混合混沌优化方法及其在非线性规划问题中的应用

结合逐次优化、禁忌搜索和变尺度混沌优化方法的优点，提出了一种混合混沌优化方法。该方法具有逐次优化算法的隐性并行性和收敛性，禁忌搜索的智能性和变尺度混沌优化方法的快速性。仿真计算表明，该方法具有实现简单，优化效率高，鲁棒性强等特点。     

Multidimensional Cube Packing

We consider the d-dimensional cube packing problem (d-CPP): given a list L of d-dimensional cubes and (an unlimited quantity of) d-dimensional unit-capacity cubes, called bins, find a packing of L into the minimum number of bins. We present two approximation algorithms for d-CPP, for fixed d. The first algorithm has an asymptotic performance bound that can be made arbitrarily close to 2 – (1/2)^d . The second algorithm is an improvement of the first and has an asymptotic performance bound that can be made arbitrarily close to 2 – (2/3)^d . To our knowledge, these results improve the bounds known so far for d = 2 and d = 3, and are the first results with bounds that are not exponential in the dimension.     

On the optimal design of elastic beams

In this paper we investigate the optimal dynamics of simply supported nonlinearly elastic beams with rectangular cross-sections. We consider the elastic beam under the assumption of time-dependent intensive transverse loading. The state of the beam is described by a system of partial differential equations of the fourth order. We deal with the problem of choosing the optimal shape for the beam. The optimal shape is determined in such a way that the deflection of the nonlinearly elastic beam for any given time is minimal. The problem of choosing the optimal shape is formulated as an optimal control problem. To solve the obtained problem effectively, we use the optimality principle of Bellman (Bellman and Dreyfus 1962; Bryson and Ho 1975) and the penalty function method (Polyak 1987). We present a constructive algorithm for the optimal design of nonlinearly elastic beams. Some simple examples of the implementation of the proposed numerical algorithm are given.     

Probability distribution of energetic-statistical size effect in quasibrittle fracture

The physical sources of randomness in quasibrittle fracture described by the cohesive crack model are discussed and theoretical arguments for the basic form of the probability distribution are presented. The probability distribution of the size effect on the nominal strength of structures made of heterogeneous quasibrittle materials is derived, under certain simplifying assumptions, from the nonlocal generalization of Weibull theory. Attention is limited to structures of positive geometry failing at the initiation of macroscopic crack growth from a zone of distributed cracking. It is shown that, for small structures, which do not dwarf the fracture process zone (FPZ), the mean size effect is deterministic, agreeing with the energetic size effect theory, which describes the size effect due to stress redistribution and the associated energy release caused by finite size of the FPZ formed before failure. Material randomness governs the statistical distribution of the nominal strength of structure and, for very large structure sizes, also the mean. The large-size and small-size asymptotic properties of size effect are determined, and the reasons for the existence of intermediate asymptotics are pointed out. Asymptotic matching is then used to obtain an approximate closed-form analytical expression for the probability distribution of failure load for any structure size. For large sizes, the probability distribution converges to the Weibull distribution for the weakest link model, and for small sizes, it converges to the Gaussian distribution justified by Daniels' fiber bundle model. Comparisons with experimental data on the size-dependence of the modulus of rupture of concrete and laminates are shown. Monte Carlo simulations with finite elements are the subject of ongoing studies by Pang at Northwestern University to be reported later.     

Assessing the quality of identified models through the asymptotic theory—when is the result reliable?

In this paper, the problem of estimating uncertainty regions for identified models is considered. A typical approach in this context is to resort to the asymptotic theory of Prediction Error Methods for system identification, by means of which ellipsoidal uncertainty regions can be constructed for the uncertain parameters.We show that the uncertainty regions worked out through the asymptotic theory can be unreliable in certain situations, precisely characterized in the paper.Then, we critically analyze the theoretical conditions for the validity of the asymptotic theory, and prove that the asymptotic theory also applies under new assumptions which are less restrictive than the usually required ones. Thanks to this result, we single out the classes of models among standard ones (ARX, ARMAX, Box-Jenkins, etc.) where the asymptotic theory can be safely used in practical applications to assess the quality of the identified model.These results are of interest in many applications, including iterative controller design schemes.     

A geometric approach for adaptive estimation of unknown growth kinetics in bioreactors

This paper proposes a new approach for the estimation of unknown and time-varying specific growth rate in fed-batch bioprocess. A novel adaptive estimation technique based on the concept of invariant manifold is proposed as an effective approach to estimate growth kinetic parameters. An asymptotic nonlinear observer is used to provide simultaneous on-line estimation of biomass concentration and growth kinetic. The method is easy to implement and requires only one tuning parameter. The effectiveness of the proposed algorithm is illustrated with representative bioreactor simulation examples.     

Distribution of Quasimidranges and Associated Mixtures

In this paper are presented and discussed tabulations of the cumulative distribution functions of quasimidranges and mixtures of quasimidranges of samples from a normal distribution. The tabulations extend up to samples of size 21. For quasimidranges not involving the extreme values of the sample, the departure from normality is very small. The physical problem giving rise to the mixtures is discussed.     

摩擦接触系统多极边界元法二次建模与数值优化

讨论了摩擦接触系统的建模与求解问题。将系统方程组的多极边界元法求解归结为变分问题并证明其等价性。在系统最优化数学模型的基础上,通过引入严格凸二次函数建立系统的二次规划模型,证明其最优解存在且唯一,并给出模型求解的最优性条件。     

Asymptotic Properties of a Probabilistic‐Statistical Model of Particle Classification in Hydrocyclones

The peculiarities of practical implementation of a probabilistic‐statistical model for a hydrodynamic stage of particle classification process of liquid‐solid polydisperse systems in cylinder‐conic hydrocyclones of small size have been investigated. Within reasonable assumptions, stationary solutions of the Fokker‐Planck‐Kolmogorov kinetic equation were obtained for the considered separation process. In order to describe changes in characteristics of suspension separation in hydrocyclones it was proposed to use stationary distributions, which parameters depend not only on hydraulic and dynamic features of flows inside an apparatus, but also are determined by relative magnitudes of the impact of particle classification and centrifugal forces in comparison with the intensity of random perturbations.     

Comprehensive Pareto Efficiency in robust counterpart optimization

In this paper, an innovative concept named Comprehensive Pareto Efficiency is introduced in the context of robust counterpart optimization, which consists of three sub-concepts: Pareto Robust Optimality (PRO), Global Pareto Robust Optimality (GPRO) and Elite Pareto Robust Optimality (EPRO). Different algorithms are developed for computing robust solutions with respect to these three sub-concepts. As all sub-concepts are based on the Probability of Constraint Violation (PCV), formulations of PCV under different probability distributions are derived and an alternative way to calculate PCV is also presented. Numerical studies are drawn from two applications (production planning problem and orienteering problem), to demonstrate the Comprehensive Pareto Efficiency. The numerical results show that the Comprehensive Pareto Efficiency has important significance for practical applications in terms of the evaluation of the quality of robust solutions and the analysis of the difference between different robust counterparts, which provides a new perspective for robust counterpart optimization.