On the use of Kronecker's algorithm in the generalized rational interpolation problem

Kronecker's algorithm can be used to solve the generalized rational interpolation problem. In order to present the algorithm, rational forms are used here instead of too restrictive rational fractions. The proposed algorithm is reliable as soon as the functionals that characterize the problem satisfy two precise conditions. These conditions are fulfilled in the modified Hermite rational interpolation problem and, as a consequence, in the special case of the Cauchy problem and of the Padé approximation problem. This reliability covers two properties: on one hand, every rational form resulting from the algorithm is a solution of the problem whereas, on the other hand, every solution of the problem is found by the algorithm (with the exception of a possible reduction of the rational form). However, if the algorithm yields a non-reduced rational form, then the corresponding rational fraction is not a solution of the problem.     

置换流水车间调度问题的中心引力优化算法求解

目前求解置换流水车间调度问题的智能优化算法都是随机型优化方法,存在的一个问题是解的稳定性较差。针对该问题,本文给出一种确定型智能优化算法——中心引力优化算法的求解方法。为处理基本中心引力优化算法对初始解选择要求高的问题,利用低偏差序列生成初始解,提高初始解质量;利用加速度和位置迭代方程更新解的状态;利用两位置交换排序法进行局部搜索,提高算法的优化性能。采用置换流水车间调度问题标准测试算例进行数值实验,并和基本中心引力优化算法、NEH启发式算法、微粒群优化算法和萤火虫算法进行比较。结果表明该算法不仅具有更好的解的稳定性,而且具有更高的计算精度,为置换流水车间调度问题的求解提供了一种可行有效的方法。     

Numerical Methods for Single Machine Scheduling with Non-linear Cost Functions to Minimize Total Cost

In this paper we are concerned with the problem of sequencing a given set of jobs without preemption on a single machine so as to minimize total cost, where associated with each job is a processing time and a differentiable cost function defined on the completion time of the job. The problem, in general, is NP-complete and, therefore, there is unlikely to be an algorithm to solve the problem in reasonable time, thus a heuristic algorithm is desirable. We present two heuristic algorithms to solve the problem. The first algorithm is based on the differential of the cost functions, and the second algorithm is based on the least square approximation of the cost functions. Computational experiences for the case of quadratic, cubic, and exponential cost functions are presented.     

Expanding neighborhood search–GRASP for the probabilistic traveling salesman problem

The Probabilistic Traveling Salesman Problem is a variation of the classic traveling salesman problem and one of the most significant stochastic routing problems. In probabilistic traveling salesman problem only a subset of potential customers need to be visited on any given instance of the problem. The number of customers to be visited each time is a random variable. In this paper, a variant of the well-known Greedy Randomized Adaptive Search Procedure (GRASP), the Expanding Neighborhood Search–GRASP, is proposed for the solution of the probabilistic traveling salesman problem. expanding neighborhood search–GRASP has been proved to be a very efficient algorithm for the solution of the traveling salesman problem. The proposed algorithm is tested on a numerous benchmark problems from TSPLIB with very satisfactory results. Comparisons with the classic GRASP algorithm and with a Tabu Search algorithm are also presented. Also, a comparison is performed with the results of a number of implementations of the Ant Colony Optimization algorithm from the literature and in six out of ten cases the proposed algorithm gives a new best solution.     

Comparison of two algorithms for solving a two‐stage bilinear stochastic programming problem with quantile criterion

The paper is devoted to solving the two‐stage problem of stochastic programming with quantile criterion. It is assumed that the loss function is bilinear in random parameters and strategies, and the random vector has a normal distribution. Two algorithms are suggested to solve the problem, and they are compared. The first algorithm is based on the reduction of the original stochastic problem to a mixed integer linear programming problem. The second algorithm is based on the reduction of the problem to a sequence of convex programming problems. Performance characteristics of both the algorithms are illustrated by an example. A modification of both the algorithms is suggested to reduce the computing time. The new algorithm uses the solution obtained by the second algorithm as a starting point for the first algorithm. Copyright © 2015 John Wiley & Sons, Ltd.     

On the algorithm of the solution of the signorini problem

An algorithm is proposed for solving the Signorini problem /1/ in the formulation of a unilateral variational problem for the boundary functional in the zone of possible contact /2/. The algorithm is based on a dual formulation of Lagrange maximin problems for whose solution a decomposition approach is used in the following sense: a Ritz process in the basis functions that satisfy the linear constraint of the problem, the differential equation in the domain, is used in solving the minimum problem (with fixed Lagrange multipliers); the maximum problem is solved by the method of descent (a generalization of the Frank-Wolf method) under convexity constraints on the Lagrange multipliers. The algorithm constructed can be conisidered as a modification of the well-known algorithm to find the Udzawa-Arrow-Hurwitz saddle points /3, 4/. The convergence of the algorithm is investigated. A numerical analysis of the algorithm is performed in the example of a classical contact problem about the insertion of a stamp in an elastic half-plane under approximation of the contact boundary by isoparametric boundary elements. The comparative efficiency of the algorithm is associated with the reduction in the dimensionality of the boundary value problem being solved and the possibility of utilizing the calculation apparatus of the method of boundary elements to realize the solution.     

