大变量多输出逻辑函数实质项识别算法

在对Espresso算法进行分析改进的基础上，提出了一种基于全域识别的多输入多输出逻辑函数实质本源项、完全冗余项和相对冗余项生成算法，该算法通过对基于积项表示的多输入多输出逻辑函数的余因子计算来进行全域判断，根据全域判断结果来识别实质本源项、完全冗余项和相对冗余项，从而构成实质本源项集合、完全冗余项集合和相对冗余项集合。对基于二级SOP型的多输入多输出逻辑函数设计了多输入多输出逻辑函数优化识别软件系统，允许的最大输入变量数为128、最大输出变量数为256、最大输入输出变量总和为300、最大输入积项数为20 000。软件系统在Pentium 1.8GHz、512MB内存的计算机上通过了Benchmark例题的测试。     

蕴涵项的扩展算法

本文提出了一个把逻辑函数的积项扩展为本源蕴涵项的算法。用此算法得到的本源蕴涵项集合通过去冗过程产生的最后结果最接近绝对最小化的解。     

逻辑函数求补算法及其改进

逻辑函数求补算法存在的主要问题是时间开销大及需要的存储空间过大。该文在对递归裂变求补算法和基于最小项求补算法进行分析研究的基础上,提出了积项输入、邻项合并、积项输出的无冗余覆盖的逻辑函数求补算法。该求补算法的时间、空间的需求将大大缩小。     

超大变量多值单边逻辑函数优化算法的研究

单边多值逻辑函数是逻辑函数的一种特例,对于超大变量的逻辑函数优化,存储开销对输入变量呈2幂次方增长.针对多输入多输出单边逻辑函数的特性,通过引入特征矩阵和状态矢量的描述,求解多输出单边逻辑函数补集,以积项扩展为基础,完成多输出单边逻辑函数无冗余覆盖.通过编程实现了多输入多输出单边函数逻辑优化的算法,对影响单边函数逻辑优化效率的因素进行了分析,软件系统在奔腾1.8GHz,512MB RAM的计算机上通过了正确性验证与测试,测试结果表明性能良好,有效降低了系统的存储空间和时间开销.在相同输出变量数、积项数和无关项因子的情况下,随输入变量数的增长,优化效率随之下降;在相同输入变量数、输出变量数和积项数的情况下,随无关项因子值的增长,优化效率随之下降;在相同输入变量数、输出变量数、和无关项因子的情况下,随积项数的增长优化效率随之提高.     

大变量多输出逻辑函数实质项识别算法

在对Espresso算法进行分析改进的基础上,提出了一种基于全域识别的多输入多输出逻辑函数实质本源项、完全冗余项和相对冗余项生成算法,该算法通过对基于积项表示的多输入多输出逻辑函数的余因子计算来进行全域判断,根据全域判断结果来识别实质本源项、完全冗余项和相对冗余项,从而构成实质本源项集合、完全冗余项集合和相对冗余项集合.对基于二级SOP型的多输入多输出逻辑函数设计了多输入多输出逻辑函数优化识别软件系统,允许的最大输入变量数为128、最大输出变量数为256、最大输入输出变量总和为300、最大输入积项数为20 000.软件系统在Pentium 1.8GHz、512MB内存的计算机上通过了Benchmark例题的测试.     

重叠积项的分离算法

本文提出了一个分离重叠积项的算法。该算法在逻辑测试，函数最小化等逻辑综合的领域有重要作用。     

扩展Toffoli门及其在多输出电路设计中的应用

用量子计算电路实现布尔逻辑运算是发展量子计算的一个重要目标。提出了量子扩展Toffoli门,及其在实现多输出逻辑电路中的转换算法。该算法将传统PLA文件的SOP积项转换到实现等价逻辑功能的量子Toffoli积项,能够用量子扩展Toffoli门实现。通过MCNC基准电路的测试结果表明,与经典PLA描述相比,用扩展Toffoli门能够更有效地描述多输出逻辑函数。     

接近最小化积之和式的简化方法

本文介绍一个将任意布尔函数最小化的算法。其方法与先前首先求得全部质蕴涵项然后确定最小覆盖的方法不同。这个算法为了获得接近最小的积之和的实现,运用一组条件来选择质蕴涵项。并把它推广到多输出和不完全规定函数的情况。所提出的算法的主要特点是求解同一问题所化费的机器时间比用其它的算法少。如果只要求结果是较少的乘积项时,MINI算法对于输入、输出数目多的布尔函数可以给出较好的结果。这个算法也适合于寻求内部按积之和实现的大的布尔函数的可编程序阵列(PLA)的解。     

