面向图分割问题的确定性退火控制算法

图分割问题是一种典型的NP-hard 问题, 如何对其进行高效求解一直都是学界和工业界的一个难题. 本文构建了一种新型的确定性退火控制算法, 提供了图分割问题的一种高质量近似解法. 算法主要由两部分构成: 全局收敛的迭代过程以及屏障函数最小点组成的收敛路径. 我们证明了,当屏障因子从足够大的实数降为0, 沿着一系列由屏障问题最小点组成的收敛路径可以得到图分割问题的一种高质量的近似解. 仿真计算结果表明本文所构建算法相比已有方法的优越性     

求解合作伙伴选择问题的高效蚁群算法

敏捷制造中的合作伙伴优化选择问题属于组合优化领域的NP-hard问题,随着规模的增大,应用传统的方法求解非常困难,甚至不可能.对敏捷制造中的合作伙伴选择问题进行了分析,建立了数学模型,设计了一个适合求解该问题的蚁群算法.实验结果表明,该算法求解效率高,性能稳定.     

A parallel graph partitioning algorithm for a message-passing multiprocessor

We develop a parallel algorithm for partitioning the vertices of a graph intop2 sets in such a way that few edges connect vertices in different sets. The algorithm is intended for a message-passing multiprocessor system, such as the hypercube, and is based on the Kernighan-Lin algorithm for finding small edge separators on a single processor.⁽¹⁾ We use this parallel partitioning algorithm to find orderings for factoring large sparse symmetric positive definite matrices. These orderings not only reduce fill, but also result in good processor utilization and low communication overhead during the factorization. We provide a complexity analysis of the algorithm, as well as some numerical results from an Intel hypercube and a hypercube simulator.Publication of this report was partially supported by the National Science Foundation under Grant DCR-8451385 and by AT&T Bell Laboratories through their Ph.D scholarship program.     

Addressing a nonlinear fixed-charge transportation problem using a spanning tree-based genetic algorithm

In this paper, we consider the fixed-charge transportation problem (FCTP) in which a fixed cost, sometimes called a setup cost, is incurred if another related variable assumes a nonzero value. To tackle such an NP-hard problem, there are several genetic algorithms based on spanning tree and Prüfer number representation. Contrary to the findings in previous works, considering the genetic algorithm (GA) based on spanning tree, we present a pioneer method to design a chromosome that does not need a repairing procedure for feasibility, i.e. all the produced chromosomes are feasible. Also, we correct the procedure provided in previous works, which designs transportation tree with feasible chromosomes. We show the previous procedure does not produce any transportation tree in some situations. Besides, some new crossover and mutation operators are developed and used in this work. Due to the significant role of crossover and mutation operators on the algorithm’s quality, the operators and parameters need to be accurately calibrated to ensure the best performance. For this purpose, various problem sizes are generated at random and then a robust calibration is applied to the parameters using the Taguchi method. In addition, two problems with different sizes are solved to evaluate the performance of the presented algorithm and to compare that performance with LINGO and also with the solution presented in previous work.     

带权图的均衡k划分

带权图的均衡k划分是把一个图的顶点集分成k个不相交的子集,使得任意2个子集中顶点的权值之和的差异达到极小,并且连接不同子集的边权之和也达到极小.这种图的k划分问题已被应用在软硬件协同设计、大规模集成电路设计和数据划分等领域,它已被证明是NP完全问题.首先针对带权图的均衡k划分问题提出了能够生成优质近似解的启发式算法.该算法在保证子集均衡的条件下,采用最大化同一子集内部边权之和的策略来构造每一个顶点子集;构建子集S的思想是每次从候选集中选择与子集S相连的具有最大增益的顶点放入子集S中,直到子集S的顶点权值之和满足要求.此外,采用了定制的禁忌搜索算法对生成的初始近似解实施进一步优化.实验结果表明,当k分别取值为2,4,8时所提算法分别在86%,81%,68%的基准图上求得的平均解优于当前最新算法求得的平均解;解的最大改进幅度可达60%以上.     

