基于遗传算法的临床营养治疗食谱优化研究

提出一种基于MATLAB遗传算法的线性整数规划算法,求解临床营养上的治疗食谱优化问题,建立满足营养素要求的约束方程和最小化花费等式的整数线性规划数学模型,利用matlab中的遗传算法与直接搜索工具箱GADS求解,很好地解决临床的治疗食谱优化问题。     

基于信息素的整数规划的演化求解

将蚁群算法中基于信息素的正反馈方法引入到求解整数规划演化算法之中,实现了每一个体等位基因的优化,使算法稳定地收敛到全局最优解.以下料问题为例,对算法进行了实验分析.运算结果表明,该算法对于整数规划问题有很好的效果.     

基于抗原中介三链DNA结构的0-1整数规划

利用同源的存在抗原蛋白质的脱氧核苷酸定位于双链DNA中很容易形成三螺旋结构的DNA链,可以利用这种独特的结构来研究一些可能的或可行的的计算模型。尝试了用三螺旋结构的DNA链来解决简单的0-1整数规划问题。而对于整数规划和可满足问题都可以转化为0-1整数规划来解决,从而都可以利用三链DNA计算模型得以解决。     

改进和声搜索算法求解一般整数规划问题

设计了一种改进的和声搜索算法对一般的整数规划问题进行求解,在计算机上予以实现。经实验测试,相对遗传模拟退火算法和混合遗传算法,获得了同样甚至更好的解。由于改进和声搜索算法使用灵活,因此对于线性和非线性的整数规划问题都能进行求解。     

CDF97整数小波变换在DM642上的实现与优化

本文基于T1的TMS320DM642芯片.提出了一套CDF97小波的整数实现方案.使用QDMA实现了图像数据在存储空间中的高速搬移,并对小波算法部分进行了线性汇编优化,进而提高了实时性,达到了应用所需的计算速率,对于256x256的灰度图,分解层数为两层时.计算速率可达100帧/s.     

柔性制造系统的托盘优化

本文讨论Job-shop型柔性制造系统的托盘优化问题,给出了求最小托盘数的算法,把托 盘优化问题化成了求解线性整数规划问题.     

基于多级抽取的0-1整数规划问题的DNA算法

DNA计算是一种借助于分子生物技术进行计算的新方法,在解决一类困难问题特别是NP-完全问题上具有硅计算机无法比拟的优势,利用DNA计算求解0-1整数规划问题的研究具有重大的意义.基于多级分离模型解决0-1整数规划问题,且给出DNA算法.通过一个实例给出了操作的步骤.     

基于粒子群算法的分布式计算系统能效优化方法

在分布式计算领域中,需要合理分配计算资源.传统方法通过建立精确的复杂模型并转换为近似线性整数规划模型进行求解,会造成较大误差.对此,提出一种粒子群优化算法,直接使用精确非线性整数规划模型,在基本的粒子群优化算法中加入问题的约束.同时对粒子进行离散化,使用真实的目标函数值来评估粒子的适应度,能够在较短时间内收敛且离最优解的误差相对较小.仿真实验表明,该算法在单位利润、完工时间、总能量消耗方面均取得了不错的效果.     

Matlab语言在整数规划中的应用

该文提出了用枚举法解决线性函数中的整数规划问题。应用Matlab语言的线性规划函数linprog,先取消整数限制求解;因目标函数为线性函数,它具有一致倾斜性,再求出整数规划的最优解。由于文章所提算法可以很便捷算出整数规划的最优解,因而避免了原有算法的一些困境。     

基于粒子群优化的军事物流配送中心选址

针对当前军事物流配送改革中配送中心选址问题,在成本最小的基础上,构建了一个混合整数规划模型,并将粒子群优化算法(PSO)引入到模型的求解中,采用离散PSO解决物流配送中心选择问题,用基本PSO解决货物运输分配问题,通过嵌套调用离散PSO和基本PSO,得到模型最优解.该方法降低了计算复杂度,有效选择了物流配送中心,优化了军事物流网络.实例表明了方法的可行性和有效性.     

An Integer Linear Programming Problem with Multi-Criteria and Multi-Constraint Levels: a Branch-and-Partition Algorithm

In this paper, we propose a branch-and-partition algorithm to solve the integer linear programming problem with multi-criteria and multi-constraint levels (MC-ILP). The procedure begins with the relaxation problem that is formed by ignoring the integer restrictions. In this branch-and-partition procedure, an MC linear programming problem is adopted by adding a restriction according to a basic decision variable that is not integer. Then the MC-simplex method is applied to locate the set of all potential solutions over possible changes of the objective coefficient parameter and the constraint parameter for a regular MC linear programming problem. We use parameter partition to divide the (λ, γ) space for integer solutions of MC problem. The branch-and-partition procedure terminates when every potential basis for the relaxation problem is a potential basis for the MC-ILP problem. A numerical example is used to demonstrate the proposed algorithm in solving the MC-ILP problems. The comparison study and discussion on the applicability of the proposed method are also provided.     