函数分析与组合逻辑电路延迟时间计算

准确计算组合逻辑电路的延迟时间对电路的性能评估与优化设计十分重要。本文分析组合逻辑电路的函数功能与通路延迟时间计算的关系，提出通路延迟时间的计算方法。该方法排除了伪路径（ＦａｌｓｅＰａｔｈ）及不可见路径（ＩｎｖｉｓｉｂｌｅＰａｔｈ）对延迟时间计算的影响，用Ｃ语言在ＳｕｎＳＰＡＲＣⅡ上实现的算法表明：通路延迟时间的分析、计算结果比文献［１］、［３］介绍的方法更接近于实际结果，实验结果表明：该方法计算速度快，能适应大规模电路的延迟时间分析与计算。     

逻辑函数的计算机化简

本文针对中型逻辑函数，提出了易于计算机实现的化简方法，即在化简过程中引入代数拓扑运算，在用星积运算求素项的基础上，用选择极值法求最小覆盖，大量的实验证明了该算法的正确性和易于计算机实现的有效性。     

A computational algorithm for the super-optimal solution of the model matching problem

In this paper, we develop a computational algorithm to implement the strengthened minimization technique [1] in the model matching problem which arises in robust controller design and weighted sensitivity minimization.A general algorithm is proposed for constructing unitary matrices and the extremal functions for the H^∞-optimization problem are diagonalized using the constructed unitary matrices. We impose stronger minimization conditions to force the solution of the optimization problem to be unique and explain their physical significance.     

Using sliding modes in static optimization and nonlinear programming

The paper is concerned with methods for solution of conventional optimization and mathematical programming problems [1–4] using discontinuous control algorithms. Deliberate introduction of sliding modes [5–7] into the system ensures that the output of the plant to be optimized follows the monotonically decreasing reference input, in the case of minimization, and that the constraints on the plant input parameters hold. This approach eliminates the need in hardware to obtain information on the gradients of the function to be optimized or constraining functions.The paper separately treats optimization algorithms without constraints on output parameters and with constraints of the equality and inequality types. The relation of the methods reported in the paper and gradient procedures for solution of mathematical programming problems using a special kind of penalty function is indicated.     

大变量逻辑函数最佳覆盖问题研究

逻辑函数的最佳覆盖，一直是逻辑综合领域的关键环节。尤其是大变量逻辑函数最佳覆盖，对复杂的逻辑综合更为重要，但也更加困难。本文在对逻辑覆盖算法研究的基础上，提出了适合大变量逻辑函数最佳覆盖的Beister改进算法。经过大量算题的测试表明，改进的列覆盖算法在时间复杂度和选择效果方面均优于Beister算法。     

Stabilization of continuous‐time homogeneous bilinear systems by constant inputs through nonlinear minimization with applications to the static output feedback stabilization problem

An algorithm to provide constant‐input stabilizing control inputs for multi‐input continuous‐time bilinear systems is proposed in this paper. The algorithm is based on the formal discrete‐time approximation of the system and the unconstrained nonlinear minimization. The key features of the new algorithm are as follows. First, the formal discrete‐time approximation makes the set of stabilizing control inputs star‐shaped centred at the origin, hence the minimization is to be performed only in a neighbourhood of the origin selected by the designer. Second, the algorithm is always capable of finding a solution if one exists, as long as the minimization inside the neighbourhood is successful. Third, by a slight modification, the algorithm permits us to place all the eigenvalues of the system inside a rectangular region in the complex plane, as long as it is feasible. The algorithm is also applicable to the static output feedback stabilization problem of linear time‐invariant systems. Copyright © 2007 John Wiley & Sons, Ltd.     

Constrained texture synthesis via energy minimization

This paper describes CMS (constrained minimization synthesis), a fast, robust texture synthesis algorithm that creates output textures while satisfying constraints. We show that constrained texture synthesis can be posed in a principled way as an energy minimization problem that requires balancing two measures of quality: constraint satisfaction and texture seamlessness. We then present an efficient algorithm for finding good solutions to this problem using an adaptation of graphcut energy minimization. CMS is particularly well suited to detail synthesis, the process of adding high-resolution detail to low-resolution images. It also supports the full image analogies framework, while providing superior image quality and performance. CMS is easily extended to handle multiple constraints on a single output, thus enabling novel applications that combine both user-specified and image-based control     