Floorplan design problem using improved genetic algorithm

Genetic algorithms (GA) are applicable to many kinds of difficult problems. When a population keeps enough diversity and similarity, GA can obtain good solutions quickly. However, because these often compete with each other, it is difficult to fulfill both of these conditions simultaneously. In this article, taking these into consideration, we propose a new GA for the floorplan design problem, and aimed at improving the efficiency of calculation, the maintenance of the solution’s population diversity, and reduction of the number of parameters. We applied it to two MCNC (originally established as the Microelectronics Center of North Carolina) benchmark problems. The experimental results showed that the proposed method performed better than the existing methods. This work was presented, in part, at the 8th International Symposium on Artificial Life and Robotics, Oita, Japan, January 24#x2013;26, 2003     

一种快速求解最短路径巡游问题的涟漪扩散算法

针对最短路径巡游问题（SPTP）,提出了基于涟漪扩散算法（RSA）特征的SPTP分解方法。RSA通过模拟水面上涟漪传播的现象,在SPTP子问题间建立联系,相较于其他基于问题分解的算法减少了计算冗余度。进一步改进RSA,使其在维持时间复杂度不变的情况下求解多起点—多终点SPTP。在多种拓扑结构的网络中进行对比实验,结果表明,RSA在保证最优性的同时运算效率最高。RSA对于多起点—多终点SPTP的高效求解,可为多种现实问题快速提供解决方案,具有很高的应用价值。     

蚁群算法在网络最大流问题中的应用

网络最大流问题是一个经典组合优化问题,是计算机科学和运筹学的重要内容。根据蚁群算法的特点,将网络最大流问题进行相应地转化,然后利用蚁群算法进行求解。仿真结果表明,该算法能方便快捷地解决最大流问题,是行之有效的方法。     

An algorithm for a super-stable roommates problem

In this paper, we describe an efficient algorithm that decides if a stable matching exists for a generalized stable roommates problem, where, instead of linear preferences, agents have partial preference orders on potential partners. Furthermore, we may forbid certain partnerships, that is, we are looking for a matching such that none of the matched pairs is forbidden, and yet, no blocking pair (forbidden or not) exists.To solve the above problem, we generalize the first algorithm for the ordinary stable roommates problem.     

拟牛顿粒子群优化算法求解调度问题

针对资源受限的项目调度问题,将粒子群优化算法与拟牛顿优化算法相结合,提出了一种混合粒子群算法。本算法利用粒子群算法求得优化解,然后利用拟牛顿方法对所得到的解进行局部优化,以尽量达到或接近全局最优点。结果表明,本算法能够有效地求解大规模项目调度问题,具有较好的应用价值。     

求解不确定TSP问题的蚂蚁算法

提出了不确定旅行商问题模型,该模型将路径长度看作动态可变的。从实际应用来说,该模型考虑了交通运行中的不确定情况,比经典旅行商问题更具有灵活性及实用价值,利用该模型得到的结果将更适于指导车辆对运行路线的选择。同时提出了一种基于蚂蚁算法的混合方法求解不确定旅行商问题,并给出了解的评价标准。实验结果显示,该方法能够加速蚂蚁算法的收敛性,可以有效求解不确定旅行商问题。     

求解互补问题的极大熵差分进化算法*

针对传统算法无法获得互补问题多个最优解的困难, 提出了求解互补问题的差分进化算法。首先利用NCP函数, 将互补问题转换为一个非光滑方程组问题, 然后用凝聚函数对其进行光滑化, 进而把互补问题的求解转换为无约束优化问题, 利用差分进化算法对其进行求解。该算法对目标函数的解析性质没有要求且容易实现, 数值结果表明了该方法在求解互补问题中的有效性。     

哈密尔顿回路问题的DNA表面计算模型

首次提出用DNA表面计算模型来解决无向图哈密尔顿回路问题。该模型基于哈密尔顿回路问题的解空间,将问题解空间的DNA分子固定在固体载体上,对其进行荧光标记,然后通过相应的生化反应筛选出哈密尔顿回路问题的所有解。与已有的哈密尔顿路径问题的其它模型相比,新模型具有错误率低,编码简易,读取方便等更好的性能。     

