Optimization of technology parameters for the plane-strain component in the process of gas quenching

The paper introduces an optimization method for the technology parameters of the plane-strain component in the process of gas quenching. Distortion, residual stress, average surface hardness and standard deviation of surface hardness are regarded as the optimization objectives. A new heat transfer coefficient model is presented, five distinct heat transfer coefficients are used at various regions of the model. The five heat transfer coefficients are regarded as the design variables, and four regressive equations are established by using response surface method. The four equations, respectively represent the relations between the four optimization objectives and the design variables. A multi-objectives optimization model is established, and the multi-objectives optimization model is optimized by the non-linear method. The optimized technology parameters are used to simulate the gas quenching process by FEM software. The quenching results after optimization are compared with those before optimization. The comparison shows that the quenching quality after optimization is better than that before optimization. After optimization, the four optimization objectives are all improved.     

A filled function method for constrained global optimization

In this paper, a filled function method for solving constrained global optimization problems is proposed. A filled function is proposed for escaping the current local minimizer of a constrained global optimization problem by combining the idea of filled function in unconstrained global optimization and the idea of penalty function in constrained optimization. Then a filled function method for obtaining a global minimizer or an approximate global minimizer of the constrained global optimization problem is presented. Some numerical results demonstrate the efficiency of this global optimization method for solving constrained global optimization problems.     

Successive Optimization Method via Parametric Monotone Composition Formulation*

In this paper a successive optimization method for solving inequality constrained optimization problems is introduced via a parametric monotone composition reformulation. The global optimal value of the original constrained optimization problem is shown to be the least root of the optimal value function of an auxiliary parametric optimization problem, thus can be found via a bisection method. The parametric optimization subproblem is formulated in such a way that it is a one-parameter problem and its value function is a monotone composition function with respect to the original objective function and the constraints. Various forms can be taken in the parametric optimization problem in accordance with a special structure of the original optimization problem, and in some cases, the parametric optimization problems are convex composite ones. Finally, the parametric monotone composite reformulation is applied to study local optimality.     

线性约束三次规划问题的全局最优性必要条件和最优化算法

讨论了带线性不等式约束三次规划问题的最优性条件和最优化算法. 首先, 讨论了带有线性不等式约束三次规划问题的 全局最优性必要条件. 然后, 利用全局最优性必要条件, 设计了解线性约束三次规划问题的一个新的局部最优化算法(强局部最优化算法). 再利用辅助函数和所给出的新的局部最优化算法, 设计了带有线性不等式约束三 规划问题的全局最优化算法. 最后, 数值算例说明给出的最优化算法是可行的、有效的.     

施工网络计划优化的极值种群遗传算法

针对普通遗传算法用于施工网络计划优化的缺点,通过种群划分与极值搜索,建立了网络计划优化的极值种群改进遗传算法模型,有效地避免了陷入局部极值点,应用证明,该算法与普通遗传算法相比,具有优化速度快、求解精度高,全局寻优能力强等优点,尤其适合于大型复杂工程网络的优化计算。     

Time-dependent reliability-based design optimization with probabilistic and interval uncertainties

Time-dependent reliability-based design optimization with both probabilistic and interval uncertainties is a cost-consuming problem in engineering practice which generally needs huge computational burden. In order to deal with this issue, a sequential single-loop optimization strategy is established in this work. The established sequential single-loop optimization strategy converts the original triple-loop optimization into a sequence of deterministic optimization, the estimations of time instant and interval value that corresponding to the worst case scenario, and the minimum performance target point searching. Two key points in the sequential single-loop optimization strategy guarantee the high efficiency of the proposed strategy. One is that no iterative searching step is needed to find the minimum performance target point at each iteration in the proposed sequential single-loop optimization strategy. The other is that only the correction step needs the reliability analysis to correct the design parameter solutions. In the example section, four minimum performance target point searching techniques are combined with the sequential single-loop optimization strategy to solve the corresponding optimization problems so to illustrate the effectiveness of the established strategy.     

