Optimization of spatial tracks using a morphing approach

This paper describes an approach for optimizing multibody systems involving spatial tracks, addressing the problem of finding an optimal set of design parameters when no good initial guess is available. In this setting, it is common that, due to nonlinearities of the objective function and singularities in the kinematic model, the optimization fails to converge or to find feasible points at all. The present paper presents a three-stage procedure for sequentially guiding a standard optimization routine from an arbitrary initial guess to the optimal configuration. The approach has been tested when optimizing real roller coaster tracks with respect to passenger acceleration and compared with a genetic algorithm implementation, showing that objective function morphing renders faster for the regarded type of systems. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the eigenvalues of the saddle point matrices discretized from Navier–Stokes equations

In this paper, we proposed an implementation of stochastic perturbation of reduced gradient and bisection (SPRGB) method for optimizing a non-convex differentiable function subject to linear equality constraints and non-negativity bounds on the variables. In particular, at each iteration, we compute a search direction by reduced gradient, and optimal line search by bisection algorithm along this direction yields a decrease in the objective value. SPRGB method is desired to establish the global convergence of the algorithm. An implementation and tests of SPRGB algorithm are given, and some numerical results of large-scale problems are presented, which show the efficient of this approach.     

On the evolution of recombination in haploids and diploids: II. Stochastic models

In this article, we continue an investigation into the evolution of modifiers of recombination, comparing haploid and diploid models begun in Vol. 1, Issue 1, of Complexity. Here, we examine selection schemes that have been used recently in numerical studies of finite diploid populations and ask how recombination evolves in haploid versions of these models. Although the analysis keeps track of the recombination controlling locus rather than the time until a desired bit-string appears, our result may be of use to the practitioners of genetic algorithms (GA's). We find that as a rule high recombination evolves more easily when selection is on haploids than it does in the diploid case. This is especially true of Gaussian selection schemes with high recombination recessive to low recombination. When the fitness regime is more jagged, however, the results depend on the level of jaggedness, with high recombination favored under smoother regimes. We also find that the direction of mutation and dominance relationships among the modifying alleles affect the results. Although there remains much to be done in reconciling population genetic theory with the properties of genetic algorithms, many new and interesting questions have emerged from, and will continue to be stimulated by, interactions between practitioners of each approach.     

On Optimization of the Full Radiative Heat Transfer System

Solving the full radiative heat transfer equation, moderately discretized in space, time, frequency and direction, results in a tremendously huge system of equations. A common approach to avoid this problem is to use moment methods neglecting the directional dependence on radiation. Our approach, however, is to solve the full radiative heat transfer system with all dependencies and to optimize the heat distribution and the radiative flux, respectively, for a desired temperature function or desired radiative flux function. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization of two-step investment in a production process

We consider the problem of optimizing the control of a production process. The control parameters are the capacity utilization and the investment in the growth of the production capacity. We assume that the investments are divided into two parts: initial investment aimed at creating production facilities, and investment aimed at increasing the capacity during the production process. The initial and increased capacities and the moment of changing the capacity are variable parameters to be specified. The price of the product is assumed to be a random process. The problem is to optimize the production process and to construct a control strategy that maximizes the average discounted profit. We propose an approach to the construction of an optimal adaptive strategy for controlling the production. The approach is based on the dynamic programming method.     

Linearly constrained global optimization via piecewise-linear approximation

This paper considers the problem of optimizing a continuous nonlinear objective function subject to linear constraints via a piecewise-linear approximation. A systematic approach is proposed, which uses a lattice piecewise-linear model to approximate the nonlinear objective function on a simplicial partition and determines an approximately globally optimal solution by solving a set of standard linear programs. The new approach is applicable to any continuous objective function rather than to separable ones only and could be useful to treat more complex nonlinear problems. A numerical example is given to illustrate the practicability.     

