A Monte Carlo method for an objective Bayesian procedure

This paper describes a method for an objective selection of the optimal prior distribution, or for adjusting its hyper-parameter, among the competing priors for a variety of Bayesian models. In order to implement this method, the integration of very high dimensional functions is required to get the normalizing constants of the posterior and even of the prior distribution. The logarithm of the high dimensional integral is reduced to the one-dimensional integration of a cerain function with respect to the scalar parameter over the range of the unit interval. Having decided the prior, the Bayes estimate or the posterior mean is used mainly here in addition to the posterior mode. All of these are based on the simulation of Gibbs distributions such as Metropolis' Monte Carlo algorithm. The improvement of the integration's accuracy is substantial in comparison with the conventional crude Monte Carlo integration. In the present method, we have essentially no practical restrictions in modeling the prior and the likelihood. Illustrative artificial data of the lattice system are given to show the practicability of the present procedure.     

An algorithm for the linear complementarity problem with upper and lower bounds

In this paper, we adapt the octahedral simplicial algorithm for solving systems of nonlinear equations to solve the linear complementarity problem with upper and lower bounds. The proposed algorithm generates a piecewise linear path from an arbitrarily chosen pointz ⁰ to a solution point. This path is followed by linear programming pivot steps in a system ofn linear equations, wheren is the size of the problem. The starting pointz ⁰ is left in the direction of one of the 2 ⁿ vertices of the feasible region. The ray along whichz ⁰ is left depends on the sign pattern of the function value atz ⁰. The sign pattern of the linear function and the location of the points in comparison withz ⁰ completely govern the path of the algorithm.This research is part of the VF-Program Equilibrium and Disequilibrium in Demand and Supply, approved by the Netherlands Ministry of Education, Den Haag, The Netherlands.     

Recursive solution of linear-quadratic Nash games for weakly interconnected systems

A recursive method is developed for the solution of coupled algebraic Riccati equations and corresponding linear Nash strategies of weakly interconnected systems. It is shown that the given algorithm converges to the exact solution with the rate of convergence ofO(²), where is a small coupling parameter. In addition, only low-order systems are involved in algebrdic computations; the amount of computations required does not grow per iteration and no analyticity assumption is imposed on the system coefficients.This work was supported by Rutgers University Research Council under Grant No. 2-02188.     

Minimum concave cost production system: A further generalization of multi-echelon model

We will consider a concave minimization problem associated with a series production system in which raw material is processed inm consecutive facilities. The products at some facility are either sent to the next facility or stocked in the warehouse. The amount of demand for the final products during periodi, i = 1,,n, are known in advance. Our problem is to minimize the sum of processing, holding and backlogging cost, all of which are assumed to be concave.The origin of this model is the classical economic lot size problem of Wagner and Whitin and was extensively studied by Zangwill. This model is very important from the theoretical as well as practical point of view and this is one of the very rare instances in which polynomial time algorithm has been constructed for concave minimization problems.The purpose of this paper is to extend the model further to the situation in which time lag is associated with processing at each facility. We will propose an efficient O(n ⁴ m) algorithm for this class of problems.     

Dynamic optimization problems with bounded terminal conditions

Bounded terminal conditions of nonlinear optimization problems are converted to equality terminal conditions via the Valentine's device. In so doing, additional unknown parameters are introduced into the problem. The transformed problems can still be easily solved using the sequential gradient-restoration algorithm (SGRA) via a simple augmentation of the unknown parameter vector . Three example problems with bounded terminal conditions are solved to verify this technique.This research was supported in part by the National Aeronautics and Space Administration under NASA Grant No. NCC 2-106.     

On the average length of lexicographic paths

A bound is given for the average length of a lexicographic path, a definition that is motivated by degeneracies encountered when using the randomized simplex method.     