Scalarization of the fuzzy optimization problems

Scalarization of the fuzzy optimization problems using the embedding theorem and the concept of convex cone (ordering cone) is proposed in this paper. Two solution concepts are proposed by considering two convex cones. The set of all fuzzy numbers can be embedded into a normed space. This motivation naturally inspires us to invoke the scalarization techniques in vector optimization problems to solve the fuzzy optimization problems. By applying scalarization to the optimization problem with fuzzy coefficients, we obtain its corresponding scalar optimization problem. Finally, we show that the optimal solution of its corresponding scalar optimization problem is the optimal solution of the original fuzzy optimization problem.     

基于动力系统的线性不等式组的解法

本文提出了一种新的求解线性不等式组可行解的方法-基于动力系统的方法．假设线性不等式组的可行域为非空,在可行域的相对内域上建立一个非线性关系表达式,进而得到一个结构简单的动力系统模型．同时,定义了穿越方向。文章最后的数值实验结果表明此算法是有效的．     

求解线性不等式组的方法

本提出了一个新的求解线性不等式组可行解的方法－－无约束极值方法。通过在线性不等式组的非空可行域的相对内域上建立一个非线性极值问题，根据对偶关系，得到了一个对偶空间的无约束极值及原始，对偶变量之间的简单线性映射关系，这样将原来线性不等式组问题的求解转化为一个无约束极值问题。中主要讨论了求解无约束极值问题的共轭梯度算法。同时，在寻找不等式组可行解的过程中，定义了穿越方向，这样大大减少计算量。中最后数值实验结果表明此算法是有效的。     

UNIFORM APPROXIMATION OF A MULTIOBJECTIVE OPTIMIZATION SEQUENCE

In this paper the Pareto efficiency of a uniformly convergent multiobjective optimization sequence is studied. We obtain some relation between the Pareto efficient solutions of a given multiobjective optimization problem and those of its uniformly convergent optimization sequence and also some relation between the weak Pareto efficient solutions of the same optimization problem and those of its uniformly convergent optimization sequence. Besides, under a compact convex assumption for constraints set and a certain convex assumption for both objective and constraint functions, we also get some sufficient and necessary conditions that the limit of solutions of a uniformly convergent multiobjective optimization sequence is the solution of a given multiobjective optimization problem.     

Necessary Optimality Conditions and New Optimization Methods for Cubic Polynomial Optimization Problems with Mixed Variables

Multivariate cubic polynomial optimization problems, as a special case of the general polynomial optimization, have a lot of practical applications in real world. In this paper, some necessary local optimality conditions and some necessary global optimality conditions for cubic polynomial optimization problems with mixed variables are established. Then some local optimization methods, including weakly local optimization methods for general problems with mixed variables and strongly local optimization methods for cubic polynomial optimization problems with mixed variables, are proposed by exploiting these necessary local optimality conditions and necessary global optimality conditions. A global optimization method is proposed for cubic polynomial optimization problems by combining these local optimization methods together with some auxiliary functions. Some numerical examples are also given to illustrate that these approaches are very efficient.     

Global optimization method using adaptive and parallel ensemble of surrogates for engineering design optimization

As a robust and efficient technique for global optimization, surrogate-based optimization method has been widely used in dealing with the complicated and computation-intensive engineering design optimization problems. It’s hard to select an appropriate surrogate model without knowing the behaviour of the real system a priori in most cases. To overcome this difficulty, a global optimization method using an adaptive and parallel ensemble of surrogates combining three representative surrogate models with optimized weight factors has been proposed. The selection of weight factors is treated as an optimization problem with the desired solution being one that minimizes the generalized mean square cross-validation error. The proposed optimization method is tested by considering several well-known numerical examples and one industrial problem compared with other optimization methods. The results show that the proposed optimization method can be a robust and efficient approach in surrogate-based optimization for locating the global optimum.     

A rolling window optimization method for large-scale WCDMA base stations planning problem

The large-scale base station planning problem for wideband code division multiple access (WCDMA) wireless networks is studied in this paper. A new rolling window optimization method is presented, where the global optimization problem is decomposed into small optimization sub-problems, which are defined on a series of successive rolling windows. Effective rolling strategies are designed in the rolling optimization method based on the prediction of the interference among the base stations in the WCDMA wireless network. We show that the proposed method has the property that the global objective is non-increasing in the successive optimization procedure. Simulations are carried out to analyze the performance of the proposed optimization method, which show the importance of the rolling strategy.     