Some convergence properties of the conjugate gradient method

It has been conjectured that the conjugate gradient method for minimizing functions of several variables has a superlinear rate of convergence, but Crowder and Wolfe show by example that the conjecture is false. Now the stronger result is given that, if the objective function is a convex quadratic and if the initial search direction is an arbitrary downhill direction, then either termination occurs or the rate of convergence is only linear, the second possibility being more usual. Relations between the starting point and the initial search direction that are necessary and sufficient for termination in the quadratic case are studied.     

Template-Based Stabilization of Relative Equilibria in Systems with Continuous Symmetry

We present an approach to the design of feedback control laws that stabilize relative equilibria of general nonlinear systems with continuous symmetry. Using a template-based method, we factor out the dynamics associated with the symmetry variables and obtain evolution equations in a reduced frame that evolves in the symmetry direction. The relative equilibria of the original systems are fixed points of these reduced equations. Our controller design methodology is based on the linearization of the reduced equations about such fixed points. We present two different approaches of control design. The first approach assumes that the closed loop system is affine in the control and that the actuation is equivariant. We derive feedback laws for the reduced system that minimize a quadratic cost function. The second approach is more general; here the actuation need not be equivariant, but the actuators can be translated in the symmetry direction. The controller resulting from this approach leaves the dynamics associated with the symmetry variable unchanged. Both approaches are simple to implement, as they use standard tools available from linear control theory. We illustrate the approaches on three examples: a rotationally invariant planar ODE, an inverted pendulum on a cart, and the Kuramoto-Sivashinsky equation with periodic boundary conditions.     

On the Center of Mass of Asymptotically Hyperbolic Initial Data Sets

We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center of mass of suitably asymptotically Euclidean time-slices of asymptotically Minkowskian spacetimes (isolated systems). In particular, we unite—an altered version of—the approach based on Hamiltonian charges with an approach based on CMC-foliations near infinity. The newly defined center of mass transforms appropriately under changes of the asymptotic coordinates and evolves in the direction of an appropriately defined linear momentum under the Einstein evolution equations.     

一种基于自适应混合遗传算法的非线性函数优化方法

遗传算法因其具有的特性,它采用交换、复制和突变等方法,获取的解为全局最优解,而且无需计算函数的导数,是一种只考虑输入与输出关系的黑箱问题,适用于处理各种复杂问题.此文基于最优保存的思想,把最速下降法与最优保存和自适应遗传算法相结合,用于求解非线性函数优化问题,提出一种基于自适应混合遗传算法的非线性函数全局优化方法.     

Synchronization of complex networks with time‐varying inner coupling and outer coupling matrices

Synchronization of complex networks with time‐varying coupling matrices is studied in this paper. Two kinds of time‐varying coupling are taken into account. One is the time‐varying inner coupling in the node state space and the other is the time‐varying outer coupling in the network topology space. By respectively setting linear controllers and adaptive controllers, time‐varying complex networks can be synchronized to a desired state. Meanwhile, different influences of the control parameters of linear controllers and adaptive controllers on the synchronization have also been investigated. Based on the Lyapunov function theory, we construct appropriate positive‐definite functions, and several sufficient synchronization criteria are obtained. Numerical simulations further illustrate the effectiveness of conclusions. Copyright © 2017 John Wiley & Sons, Ltd.     

CFD-based optimization of fuel injection strategies in a diesel engine using an adaptive gradient method

A computationally efficient computational fluid dynamics (CFD)-based optimization method with the capability of finding optimal engine operating conditions with respect to emissions and fuel consumption has been developed. The approach taken uses a steepest descent method for an adaptive cost function, where the line search is performed with a backtracking algorithm. The backtracking algorithm utilizes quadratic and cubic polynomials to accelerate the convergence, and the initial backtracking step employs an adaptive step size mechanism which depends on the steepness of the search direction. The adaptive cost function is based on the penalty method such that the penalty term is stiffened after every line search. The engine simulations are performed with a KIVA-3-based CFD code which is equipped with well-established spray, combustion and emission models. The application of this optimization tool is demonstrated for a non-road, medium-speed DI diesel engine which, for these simulations, utilizes a multi-orifice, asynchronous injection system. It has been demonstrated that this new injection method has a large potential for reducing emissions while maintaining a low fuel consumption. In addition, this optimization approach is computationally very efficient when good enough initial values are available.     