Fixed point optimization algorithm and its application to network bandwidth allocation

A convex optimization problem for a strictly convex objective function over the fixed point set of a nonexpansive mapping includes a network bandwidth allocation problem, which is one of the central issues in modern communication networks. We devised an iterative algorithm, called a fixed point optimization algorithm, for solving the convex optimization problem and conducted a convergence analysis on the algorithm. The analysis guarantees that the algorithm, with slowly diminishing step-size sequences, weakly converges to a unique solution to the problem. Moreover, we apply the proposed algorithm to a network bandwidth allocation problem and show its effectiveness.     

A scatter search algorithm for the single row facility layout problem

The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, with the objective of minimizing the weighted sum of the distances between all pairs of facilities. The problem is NP-hard and research has focused on heuristics to solve large instances of the problem. In this paper we present a scatter search algorithm to solve large size SRFLP instances. Our computational experiments show that the scatter search algorithm is an algorithm of choice when solving large size SRFLP instances within limited time.     

灾情巡视问题的蚁群两目标优化算法研究

分析目前灾情巡视问题求解方法存在的缺陷,归纳出灾情巡视问题两目标优化模型.针对灾情巡视问题模型特点,引入蚁群算法和多目标优化理论,提出两个灾情巡视问题的蚁群两目标优化算法:算法1将灾情巡视问题的道路网络转化为完全图,增加m-1个(m为巡视组数)虚拟巡视起点,将灾情巡视两目标优化问题转化为单旅行商两目标优化问题,然后使用蚁群算法和多目标优化理论进行迭代求解.算法2使用一只蚂蚁寻找一个子回路,m个子回路构成一个灾情巡视可行方案,采用罚函数法和多目标优化理论构建增广两目标优化评价函数,使用g组,共g×m只蚂蚁共同协作来发现灾情巡视问题的最优解.算法特点:①算法1将灾情巡视两目标优化问题转化为单旅行商两目标优化问题,可以充分利用已有蚁群算法求解单旅行商问题的研究成果;②两个算法引入蚁群算法,提高了算法效率;③两个算法克服目前灾情巡视问题的求解方法不严密性缺陷;④两目标优化算法可以为用户提供多个满足约束条件的Pareto组合解,扩大了用户选择范围,增强了算法的适用性.算法测试表明:灾情巡视问题的蚁群两目标优化算法是完全可行和有效的.     

求解无容量设施选址问题的拉格朗日蝙蝠算法

无容量设施选址问题(Uncapacitated Facility Location Problem,UFLP)是一类经典的组合优化问题,被证明是一种NP-hard问题,易于描述却难于求解.首先根据UFLP的数学模型及其具体特征,重新设计了蝙蝠算法的操作算子,给出了求解UFLP的蝙蝠算法.其次构建出三种可行化方法,并将其与求解UFLP的蝙蝠算法和拉格朗日松弛算法相结合,设计了求解该问题的拉格朗日蝙蝠算法.最后通过仿真实例和与其他算法进行比较的方式,验证了该混合算法用来求解UFLP的可行性,是解决离散型问题的一种有效方式.     

Computation of the optimal tolls on the traffic network

The present paper is devoted to the computation of optimal tolls on a traffic network that is described as fuzzy bilevel optimization problem. As a fuzzy bilevel optimization problem we consider bilinear optimization problem with crisp upper level and fuzzy lower level. An effective algorithm for computation optimal tolls for the upper level decision-maker is developed under assumption that the lower level decision-maker chooses the optimal solution as well. The algorithm is based on the membership function approach. This algorithm provides us with a global optimal solution of the fuzzy bilevel optimization problem.     

An algorithm for the capacitated vehicle routing problem with route balancing

In this paper, we present a multi-objective evolutionary algorithm for the capacitated vehicle routing problem with route balancing. The algorithm is based on a formerly developed multi-objective algorithm using an explicit collective memory method, namely the extended virtual loser (EVL). We adapted and improved the algorithm and the EVL method for this problem. We achieved good results with this simple technique. In case of this problem the quality of the results of the algorithm is similar to that of other evolutionary algorithms.     

