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.     

COMBINED PARTIAL OXIDATION AND CARBONDIOXIDE REFORMING OF METHANE PROCESS TO SYNTHESIS GAS

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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.     

(BN)n(n≤12)团簇的结构及成键性质

利用遗传算法和Gastreich提出的经验势函数研究了(BN)_n(n≤12)团簇的可能稳定结构, 并对能量较低的异构体在HF/6-31G(d)水平进行优化, 得到了(BN)_n(n≤12)团簇的线状、蒲扇形、单环、双环、三环和笼状结构, 讨论了各种结构的特征及相对稳定性. 分析了BN团簇中原子的成键性质, 在单环结构中, N原子以sp2杂化成键, B原子以sp杂化成键, 而在节点处B原子以sp2杂化成键. (BN)6是唯一没有张力的单环结构.     

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。     

Properties of a genetic algorithm extended by a random self-learning operator and asymmetric mutations: A convergence study for a task of powder-pattern indexing

Genetic algorithms represent a powerful global-optimisation tool applicable in solving tasks of high complexity in science, technology, medicine, communication, etc. The usual genetic-algorithm calculation scheme is extended here by introduction of a quadratic self-learning operator, which performs a partial local search for randomly selected representatives of the population. This operator is aimed as a minor deterministic contribution to the (stochastic) genetic search. The population representing the trial solutions is split into two equal subpopulations allowed to exhibit different mutation rates (so called asymmetric mutation). The convergence is studied in detail exploiting a crystallographic-test example of indexing of powder diffraction data of orthorhombic lithium copper oxide, varying such parameters as mutation rates and the learning rate. It is shown through the averaged (over the subpopulation) fitness behaviour, how the genetic diversity in the population depends on the mutation rate of the given subpopulation. Conditions and algorithm parameter values favourable for convergence in the framework of proposed approach are discussed using the results for the mentioned example. Further data are studied with a somewhat modified algorithm using periodically varying mutation rates and a problem-specific operator. The chance of finding the global optimum and the convergence speed are observed to be strongly influenced by the effective mutation level and on the self-learning level. The optimal values of these two parameters are about 6 and 5%, respectively. The periodic changes of mutation rate are found to improve the explorative abilities of the algorithm. The results of the study confirm that the applied methodology leads to improvement of the classical genetic algorithm and, therefore, it is expected to be helpful in constructing of algorithms permitting to solve similar tasks of higher complexity.