一类系数为梯形模糊数的整数规划

介绍了模糊数学和整数规划的背景、现状、以及发展趋势,并以模糊结构元理论定义了梯形模糊加权序,进一步证明了模糊整数规划模型的最优解等价于整数规划模型的最优解,再利用整数规划模型的最优解的求解方法求解模糊整数规划模型的最优解,最后,通过算例验证方法的可行性.     

一类特殊二维0-1规划的广义指派模型求解

二维0-1整数规划模型应用广泛,对广义指派问题的研究,解决了一些二维0-1整数规划问题.但有些实际问题具有特殊上限约束,目前还没有对应的方法.针对该实际情形,本文建立了相应的数学模型,利用对指派模型的推广,求得问题最优解,从理论上解决了这一类特殊约束二维0-1整数规划的最优解求取问题.并通过算例说明了方法的使用.     

求解一个整数方程的新解法

ni=1aixi =p是一个由实验数据问题抽象而出的整数方程求非负整数解的数学模型 .为了使该问题实现计算机求解的可能 ,本文首先将原问题转化为讨论一类整数规划最优解问题 .从对应松弛规划问题的目标函数值为 0的最优解出发 ,根据舍入凑整法原则 ,再次将问题转化为另一简化后的整数方程 ,这样大大缩小了解的范围 ,及进一步迅速降低了方程右端的 p值 ,使其在计算机上求解的运算量大大降低而能得以实现     

一个基于离散填充函数的整数线性规划方法

本文提出了一个有效的解决整数线性规划的新算法.如果离散化的局部搜索过程陷入局部最优解,则构造相应的离散填充函数,引导搜索过程跳出局部最优解并得到更好的解.该方法是在离散空间中进行优化的,无需增加新的约束,且一直保持整数可行性,收敛的速度非常快.该方法也为一般整数规划提出了一种新的途径.数值实例表明,与现有的方法相比,该算法能够较快的找到最优解.     

进化规划与进化策略的变异算子

进化算法是研究全局优化算法中最重要的随机算法之一,本文给出了进化规划和进化策略的变异算子的数学描述,并提出变异函数的概念,在此基础上,给出了用均匀分布的随机数构造变异算子的几种方法和若干例子.结果表明.利用本文给出的方法,不仅可以构造出目前进化策略和进化规划算法普遍采用的几种变异算子,还可以构造出新的变异算子.针对一般的变异算子,在不要求目标函数连续的情况下,证明了保持最优个体的进化规划和进化策略,迭代产生的最优个体的函数值收敛到问题的最优值的ε-邻域的概率为1.     

整数规划的渐进强对偶方法

虽然整数规划中经典的Lagrange对偶方法是一个有效的方法，但是由于对偶缝隙的原因它经常不能求出原问题的最优解。该文提出一个用于有界整数规划的指数对偶公式。此公式具有渐进强对偶的特性并且可以保证找到原问题的最优解。它的另一个特性是当参数选择的合适时不需要进行实际的对偶搜索。     

求整数最优解的方法

在“线性规划”教材中,求目标函数的最优 解,是通过平移直线的方法得出的,但平移直 线得出的最优解往往不是整数,而在实际的线 性规划问题中,经常要求的最优解是整数．人 教版《数学》第二册(上)63页例4在解答过程 中给出了求整数最优解的概念和答案,但没有 给出详细求法及理由,因此多数学生对此类问 题的求解感到无从下手．本文通过一道例题介 绍五种求整数最优解的方法及详细解答过程, 供大家参考．     

混合整数二次规划问题的全局最优性条件

本文给出了混合整数二次规划问题的全局最优性条件,包括全局最优充分性条件和全局最优必要性条件.我们还给出了一个数值实例用以说明如何利用本文所给出的全局最优性条件来判定一个给定点是否是全局最优解.     

整数规划中割平面法的研究

割平面法是求解整数规划问题常用方法之一.用割平面法求解整数规划的基本思路是:先用单纯形表格方法去求解不考虑整数约束条件的松弛问题的最优解,如果获得的最优解的值都是整数,即为所求,运算停止.如果所得最优解不完全是整数,即松弛问题最优解中存在某个基变量为非整数值时,就从最优表中提取出关于这个基变量的约束等式,再从这个约束式出发构造一个割平面方程加入最优表中,再求出新的最优解,这样不断重复的构造割平面方程,直到找到整数解为止.主要研究以下四个关键点:一是研究从最优表中提取出的、关于基变量的约束等式出发,通过将式中的系数进行整数和非负真分数的分解,从而得到一个小于等于0的另外一个不等式的推导过程;二是总结出从小于等于0的那个约束不等式出发构造割平面方程的四种方法;三是分析构造割平面方程的这四种方法相互之间的区别和联系;四是探讨割平面法的几何意义.通过对这四个方面的分析和研究,对割平面法进行透彻的剖析,使读者能够全面把握割平面法.     