A new hybrid stochastic approximation algorithm

In this paper, we consider optimizing the performance of a stochastic system that is too complex for theoretical analysis to be possible, but can be evaluated by using simulation or direct experimentation. To optimize the expected performance of such system as a function of several input parameters, we propose a hybrid stochastic approximation algorithm for finding the root of the gradient of the response function. At each iteration of the hybrid algorithm, alternatively, either an average of two independent noisy negative gradient directions or a scaled noisy negative gradient direction is selected. The almost sure convergence of the hybrid algorithm is established. Numerical comparisons of the hybrid algorithm with two other existing algorithms in a simple queueing system and five nonlinear unconstrained stochastic optimization problems show the advantage of the hybrid algorithm.     

The continuous dependence of solutions to algebraic differential systems on the initial data

We consider a nonlinear system of ordinary differential equations which is unsolved with respect to the derivative of the desired vector function and identically degenerate in the definition domain. We study the consistency manifold under assumptions that guarantee the existence of a solution. We prove an analog of the theorem on the continuous dependence of solutions on the initial data, assuming that the latter belong to the consistency manifold.     

A computer‐aided methodology for the optimization of electrostatic separation processes in recycling

The rapid growth of technological products has led to an increasing volume of waste electrical and electronic equipments (WEEE), which could represent a valuable source of critical raw materials. However, current mechanical separation processes for recycling are typically poorly operated, making it impossible to modify the process parameters as a function of the materials under treatment, thus resulting in untapped separation potentials. Corona electrostatic separation (CES) is one of the most popular processes for separating fine metal and nonmetal particles derived from WEEE. In order to optimize the process operating conditions (i.e., variables) for a given multi‐material mixture under treatment, several technological and economical criteria should be jointly considered. This translates into a complex optimization problem that can be hardly solved by a purely experimental approach. As a result, practitioners tend to assign process parameters by few experiments based on a small material sample and to keep these parameters fixed during the process life‐cycle. The use of computer experiments for parameter optimization is a mostly unexplored area in this field. In this work, a computer‐aided approach is proposed to the problem of optimizing the operational parameters in CES processes. Three metamodels, developed starting from a multi‐body simulation model of the process physics, are presented and compared by means of a numerical and simulation study. Our approach proves to be an effective framework to optimize the CES process performance. Furthermore, by comparing the predicted response surfaces of the metamodels, additional insight into the process behavior over the operating region is obtained. Copyright © 2015 John Wiley & Sons, Ltd.     

Blowup solutions in a problem for the nonlinear heat equation on a small interval

The article considers a one-dimensional quasi-linear heat equation with a volume heat source and a nonlinear thermal conductivity. The analysis is conducted for parameter values where selfsimilar solutions of the equations evolve in an LS-regime with blowup. Heat localization is observed in this case, and the combustion process in the developed stage is in the form of simple or complex structures of contracting half-width. We study the evolution dynamics of various initial distributions and their achievement of the self-similar regime, and also the dependence of the size of the localization region on the shape of the initial compactly supported distribution. The possibility of cyclic evolution of solutions against the background of overall growth with blowup is demonstrated. We particularly focus on the case when the size of the spatial region is much less than the characteristic size of the localization region, and heat flow is obstructed by the physical boundaries. In this case all initial perturbations achieve the self-similar regime, but the corresponding scenario has certain specific features. We present an example of formation of a complex spatial structure that evolves with blowup on a small interval. Translated from Prikladnaya Matematika i Informatika, No. 29, 2008, pp. 88–112.     

