Solving Linear Optimization Problems on Arrangements by the Truncation Method

An exact combinatorial truncation method is proposed for solving Euclidean combinatorial optimization problems on arrangements with a linear objective function and linear additional constraints. An algorithm for this method is developed and justified.     

Solving Extremum Problems with Linear Fractional Objective Functions on the Combinatorial Configuration of Permutations Under Multicriteriality

The authors consider the extremum optimization problem with linear fractional objective functions on combinatorial configuration of permutations under multicriteria condition. Solution methods for linear fractional problems are analyzed to choose the approach to problem’s solution. A solution technique based on graph theory is proposed. The algorithm of the modified coordinate method’s subprogram with search optimization is described. It forms a set of points that satisfy additional constraints of the problem. The general solution algorithm without linearization of the objective function and it’s block diagram are proposed. Examples of the algorithm are described.     

Solving Linear Conditional Completely Combinatorial Optimization Problems on Permutations by the Branch and Bound Method

A conditional linear fully combinatorial minimization problem on permutations is analyzed. The methods of branching, pruning, and estimating in the branch and bound method are proposed for this problem. An illustrative example of applying the method to the problem is presented. The property of the proposed estimation of the admissible subset, which increases the efficiency of branching and pruning, is proved.     

组合优化调度问题求解方法

1.引言优化是指一个从一组解中选取出最优解或最适应解的过程。优化方法涉及的工程领域很广,问题种类与性质繁多。归纳而言,最优化问题可分为函数优化问题和组合优化问题。其中函数优化的对象是一定区间内的连续变量,而组合优化的对象则是解空间中的离散状态。函数优化问题通常可描述为:令S为R~n上的有界子集(即变量的定义域),f:S→R为n维     

用Hopfield模型求解组合优化问题的拟人策略

文章对Hopfield网络状态的更新准则，提出了一个自适应的拟人策略。数值模拟表明，引入拟人策略的Hopfield模型对求解组合优化问题非常有效。     

An Efficient Algorithm of Dead-End Controls for Solving Combinatorial Optimization Problems

Automation and Remote Control - We propose a dead-end control algorithm for the exact solution of NP-hard combinatorial optimization problems. The efficiency of the algorithm is demonstrated by...     

基于文化差分算法的无约束优化问题研究

无约束优化问题是一个较古老的数学问题,随着智能计算科学的发展,解决此类优化问题,除了使用经典数学方法外,还可以使用智能化方法进行寻优。本文使用经典文化算法双层进化结构,将差分进化算法引入信度空间的更新操作,实现差分进化算法在进化过程中形势知识更新,保证了种群合理的进化方向,从而引导种群空间中个体进行有效进化,使得寻优能力有所提高,并选用6个基准函数对改进前后的算法进行测试,实验表明优化性能得到了提高。     

Solution of Mixed Combinatorial Optimization Problems on Arrangements by the Method of Construction of Lexicographic Equivalence

The paper considers the solution of mixed combinatorial optimization problems on arrangements by the method of construction of lexicographic equivalence. A generalization of the relation of equivalence, which is used for space splitting, is proposed and its properties are analyzed. The algorithms of the method known earlier are modified, an approximated algorithm is validated.     

一种求解约束优化问题的线性进化算法

提出一种基于实数编码处理约束优化问题的线性算法,并对其复杂度和收敛性进行分析.该算法将约束优化问题的高维搜索空间通过线性变换映射到二维空间,在二维空间中探索原优化问题的解,从数学分析的角度给出一种线性适应度函数.算法中融入一种基于密度函数的交叉算子和变异算法,采用基于分级聚类的平均联接方式以维持Pareto最优解集个体数目.3组典型优化问题的测试表明,该算法是可行和有效的,解集分布的均匀性与多样性均较理想.     

一种减小方差求解非光滑问题的随机优化算法

随机优化算法是求解大规模机器学习问题的高效方法之一.随机学习算法使用随机抽取的单个样本梯度代替全梯度,有效节省了计算量,但却会导致较大的方差.近期的研究结果表明:在光滑损失优化问题中使用减小方差策略,能够有效提高随机梯度算法的收敛速率.考虑求解非光滑损失问题随机优化算法COMID(compositeobjective mirror descent)的方差减小问题.首先证明了COMID具有方差形式的O(1/√T+σ²/√T)收敛速率,其中,T是迭代步数,σ²是方差.该收敛速率保证了减小方差的有效性,进而在COMID中引入减小方差的策略,得到一种随机优化算法α-MDVR(mirror descent with variance reduction).不同于Prox-SVRG(proximal stochastic variance reduced gradient),α-MDVR收敛速率不依赖于样本数目,每次迭代只使用部分样本来修正梯度.对比实验验证了α-MDVR既减小了方差,又节省了计算时间.     