Optimization of culture parameters for production of podophyllotoxin in suspension culture of Podophyllum hexandrum

The root explants of the germinated seedlings of Podophyllum hexandrum were grown in MS medium supplemented with indole acetic acid (IAA) (2 mg/L) and activated charcoal (0.5%), and healthy callus culture was obtained after incubation for 3 wk at 20°C. The cultivation of plant cells in shake flask was associated with problems such as clumping of cells and browning of media, which were solved by the addition of pectinase and polyvinylpyrrolidone. The effect of major media components and carbon source was studied on the growth and podophyllotoxin production in suspension culture. It was found that glucose was a better carbon source than sucrose and that NH₄ ⁺:NO₃ ⁻ ratio (total nitrogen concentration of 60 mM) and PO₄ ³⁻ did not have much effect on the growth and product formation. The relative effect of culture parameters (inoculum level, pH, IAA, glucose, NH₄ ⁺:NO₃ ⁻ ratio, and PO₄ ³⁻) on the overall growth and product response of the plant cell suspension culture was further investigated by Plackett-Burman design. This indicated that inoculum level, glucose, IAA, and pH had significant effects on growth and production of podophyllotoxin. To identify the exact optimum concentrations of these parameters on culture growth and podophyllotoxin production, central composite design experiments were formulated. The overall response equations with respect to growth and podophyllotoxin production as a function of these culture parameters were developed and used to determine the optimum concentrations of these parameters, which were pH 6.0, 1.25 mg/L of IAA, 72 g/L of glucose, and inoculum level of 8 g/L.     

Determining molecular structures and conformations directly from electron diffraction using a genetic algorithm.

A global optimization strategy, based upon application of a genetic algorithm (GA), is demonstrated as an approach for determining the structures of molecules possessing significant conformational flexibility directly from gas-phase electron diffraction data. In contrast to the common approach to molecular structure determination, based on trial-and-error assessment of structures available from quantum chemical calculations, the GA approach described here does not require expensive quantum mechanical calculations or manual searching of the potential energy surface of the sample molecule, relying instead upon simple comparison between the experimental and calculated diffraction pattern derived from a proposed trial molecular structure. Structures as complex as all-trans retinal and p-coumaric acid, both important chromophores in photosensing processes, may be determined by this approach. In the examples presented here, we find that the GA approach can determine the correct conformation of a flexible molecule described by 11 independent torsion angles. We also demonstrate applications to samples comprising a mixture of two distinct molecular conformations. With these results we conclude that applications of this approach are very promising in elucidating the structures of large molecules directly from electron diffraction data.     

杂合型全局优化法优化水分子团簇结构

基于遗传算法、快速模拟退火及共轭梯度方法提出了一种快速的杂合型全局优化方法(fast hybrid global optimization algorithm, FHGOA),并将这一方法应用于TIP3P和TIPS2模型水分子团簇(H2O)n结构的优化.在进行TIP3P模型水分子团簇结构的优化过程中,发现了能量比文献值更低的团簇结构,且执行效率有较大提高.把该方法应用到优化TIPS2模型的水分子团簇,发现最优结构和采用TTM2-F模型优化的水分子团簇结构在n < 17时完全相同,为全表面结构;而在n=17、19、22时为单中心水分子笼状结构;在n=25、27时为双中心水分子笼状结构.说明随着团簇中水分子个数的增加,采用TIPS2和TTM2-F势能函数优化的团簇最优结构有相同的变化趋势.     

不依赖于统计模型的手性毛细管电泳分离多指标同时优化

考虑到手性毛细管电泳分离机理的复杂性，提出了不依赖于统计模型的二进制编码遗传算法多目标优化策略。根据实验参数的多少及其重要性，采用均匀设计安排完成初步实验。并用Derringer功效函数作为多指标同时优化的评价指标，以取得较高的分离度和较快分离速度；通过对实验参数给予编码，转化为二进制字符串，根据得到的总功效函数值大小进行遗传算法操作，产生新的一组实验条件。重复上述过程直到得到最佳分离条件为止。此方法成功地应用于华法令对映体的毛细管电泳分离条件优化。