一种改进的警示传播算法求解Max-SAT问题

Max-SAT问题是SAT问题的优化版本,目标是在给定的子句集中找到一组变元赋值,使得满足子句数最多,该问题是典型的NP-hard问题。随着大数据和人工智能的深度发展,过去原有的算法已不再适用,设计新的求解算法或对已有的求解算法进行优化是目前研究的热点。针对警示传播算法求解随机Max-3-SAT问题的局限性,提出了一种基于变元权值计算的警示传播算法,结合随机游走算法,给出一种新型算法WWP+WalkSAT,通过改进求解的局限性,更好地得到一组有效的初始解,从而提高算法的局部搜索能力。利用2016年Max-SAT国际竞赛部分基准实例,将WWP+WalkSAT算法与八种局部搜索算法进行精度方面的对比实验。实验结果表明,WWP+WalkSAT算法有较好的性能。     

求解多背包问题的混合遗传算法

针对多背包问题最优解的求解,设计了一种新的价值密度;在此基础上结合传统的贪心算法,提出了一种求解多背包问题的混合遗传算法。该算法采用整数编码,并采用轮盘赌选择方法,对背包资源利用不足的可行解进行修正处理,对不可行解进行修复处理。并在大量的数值实验的基础上,将该方法与传统方法及简单遗传算法进行比较,实验结果表明,该混合遗传算法提高了问题求解的速度和精度,有一定的优越性。     

求解互补问题的极大熵和声搜索算法*

针对传统算法无法获得互补问题的多个最优解的困难, 提出了求解互补问题的和声搜索算法。利用NCP函数, 将互补问题转换为一个非光滑方程组问题,用极大熵函数对其进行光滑换处理,进而把互补问题的求解转化为无约束优化,利用和声搜索算法对其进行求解。该算法对目标函数的解析性质没有要求且容易实现,数值结果表明了该方法在求解互补问题中的有效性。     

一种实用的所有点对之间最短路径并行算法

针对有向图中每对顶点之间的最短路径问题,在基于扩充了路径矩阵的串行Floyd算法上,提出了二维网格结构上的并行算法。选用的任务划分方法为二维均匀块分配方法。该并行算法已经在NOW上的MPI平台上实现,理论分析和数值实验表明它具有较高的扩展性和并行效率。     

Variables Bounding Based Retiming Algorithm

Retiming is a technique for optimizing sequential circuits.In this paper,we discuss this problem and propose an improved retiming algorithm based on varialbes bounding.Through the computation of the lower and upper bounds on variables,the algorithm can significantly reduce the number of constratints and speed up the execution of retiming.Furthermore,the elements of matrixes D and W are computed in a demand-driven way,which can reduce the capacity of memory,It is shown through the experimental results on ISCAS89 benchmarks that our algorithm is very effective for large-scale seuqential circuits.     

基于遗传算法的集合划分问题求解

集合划分问题是组合优化领域中有着广泛应用基础的著名问题,属于NP难问题.通过引入精英策略提出对遗传算法的改进,并为了能把遗传算法应用到集合划分问题,对数学模型进行了等价变换.针对集合划分问题,设计出一种高效的基因表示,避免了组合优化中处理约束条件的麻烦.解决了传统二进制基因编码无法精确适应离散优化问题,首次提出一种离散编码解决方案.最后,使用Visual C 6编程实现,取得较好的结果.     

Unit commitment problem with ramp rate constraint using a binary-real-coded genetic algorithm

The unit commitment problem (UCP) is a nonlinear mixed-integer optimization problem, encountered as one of the toughest problems in power systems. The problem becomes even more complicated when dynamic power limit based ramp rate constraint is taken into account. Due to the inadequacy of deterministic methods in handling large-size instances of the UCP, various metaheuristics are being considered as alternative algorithms to realistic power systems, among which genetic algorithm (GA) has been investigated widely since long back. Such proposals have been made for solving only the integer part of the UCP, along with some other approaches for the real part of the problem. Moreover, the ramp rate constraint is usually discussed only in the formulation part, without addressing how it could be implemented in an algorithm. In this paper, the GA is revisited with an attempt to solve both the integer and real parts of the UCP using a single algorithm, as well as to incorporate the ramp rate constraint in the proposed algorithm also. In the computational experiment carried out with power systems up to 100 units over 24-h time horizon, available in the literature, the performance of the proposed GA is found quite satisfactory in comparison with the previously reported results.