Combinatorial Method for Solving Systems of Linear Constraints

This article considers a combinatorial method for computing the basis of the set of solutions to systems of linear constraints over the set of real numbers and an improved method for computing a minimal generating set of solutions over the set of natural numbers. A brief review of such methods in other discrete domains is presented.     

A Numerical Method for Solving Stochastic Optimal Control Problems with Linear Control

We introduce a numerical method to solve stochastic optimal control problems which are linear in the control. We facilitate the idea of solving two-point boundary value problems with spline functions in order to solve the resulting dynamic programming equation. We then show how to effectively reduce the dimension in the proposed algorithm, which improves computational time and memory constraints. An example, motivated as an invest problem with uncertain cost, is provided, and the effectiveness of our method demonstrated.     

Lexicographic Equivalence in Mixed Combinatorial Optimization of Linear-Fractional Functions on Arrangements

The paper substantiates the method of constructing the lexicographic equivalence to solve mixed combinatorial optimization problems on arrangements with linear-fractional objective function and linear additional constraints. The method involves directed search of equivalence classes obtained by splitting polyhedral set using equivalence relation. The authors propose exact methods as well as an approximate one. The approximate method allows getting the objective function value that differs from the optimum by no more than a predetermined value.     

Design of the Inverse Function Delayed Neural Network for Solving Combinatorial Optimization Problems

We have already proposed the inverse function delayed (ID) model as a novel neuron model. The ID model has a negative resistance similar to Bonhoeffer–van der Pol (BVP) model and the network has an energy function similar to Hopfield model. The neural network having an energy can converge on a solution of the combinatorial optimization problem and the computation is in parallel and hence fast. However, the existence of local minima is a serious problem. The negative resistance of the ID model can make the network state free from such local minima by selective destabilization. Hence, we expect that it has a potential to overcome the local minimum problems. In computer simulations, we have already shown that the ID network can be free from local minima and that it converges on the optimal solutions. However, the theoretical analysis has not been presented yet. In this paper, we redefine three types of constraints for the particular problems, then we analytically estimate the appropriate network parameters giving the global minimum states only. Moreover, we demonstrate the validity of estimated network parameters by computer simulations.      

应用罚函数求解二层线性优化问题的全局优化方法

应用罚函数原理，将二层线性优化问题转化为目标函数带有罚函数子项的非线性优化问题，当罚系数大于某一数值时，库函数项为一精确项，该非线性优化问题用渐的进外逼近算法可求出其全局最优解。     

Graph Approach to Solving Problems of Combinatorial Recognition

The problem of finding two radioactive balls among a given set of balls is reduced to a combinatorial recognition problem, and the latter is solved by a series of tests. Methods of graph theory are used to solve the problem. The approach is illustrated by an example with 22 balls.     

Minimum Entropy Combinatorial Optimization Problems

We survey recent results on combinatorial optimization problems in which the objective function is the entropy of a discrete distribution. These include the minimum entropy set cover, minimum entropy orientation, and minimum entropy coloring problems.     

Gradient Methods for Nonstationary Unconstrained Optimization Problems

Problems of unconstrained optimization with an objective function depending on a scalar parameter (time) are considered. The solution of these problems also depends on time and any numerical method must keep track of this dependence. For the solution of such nonstationary problems, a discrete gradient method is treated, in which only one gradient step is taken for the varying function at each instant of time. Estimates of intervals (variations) between exact and approximate solutions are found and an asymptotic behavior of these estimates is defined.__________Translated from Avtomatika i Telemekhanika, No. 6, 2005, pp. 38–46.Original Russian Text Copyright © 2005 by Popkov.     

求解组合优化问题的双群体结构遗传算法

提出基于督导群体和进化群体的双群体遗传算法。区别于一般的遗传算法,双群体遗传算法充分利用了督导群体的监督导向作用和问题的先验知识;同时,算法设计考虑加入了邻域函数产生一定数量相异性较大的新个体,从而大大提高了算法的全局搜索性能。以(MR)TSP为例,大量数值实验表明,该算法能迅速收敛到问题的最优解。