基于混沌理论的创新网络中组织间信任演化研究

以往关于信任的研究是在稳定均衡的假设下进行的,然而信任演化过程中会表现出非线性的混沌状态,具有复杂系统的特征。基于演化博弈理论和混沌理论,建立了创新网络中组织间信任演化模型,分析了创新网络中组织间信任的复杂性、初值敏感性、分岔行为及内随机性等混沌特性,推导出信任演化方程与Logistic映射之间的关系,采用Lyapunov稳定性理论进行混沌性判定,证明创新网络中组织间信任通过倍周期分岔通往混沌,得到了信任从有序进入混沌的一般条件,运用算例进行仿真展示信任演化通往混沌的过程,分析创新网络中信任演化进入混沌区的实际意义,并选择硅谷和筑波科技城两个实例做对比分析,验证了该研究的实用性和有效性。创新网络中组织间信任的混沌演化反映出信任发展的非线性特点,为创新网络中组织间信任的混沌利用和控制提供理论指导。     

Nonlinear generalized master equations and accounting for initial correlations

We develop a new method based on using a time-dependent operator (generally not a projection operator) converting a distribution function (statistical operator) of a total system into the relevant form that allows deriving new exact nonlinear generalized master equations (GMEs). The derived inhomogeneous nonlinear GME is a generalization of the linear Nakajima-Zwanzig GME and can be viewed as an alternative to the BBGKY chain. It is suitable for obtaining both nonlinear and linear evolution equations. As in the conventional linear GME, there is an inhomogeneous term comprising all multiparticle initial correlations. To include the initial correlations into consideration, we convert the obtained inhomogeneous nonlinear GME into the homogenous form by the previously suggested method. We use no conventional approximation like the random phase approximation (RPA) or the Bogoliubov principle of weakening of initial correlations. The obtained exact homogeneous nonlinear GME describes all evolution stages of the (sub)system of interest and treats initial correlations on an equal footing with collisions via the modified memory kernel. As an application, we obtain a new homogeneous nonlinear equation retaining initial correlations for a one-particle distribution function of the spatially inhomogeneous nonideal gas of classical particles. In contrast to existing approaches, this equation holds for all time scales and takes the influence of pair collisions and initial correlations on the dissipative and nondissipative characteristics of the system into account consistently with the adopted approximation (linear in the gas density). We show that on the kinetic time scale, the time-reversible terms resulting from the initial correlations vanish (if the particle dynamics are endowed with the mixing property) and this equation can be converted into the Vlasov-Landau and Boltzmann equations without any additional commonly used approximations. The entire process of transition can thus be followed from the initial reversible stage of the evolution to the irreversible kinetic stage.     

A proof of the existence of Batanin's initial operad

In this paper we prove the existence of the n-globular operad used in Batanin's definition of weak n-category. This operad is initial in the category of n-globular operads equipped with two extra pieces of structure: a system of compositions and a contraction. Our approach closely follows a proof by Leinster of the existence of a similar n-globular operad used in his definition of weak n-category (itself a variant of Batanin's definition) – we show that there is a functor giving the free operad equipped with a contraction and system of compositions on an n-globular collection, and applying this functor to the initial collection gives the desired initial operad. Since there is no interaction between the contraction and operad structures we are able to treat their free constructions separately. This is not true of the system of compositions structure, which cannot exist separately from the operad structure, so we use an interleaving-style construction to describe the free operad with system of compositions.     

On an approach to the approximation of a solution of problems for the heat-conduction equation without boundary-value or initial conditions

We propose an approach to the approximation of solutions of problems for the heat-conduction equation without initial or boundary-value conditions. The solution is given as a sum of odd and even functions, and this allows one to reconstruct conditions missed in the initial setting of the problem. The method is illustrated with test examples. Bibliography: 1 title. Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 49–53.