对带有盒约束的二次整数规划的一种线性化方法

本文主要讨论了二次整数规划问题的线性化方法.在目标函数为二次函数的情况下,我们讨论了带有二次约束的整数规划问题的线性化方法,并将文献中对二次0-1问题的研究拓展为对带有盒约束的二次整数规划问题的研究.最终将带有盒约束的二次整数规划问题转化为线性混合本文主要讨论了二次整数规划问题的线性化方法.在目标函数为二次函数的情况下,我们讨论了带有二次约束的整数规划问题的线性化方法,并将文献中对二次0-1问题的研究拓展为对带有盒约束的二次整数规划问题的研究.最终将带有盒约束的二次整数规划问题转化为线性混合0-1整数规划问题,然后利用Ilog-cplex或Excel软件中的规划求解工具进行求解,从而解决原二次整数规划.     

PSOHS: an efficient two-stage approach for data clustering

Cluster analysis is an important task in data mining and refers to group a set of objects such that the similarities among objects within the same group are maximal while similarities among objects from different groups are minimal. The particle swarm optimization algorithm (PSO) is one of the famous metaheuristic optimization algorithms, which has been successfully applied to solve the clustering problem. However, it has two major shortcomings. The PSO algorithm converges rapidly during the initial stages of the search process, but near global optimum, the convergence speed will become very slow. Moreover, it may get trapped in local optimum if the global best and local best values are equal to the particle’s position over a certain number of iterations. In this paper we hybridized the PSO with a heuristic search algorithm to overcome the shortcomings of the PSO algorithm. In the proposed algorithm, called PSOHS, the particle swarm optimization is used to produce an initial solution to the clustering problem and then a heuristic search algorithm is applied to improve the quality of this solution by searching around it. The superiority of the proposed PSOHS clustering method, as compared to other popular methods for clustering problem is established for seven benchmark and real datasets including Iris, Wine, Crude Oil, Cancer, CMC, Glass and Vowel.     

Shaping an antenna radiation diagram with discrete weights using the PSO algorithm and periodic and nest spaces

Using traditional methods, finding the weights that allow shaping a desired radiation diagram for an antenna in order to reject unwanted signals or maximize the desired signal reception, is possible.However, neither by iterative nor closed methods, can it be done while restricting the amplitudes and phases to a set of finite values for each of them. Also, it often happens that they cannot include in its formulation other types of specifications that are necessary to be achieved.Some modifications were implemented in the method Particle Swarm Optimization (PSO), which reduced the convergence time, especially in the search space of phases where there exists a periodicity that the original method does not take into account.PSO is an evolutionary algorithm, inspired by the social behavior of flocks of birds or fish, developed by Eberhart and Kennedy in 1995, and has been intensively applied in solving numerical Engineering problems.     

Discrete Capacity Assignment in IP networks using Particle Swarm Optimization

This paper presents a design methodology for IP networks under end-to-end Quality-of-Service (QoS) constraints. Particularly, we consider a more realistic problem formulation in which the link capacities of a general-topology packet network are discrete variables. This Discrete Capacity Assignment (DCA) problem can be classified as a constrained combinatorial optimization problem. A refined TCP/IP traffic modeling technique is also considered in order to estimate performance metrics for networks loaded by realistic traffic patterns. We propose a discrete variable Particle Swarm Optimization (PSO) procedure to find solutions for the problem. A simple approach called Bottleneck Link Heuristic (BLH) is also proposed to obtain admissible solutions in a fast way. The PSO performance, compared to that one of an exhaustive search (ES) procedure, suggests that the PSO algorithm provides a quite efficient approach to obtain (near) optimal solutions with small computational effort.     

A multi-swarm PSO using charged particles in a partitioned search space for continuous optimization

Particle swarm optimization (PSO) is characterized by a fast convergence, which can lead the algorithms of this class to stagnate in local optima. In this paper, a variant of the standard PSO algorithm is presented, called PSO-2S, based on several initializations in different zones of the search space, using charged particles. This algorithm uses two kinds of swarms, a main one that gathers the best particles of auxiliary ones, initialized several times. The auxiliary swarms are initialized in different areas, then an electrostatic repulsion heuristic is applied in each area to increase its diversity. We analyse the performance of the proposed approach on a testbed made of unimodal and multimodal test functions with and without coordinate rotation and shift. The Lennard-Jones potential problem is also used. The proposed algorithm is compared to several other PSO algorithms on this benchmark. The obtained results show the efficiency of the proposed algorithm.     