A solution approach based on Benders decomposition for the preventive maintenance scheduling problem of a stochastic large-scale energy system

This paper describes a Benders decomposition-based framework for solving the large scale energy management problem that was posed for the ROADEF 2010 challenge. The problem was taken from the power industry and entailed scheduling the outage dates for a set of nuclear power plants, which need to be regularly taken down for refueling and maintenance, in such a way that the expected cost of meeting the power demand in a number of potential scenarios is minimized. We show that the problem structure naturally lends itself to Benders decomposition; however, not all constraints can be included in the mixed integer programming model. We present a two phase approach that first uses Benders decomposition to solve the linear programming relaxation of a relaxed version of the problem. In the second phase, integer solutions are enumerated and a procedure is applied to make them satisfy constraints not included in the relaxed problem. To cope with the size of the formulations arising in our approach we describe efficient preprocessing techniques to reduce the problem size and show how aggregation can be applied to each of the subproblems. Computational results on the test instances show that the procedure competes well on small instances of the problem, but runs into difficulty on larger ones. Unlike heuristic approaches, however, this methodology can be used to provide lower bounds on solution quality.     

Exact procedures for solving the discrete ordered median problem

The discrete ordered median problem (DOMP) integrates classical discrete location problems, such as the N-median, N-center and Uncapacitated Facility Location problems. It was introduced by Nickel (In: Fleischmann B, Lasch R, Derigs U, Domschke W, Rieder U, editors. Operations Research Proceedings 2000, Berlin: Springer, 2001. p. 71–76), who formulated it as both a nonlinear and a linear integer program. We propose an alternative integer linear programming formulation for the DOMP, discuss relationships between both integer linear programming formulations, and show how properties of optimal solutions can be used to strengthen these formulations. Moreover, we present a specific branch and bound procedure to solve the DOMP more efficiently. We test the integer linear programming formulations and this branch and bound method computationally on randomly generated test problems.     

线性规划软件包GLPK的分析与应用

GLPK是一个求解大规模的线性规划问题(LP)、混合整数规划问题(MIP)以及相关问题的自由软件包。该文分析TGLPK的算法结构与数值计算等多方面的实现技术，并应用于解决NP-hard的调度问题。数值结果表明GLPK是研究LP和MIP问题强有力的工具。     

A branch and bound method for the line balancing problem in U-shaped assembly lines with equipment requirements

In this study we consider a U-shaped assembly line balancing problem where each task uses a specified set of equipments and each type of equipment has a specified cost. Our problem is to assign the tasks together with their equipments to the workstations so as to minimize the total equipment cost. We formulate the problem as a mixed integer linear programming model that is capable of solving small sized instances. We propose a branch and bound algorithm that uses efficient precedence relations and lower bounds. We find that the algorithm is able to solve moderate sized problem instances in reasonable times.     

基于单纯形法和局部枚举解混合整数线性规划问题

提出了一种基于单纯形法和局部枚举求解整数线性规划问题的新方法。它通过单纯形法得到松弛问题的最优解并确定变量以及目标函数取值范围,然后基于目标函数,进行局部枚举,从而得到其整数线性规划问题的最优解,与现有方法比较,新解法简单,计算量少,尤其是对于大规模整数线性规划问题,计算量少体现地更明显。     

求解Web集群文档分布的混沌搜索算法

提出Web集群文档分布方案,用M/G/1/K PS排队模型对服务器进行建模,将文档分布问题转化为0-1整数规划问题,然后求解该规划问题。针对该类0-1整数规划问题,给出一种基于混沌搜索的求解算法,该算法让多个独立的混沌变量在其各自的轨道中搜索,使得对应生成的0-1矩阵能遍历任意一种可能的分布,从而能搜索到全局最优解。设计一种基于贪婪思想的文档分布算法。测试表明,混沌搜索算法能找到全局最优解,优于传统的贪婪算法。     

An accelerated approach for solving fuzzy relation equations with a linear objective function

In literature, the optimization model with a linear objective function subject to fuzzy relation equations has been converted into a 0-1 integer programming problem by Fang and Li (1999). They proposed a jump-tracking branch-and-bound method to solve this 0-1 integer programming problem. In this paper, we propose an upper bound for the optimal objective value. Based on this upper bound and rearranging the structure of the problem, we present a backward jump-tracking branch-and-bound scheme for solving this optimization problem. A numerical example is provided to illustrate our scheme. Furthermore, testing examples show that the performance of our scheme is superior to the procedure in the paper by Fang and Li. Several testing examples show that our initial upper bound is sharp.