一种改进的禁忌搜索算法及其在连续全局优化中的应用

禁忌搜索算法是一种元启发式的全局优化算法,是局部搜索算法的一种推广,已被成功地应用于许多组合优化问题中。本文针对有界闭区域上的连续函数全局优化问题,提出了一种改进的禁忌搜索算法,并进行了理论分析和数值实验。数值实验表明,对于连续函数全局优化问题的求解该算法是可行有效的,并且结构简单,迭代次数较少,是一种较好的全局启发式优化算法。     

On relaxations of the max k-cut problem formulations

A tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max k-cut problem is a fundamental combinatorial optimization problem with multiple notorious mixed integer optimization formulations. In this paper, we explore four existing mixed integer optimization formulations of the max k-cut problem. Specifically, we show that the continuous relaxation of a binary quadratic optimization formulation of the problem is: (i) stronger than the continuous relaxation of two mixed integer linear optimization formulations and (ii) at least as strong as the continuous relaxation of a mixed integer semidefinite optimization formulation. We also conduct a set of experiments on multiple sets of instances of the max k-cut problem using state-of-the-art solvers that empirically confirm the theoretical results in item (i). Furthermore, these numerical results illustrate the advances in the efficiency of global non-convex quadratic optimization solvers and more general mixed integer nonlinear optimization solvers. As a result, these solvers provide a promising option to solve combinatorial optimization problems. Our codes and data are available on GitHub.     

A critical review of discrete filled function methods in solving nonlinear discrete optimization problems

Many real life problems can be modeled as nonlinear discrete optimization problems. Such problems often have multiple local minima and thus require global optimization methods. Due to high complexity of these problems, heuristic based global optimization techniques are usually required when solving large scale discrete optimization or mixed discrete optimization problems. One of the more recent global optimization tools is known as the discrete filled function method. Nine variations of the discrete filled function method in literature are identified and a review on theoretical properties of each method is given. Some of the most promising filled functions are tested on various benchmark problems. Numerical results are given for comparison.     

An efficient optimization method for mechanical shells considering cut-outs

In this contribution an optimization method for shell structures is presented. This method was developed in order to perform a simultaneous optimization of the shape and position of the mid surface and a topology optimization to introduce cut-outs. A topology optimization method for continuum structures is combined with a manufacturing constraint for deep drawable sheet metals. It is shown, how more than a million design variables can be handled efficiently using a mathematical optimization algorithm for the design update and the finite element method for the structural simulation. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

超越方程的优化解法

针对粒子群算法局部搜索能力差,后期收敛速度慢等缺点,提出了一种改进的粒子群算法,该算法是在粒子群算法后期加入拟牛顿方法,充分发挥了粒子群算法的全局搜索性和拟牛顿法的局部精细搜索性,从而克服了粒子群算法的不足,把超越方程转化为函数优化的问题,利用该算法求解,数值实验结果表明,算法有较高的收敛速度和求解精度。     

An (α ,β)-Optimal solution concept in Fuzzy Optimization problems

We propose an (α,β)-optimal solution concept of fuzzy optimization problem based on the possibility and necessity measures. It is well known that the set of all fuzzy numbers can be embedded into a Banach space isometrically and isomorphically. Inspired by this embedding theorem, we can transform the fuzzy optimization problem into a biobjective programming problem by applying the embedding function to the original fuzzy optimization problem. Then the (α,β)-optimal solutions of fuzzy optimization problem can be obtained by solving its corresponding biobjective programming problem. We also consider the fuzzy optimization problem with fuzzy coefficients (i.e., the coefficients are assumed as fuzzy numbers). Under a setting of core value of fuzzy numbers, we provide the Karush–Kuhn–Tucker optimality conditions and show that the optimal solution of its corresponding crisp optimization problem (the usual optimization problem) is also a (1,1)-optimal solution of the original fuzzy optimization problem.