A novel particle swarm optimization algorithm for permutation flow-shop scheduling to minimize makespan

It is well known that the flow-shop scheduling problem (FSSP) is a branch of production scheduling and is NP-hard. Now, many different approaches have been applied for permutation flow-shop scheduling to minimize makespan, but current algorithms even for moderate size problems cannot be solved to guarantee optimality. Some literatures searching PSO for continuous optimization problems are reported, but papers searching PSO for discrete scheduling problems are few. In this paper, according to the discrete characteristic of FSSP, a novel particle swarm optimization (NPSO) algorithm is presented and successfully applied to permutation flow-shop scheduling to minimize makespan. Computation experiments of seven representative instances (Taillard) based on practical data were made, and comparing the NPSO with standard GA, we obtain that the NPSO is clearly more efficacious than standard GA for FSSP to minimize makespan.     

粒子群优化的收敛分析及在广义预测控制中的应用

在进行粒子群优化的收敛性理论分析的基础上,推出了保证粒子群优化算法收敛性的参数设置区域,合理选择粒子群算法的关键参数,将粒子群优化与广义预测控制有机融合,用粒子群算法来解决广义预测控制的优化问题,提出基于粒子群优化的广义预测控制算法,通过工业过程对象的仿真并和传统的广义预测控制算法进行了对比分析,表明了该算法的有效性,特别是算法具有良好的输出跟踪精度和较强的鲁棒性.     

基于粒子群算法的非线性二层规划问题的求解算法

粒子群算法（Particle Swarm Optimization，PSO）是一种新兴的优化技术，其思想来源于人工生命和演化计算理论。PSO通过粒子追随自己找到的最好解和整个群的最好解来完成优化。该算法简单易实现，可调参数少，已得到了广泛研究和应用。本文根据该算法能够有效的求出非凸数学规划全局最优解的特点，对非线性二层规划的上下层问题求解，并根据二层规划的特点，给出了求解非线性二层规划问题全局最优解的有效算法。数值计算结果表明该算法有效。     

A Particle Swarm Optimization Algorithm with Path Relinking for the Location Routing Problem

This paper introduces a new hybrid algorithmic nature inspired approach based on particle swarm optimization, for solving successfully one of the most popular logistics management problems, the location routing problem (LRP). The proposed algorithm for the solution of the location routing problem, the hybrid particle swarm optimization (HybPSO-LRP), combines a particle swarm optimization (PSO) algorithm, the multiple phase neighborhood search – greedy randomized adaptive search procedure (MPNS-GRASP) algorithm, the expanding neighborhood search (ENS) strategy and a path relinking (PR) strategy. The algorithm is tested on a set of benchmark instances. The results of the algorithm are very satisfactory for these instances and for six of them a new best solution has been found.      

Generalized particle swarm optimization algorithm - Theoretical and empirical analysis with application in fault detection

A generalization of the particle swarm optimization (PSO) algorithm is presented in this paper. The novel optimizer, the Generalized PSO (GPSO), is inspired by linear control theory. It enables direct control over the key aspects of particle dynamics during the optimization process. A detailed theoretical and empirical analysis is presented, and parameter-tuning schemes are proposed. GPSO is compared to the classical PSO and genetic algorithm (GA) on a set of benchmark problems. The results clearly demonstrate the effectiveness of the proposed algorithm. Finally, an application of the GPSO algorithm to the fine-tuning of the support vector machines classifier for electrical machines fault detection is presented.     

Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems

Heuristic optimization provides a robust and efficient approach for solving complex real-world problems. The aim of this paper is to introduce a hybrid approach combining two heuristic optimization techniques, particle swarm optimization (PSO) and genetic algorithms (GA). Our approach integrates the merits of both GA and PSO and it has two characteristic features. Firstly, the algorithm is initialized by a set of random particles which travel through the search space. During this travel an evolution of these particles is performed by integrating PSO and GA. Secondly, to restrict velocity of the particles and control it, we introduce a modified constriction factor. Finally, the results of various experimental studies using a suite of multimodal test functions taken from the literature have demonstrated the superiority of the proposed approach to finding the global optimal solution.