular elastic disk (conductor) of variable thickness under the influence of a steady coaxial current and bearing a coaxial viscoelastic coating (insulator). In both conductor and insulator there exist a heat source generation. As a first step, the solution of purely elastic conductor and insulator is obtained. Then the problem of model with viscoelastic coating is solved using the correspondence principle and Ilyushin’s approximation method. A numerical example is given and the results are discussed in order to investigate the influences of time, temperature, and rotation on the stresses and displacements.     

Dynamic sample budget allocation in model-based optimization

Model-based search methods are a class of optimization techniques that search the solution space by sampling from an underlying probability distribution “model,” which is updated iteratively after evaluating the performance of the samples at each iteration. This paper aims to improve the sampling efficiency of model-based methods by considering a generalization where a population of distribution models is maintained and subsequently propagated from generation to generation. A key issue in the proposed approach is how to efficiently allocate the sampling budget among the population of models to maximize the algorithm performance. We formulate this problem as a generalized max k-armed bandit problem, and derive an efficient dynamic sample allocation scheme based on Markov decision theory to adaptively allocate computational resources. The proposed allocation scheme is then further used to update the current population to produce an improving population of models. Our preliminary numerical results indicate that the proposed procedure may considerably reduce the number of function evaluations needed to obtain high quality solutions, and thus further enhance the value of model-based methods for optimization problems that require expensive function evaluations for performance evaluation.     

Global dynamical analysis of a heroin epidemic model on complex networks

In this paper, a heroin epidemic model on complex networks is proposed. By the next generation matrix, the basic reproduction number $R_0$ is obtained. If $R_0<1$, then the drug-free equilibrium is globally asymptotically stable. If $R_0>1$, there is an unique endemic equilibrium and it is also globally asymptotically stable. Our results show that if the degree of the network is large enough, the drug transmission always spreads. Sensitivity analysis of the basic reproduction number with the various parameters in the model are carried out to verify the important effects for control the drug transmission. Some simulations illustrate our theoretical results     

Numerical grids used in a coastal ocean model with breaking wave effects

In coastal ocean modeling, traditional single-block rectangular (Cartesian) grids have been most commonly used for their simplicity. In many cases, these grids may be not well suited (even at very high resolutions) for regions with complicated physical fields, open boundaries, coastlines, and bottom bathymetry. The numerical curvilinear nearly orthogonal/orthogonal, single/multi-block coastline-following grids for the Mediterranean Sea, Monterey Bay and the South China Sea (SCS) are presented. These grids can be used in coastal ocean modeling to enhance model numerical solutions and save computer resources by giving better treatment of regions with high gradients such as areas of complicated coastlines and steep slopes of shelf breaks, complicated bottom topography, open boundaries, and multi-scale physical phenomenon. Grid generation techniques are used to designed these grids. This kind of grids can also easily increase horizontal resolutions in the subregion of the model domain, without increasing the computational expense, with a higher resolution over the entire domain.A three dimensional coastal ocean model with breaking wave effects is also presented and applied. The ocean system is a primitive equation modeling system with grid generation routines and a turbulent closure which is capable of taking surface breaking wave effects into account. The system also includes a grid package which allows model numerical grids to be coupled with the ocean model. The model code is written for multi-block grids, but a single-block grid is used for the South China Sea (SCS). The model with breaking wave effects and a grid of 121 × 121 grid points are used to simulate the winter circulation of the SCS as an example. The model output of the 60-day run shows the observed upwelling locations in the sea surface salinity field.