Stochastic radial basis function algorithms for large-scale optimization involving expensive black-box objective and constraint functions

This paper presents a new algorithm for derivative-free optimization of expensive black-box objective functions subject to expensive black-box inequality constraints. The proposed algorithm, called ConstrLMSRBF, uses radial basis function (RBF) surrogate models and is an extension of the Local Metric Stochastic RBF (LMSRBF) algorithm by Regis and Shoemaker (2007a) [1] that can handle black-box inequality constraints. Previous algorithms for the optimization of expensive functions using surrogate models have mostly dealt with bound constrained problems where only the objective function is expensive, and so, the surrogate models are used to approximate the objective function only. In contrast, ConstrLMSRBF builds RBF surrogate models for the objective function and also for all the constraint functions in each iteration, and uses these RBF models to guide the selection of the next point where the objective and constraint functions will be evaluated. Computational results indicate that ConstrLMSRBF is better than alternative methods on 9 out of 14 test problems and on the MOPTA08 problem from the automotive industry (Jones, 2008 [2]). The MOPTA08 problem has 124 decision variables and 68 inequality constraints and is considered a large-scale problem in the area of expensive black-box optimization. The alternative methods include a Mesh Adaptive Direct Search (MADS) algorithm (Abramson and Audet, 2006 [3]; Audet and Dennis, 2006 [4]) that uses a kriging-based surrogate model, the Multistart LMSRBF algorithm by Regis and Shoemaker (2007a) [1] modified to handle black-box constraints via a penalty approach, a genetic algorithm, a pattern search algorithm, a sequential quadratic programming algorithm, and COBYLA (Powell, 1994 [5]), which is a derivative-free trust-region algorithm. Based on the results of this study, the results in Jones (2008) [2] and other approaches presented at the ISMP 2009 conference, ConstrLMSRBF appears to be among the best, if not the best, known algorithm for the MOPTA08 problem in the sense of providing the most improvement from an initial feasible solution within a very limited number of objective and constraint function evaluations.     

适用于复杂函数优化的多群体遗传算法

提出一种适合于复杂函数寻优的多群体遗传算法。该方法对搜索区域进行划分，使每个子区域具有简单的函数形态，而对每个子区域安排一个子群体进行搜索。这个过程可并行进行。仿真表明该方法速度快，可同时获得多个局部极值点。     

Minimizing binary functions with simulated annealing algorithm with applications to binary tomography

The minimization of binary functions finds many applications in practice, and can be solved by the simulated annealing (SA) algorithm. However, the SA algorithm is designed for general combinatorial problems, not specifically for binary problems. Consequently, a direct application of the SA algorithm might not provide optimal performance and efficiency. Therefore, this study specifically investigated the performance of various implementations of the SA algorithm when applied to binary functions. Results obtained in this investigation demonstrated that 1) the SA algorithm can reliably minimize difficult binary functions, 2) a simple technique, analogous to the local search technique used in minimizing continuous functions, can exploit the special structure of binary problems and significantly improve the solution with negligible computational cost, and 3) this technique effectively reduces computational cost while maintaining reconstruction fidelity in binary tomography problems. This study also developed two classes of binary functions to represent the typical challenges encountered in minimization.     

基于多层水平集函数的三维多相图像分割

多相图像分割通常利用多个水平集函数分别定义不同区域的特征函数,其极值求解问题需要对多个函数分别求极值,计算效率较低。针对三维多相图像,提出一种改进的变分水平集模型,采用一个多层水平集函数的n层水平集隐式曲面,将图像划分为n个区域,通过对一个水平集函数求极值,实现三维多相分段常值图像的快速分割与重建。将能量泛函表达为数据项和规则项,借助规则化Heaviside函数设计区域划分的通用特征函数,采用Split-Bregman投影方法进行能量最小化求解。实验结果表明,该模型可以有效地实现三维多相图像分割,与Chan-Vese模型相比,其迭代步数较少,分割速度较快。     

Computation of signal output probability for Boolean functions represented by OBDD

In [l] and [2], two algorithms have been proposed to calculate the output probability of Boolean functions represented by OBDDs, assuming that the input variables are equiprobable and each variable is statistically independent from others. In this paper, we point out that under these assumptions, the output probability calculation is equivalent to counting the number of minterms of the corresponding Boolean functions. An algorithm is proposed to compute the output probability using simple integer arithmetic as opposed to floating point arithmetic involved in [1,2]. To compute output probability of Boolean functions represented by shared OBDI)s and OBDDs with edge negation, we further propose a generalized algorithm.