一种改进的禁忌搜索算法及其在选址问题中的应用

本文研究了选址问题中无容量限制的p-中值问题,在Rolland等人提出的有效禁忌搜索算法基础上,提出了一种以目标函数变化量作为评价函数的改进禁忌搜索算法,并进行了理论分析,然后将其与有效禁忌搜索算法作了性能比较.通过比较三个公共测试数据集的计算结果,验证了本文提出的禁忌搜索算法的可行性和有效性.     

Solving sum of quadratic ratios fractional programs via monotonic function

In this paper, a branch-reduce-bound algorithm is proposed for globally solving a sum of quadratic ratios fractional programming with nonconvex quadratic constraints. Due to its intrinsic difficulty, less work has been devoted to globally solving this problem. The proposed algorithm is based on reformulating the problem as a monotonic optimization problem, and it turns out that the optimal solution which is provided by the algorithm is adequately guaranteed to be feasible and to be close to the actual optimal solution. Convergence of the algorithm is shown and the numerical experiments are given to show the feasibility of the proposed algorithm.     

A class of on-line scheduling algorithms to minimize total completion time

We consider the problem of scheduling jobs on-line on a single machine and on identical machines with the objective to minimize total completion time. We assume that the jobs arrive over time. We give a general 2-competitive algorithm for the single machine problem. The algorithm is based on delaying the release time of the jobs, i.e., making the jobs artificially later available to the on-line scheduler than the actual release times. Our algorithm includes two known algorithms for this problem that apply delay of release times. The proposed algorithm is interesting since it gives the on-line scheduler a whole range of choices for the delays, each of which leading to 2-competitiveness.We also show that the algorithm is 2α competitive for the problem on identical machines where α is the performance ratio of the Shortest Remaining Processing Time first rule for the preemptive relaxation of the problem.     

需求区间型运输问题的求解算法

为了便于建立与需求区间型运输问题有关的决策支持系统，本给出了一个求解需求区间型运输问题的数值算法，证明了算法的理论依据，并举例说明算法的应用，该算法能求得问题的最优解，并具有易于编程实现、收敛性好等优点，大量数值实验表明该算法有较高的计算效率。     

求解摩擦接触问题的一个非内点光滑化算法

给出了一个求解三维弹性有摩擦接触问题的新算法,即基于NCP函数的非内点光滑化算法．首先通过参变量变分原理和参数二次规划法,将三维弹性有摩擦接触问题的分析归结为线性互补问题的求解;然后利用NCP函数,将互补问题的求解转换为非光滑方程组的求解;再用凝聚函数对其进行光滑化,最后用NEWTON法解所得到的光滑非线性方程组．方法具有易于理解及实现方便等特点．通过线性互补问题的数值算例及接触问题实例证实了该算法的可靠性与有效性．     

多目标0-1规划问题的蜂群算法

针对多目标0-1规划问题,本文给出一种新型的智能优化算法——蜂群算法进行求解,并通过实例验证,与遗传算法、蚁群算法和元胞蚁群算法作了相应比较。就多目标0-1规划问题而言,蜂群算法能得到更多的Pareto解,说明了蜂群算法在解决该类问题上的有效性。     

精确覆盖问题的加权分治算法

精确覆盖问题是组合优化中经典的NP-Hard问题之一,其在诸多领域具有广泛的应用价值。本文首先研究了精确覆盖问题的数学性质,并根据数学性质提出相应的分支降阶规则以缩小问题的规模;接着设计了一个基于分支降阶的回溯算法求解该问题;然后运用常规技术分析得出该精确算法的时间复杂度为O(1.4656^k);最后运用加权分治技术对该算法的时间复杂度进行分析,将该算法的时间复杂度降为O(1.3842^k)。文章最后通过一个示例进一步阐述该算法的原理,并与其他精确算法进行了对比分析,研究结果表明该算法是可行的,也是有效的。     

An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers

This article presents an exact algorithm for the precedence-constrained traveling salesman problem, which is also known as the sequential ordering problem. This NP-hard problem has applications in various domains, including operational research and compilers. In this article, the problem is presented and solved in the context of minimizing switching energy in compilers. Most previous work on minimizing switching energy in the compiler domain has been limited to simple heuristics that are not guaranteed to give an optimal solution. In this work, we present an exact algorithm for solving the switching energy minimization problem using a branch-and-bound approach. The proposed algorithm is simple and intuitive, yet powerful. It is the first exact algorithm for the switching energy problem that is shown to solve real instances of the problem within a few seconds per instance. Compared to previous work in the operational research domain, the proposed algorithm is believed to be the most powerful exact algorithm that does not require a linear programming formulation. The proposed algorithm is experimentally evaluated using instances taken from a production compiler. The results show that with a time limit of 10 ms per node, the proposed algorithm optimally solves 99.8 % of the instances. It optimally solves instances with up to 598 nodes within a few seconds. The resulting switching cost is 16 % less than that produced without energy awareness and 5 % less than that produced by a commonly used heuristic.