Fuzzy Weirstrass theorem and convex fuzzy mappings

The convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers. The local-global minimum property of real-valued convex functions is extended to convex fuzzy mappings. It is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer. Characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given. In addition, the Weirstrass theorem is extended from real-valued functions to fuzzy mappings.     

The solution of the inverse problem of gravitational potential using a set of measurements of different field elements

A numerical solution of the inverse problem of the gravitational field at a single point is obtained using six field elements for a point, a spherical cap, a differential spherical sector and a vertical segment. In the system of six equations obtained, the unknowns are the mass of the body, the depth of its center, and the second, third, and fourth degree moments. The accuracy of the solution of this system is ten times higher than when using three field elements. __________ Translated from Izmeritel’naya Tekhnika, No. 5, pp. 3–8, May, 2007.     

Optimization by random search with jumps

We give a random optimization (RO) algorithm to optimize a real‐valued function of n real variables. During the optimization process, interpolation points are examined to follow valleys, and jumps to new starting points are executed to avoid numerous iterations in local minima. Convergence with probability one to the global minimum of a function is proved. The proposed RO method is a simple, derivative‐free and computationally moderate algorithm, with excellent performance compared to other RO methods. Seven functions, which are commonly used to test the performance of optimization methods, are used to evaluate the performance of the RO algorithm given here. Copyright © 2004 John Wiley & Sons, Ltd.     

Solution of a multidimensional inverse radiation problem by means of mode reduction

The Karhunen–Loève Galerkin procedure is employed to solve an inverse radiation problem of determining the time‐varying strength of a heat source, which mimics flames in a furnace, from temperature measurements in three‐dimensional participating media where radiation and conduction occur simultaneously. The inverse radiation problem is solved through the minimization of a performance function, which is expressed by the sum of square residuals between calculated and observed temperature, using a conjugate gradient method. Through the Karhunen–Loève Galerkin procedure, one can represent the system dynamics with a minimum degree of freedom, and consequently the amount of computation required in the solution of the inverse problem is reduced drastically when the present technique is adopted. Copyright © 2004 John Wiley & Sons, Ltd.     

应用PIMS选油模型实施进口原油优化选购

应用AspenTech公司PIMS软件，模拟炼油企业生产经营过程，综合考虑原油成本、产品价格以及长岭分公司炼油厂加工流程特点和产品质量等要求，建立了适用于该厂的原油选购模型。利用该模型对该企业2002年第三季度进口原油品种进行优化选择，对综合效益好的原油实施采购。实际生产数据表明，该模型比较准确。     

HAT-095催化剂运行末期的优化探索

通过优化工艺条件,严控进料质量、改造循环氢压缩机油系统、调整二甲苯塔操作等措施,使催化剂在运行末期,也能发挥出良好的催化性能,并延长催化剂使用寿命;提高了催化剂处理C10芳烃的能力,降低重芳烃产率,提高经济效益。为催化剂运行末期操作和正常操作提供有益的探索。     

Analysis of an algorithm for solution of conditional optimization problems with linear-fractional objective functions over permutations

A method is considered to solve a conditional optimization problem with a linear-fractional objective function over permutations. The performance of sub algorithms to solve this problem is evaluated. The practical efficiency of the algorithm is analyzed by conducting numerical experiments. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 133–146, July–August 2007.     

基于多随机变量风险约束的水电站长期优化调度

针对市场环境下水电站如何综合考虑电价和来水等不确定性因素下的优化调度是当前研究的热点和难点,建立了考虑电价和来水等不确定性因素的风险约束水电站长期优化调度模型。根据此模型发电商可方便地在预期的目标收益和风险之间进行权衡,达到以较小的风险获得较大的收益的目的。以二滩电厂实算为例,表明了该模型的有效性。     

Optimal design of gating systems by gradient search methods

A numerical optimization technique based on gradient-search is applied to obtain an optimal design of a typical gating system used for the gravity process to produce aluminum parts. This represents a novel application of coupling nonlinear optimization techniques with a foundry process simulator, and it is motivated by the fact that a scientifically guided search for better designs based on techniques that take into account the mathematical structure of the problem is preferred to commonly found trial-and-error approaches. The simulator applies the finite volume method and the VOF algorithm for CFD analysis. The direct gradient optimization algorithm, sequential quadratic programming (SQP), was used to solve both a 2D and a 3D gating system design problems using two design variables. The results clearly show the effectiveness of the proposed approach for finding high quality castings when compared with current industry practices.