过程间并发程序分析不可判定的一个新证明方法

过程间并发程序分析问题是一个不可判定问题,理解这个不可判定问题的来源是发展一个有效的分析算法的基础.现有的证明[1]通过构造三个并发任务的PCP问题实例,证明过程间并发程序分析是一个不可判定问题.利用反射的思想,仅仅用两个并发任务构造该问题的一个PCP问题实例,证明在两个并发任务的情况下,过程间并发程序分析是一个不可判定问题.     

Characterization of Problem Stores

This paper introduces the concept of problem stores: static stores whose dependent loads often miss in the cache. Accurately identifying problem stores allows the early determination of addresses likely to cause later misses, potentially allowing for the development of novel, proactive prefetching and memory hierarchy management schemes. We present a detailed empirical characterization of problem stores using the SPEC2000 CPU benchmarks. The data suggests several key observations about problem stores. First, we find that the number of important problem stores is typically quite small; the worst 100 problem stores write the values that will lead to about 90% of non-cold misses for a variety of cache configurations. We also find that problem stores only account for 1 in 8 dynamic stores, though they result in 9 of 10 misses. Additionally, the problem stores’ dependent loads miss in the L2 cache a larger fraction of the time than loads not dependent on problem stores. We also observe the set of problem stores is stable across a variety of cache configurations. Finally, we found that the instruction distance from problem store to miss and problem store to evict is often greater than one million instructions, but the value is often needed within 100,000 instructions of the eviction.     

一类弱支配集问题的近似算法

支配集问题和集合覆盖问题均是图论中的经典问题,尤其是集合覆盖问题,它的近似算法在许多其他问题中均有非常多的应用,如设施选址问题、服务器的安置问题等。本文研究了支配集问题和集合覆盖问题的关系,讨论了几个弱支配集问题和弱覆盖问题、弱集合覆盖问题等,给出完全支配集问题的近似比为Inn的近似算法,分析了弱完全支配集问题的不可近似比最小规模,讨论了集合击中问题和弱集合b-覆盖问题的最小规模,同时讨论了完全支配集问题、集合d-击中等问题的不可近似性。     

基于遗传算法的物流配送路径优化问题研究

遗传算法是一种基于自然进化原理的全局搜索随机算法。遗传算法在选址问题、配送问题、调度问题、运输问题、布局问题方面意义重大。在建立物流配送路径优化问题数学模型的基础上,构造了求解该问题的遗传算法。该遗传算法采用常用的二进制编码,在个体选择上结合使用最优个体保留策略和轮盘赌法。最后以这种方法进行了实验计算,通过计算结果表明,用遗传算法进行物流配送路径优化,可以方便有效地求得问题的最优解或近似最优解。     

Josephus问题分析与探讨

Josephus问题是一个经典的递归问题。本文从问题的编程解决入手，提出静态数组、环链表、递归等3种解题方案。本文还对问题作进一步分析，考虑解的稳定点,最后提出一个优化方案，将问题的解决归约到一个较小的规模。     

基于三角环的顶点着色问题解法

图的着色问题是一个NP难问题,本文着重探讨无向图的顶点的三色问题,提出了用构造三角环的极大独立集方法判断并尝试给出顶点三色问题的可行解,解决了顶点三色的可满足性问题,克服了以前图遍历过程中的回溯问题,以及由此推论顶点四色和五色问题的极大独立集。     

信息技术营造数学教育情景的通常策略

多媒体技术的应用给数学教学改革带来一片生机。多媒体起始课问题情境需要生活性,多媒体训练思维问题情境需要启发性,多媒体突破难点问题情境需要动态性,多媒体研究性问题情境需要启发性,多媒体实验问题情境需要探究性,多媒体课后探究问题情境需要趣味性。     

一类优化问题的分解算法

讨论一类大规模系统的优化问题,提出一种递阶优化方法．该方法首先将原问题转化为多目标优化问题,证明了原问题的最优解在多目标优化问题的非劣解集中,给出了从多目标优化问题的解集中挑出原问题最优解的算法,建立了算法的理论基础．仿真结果验证了算法的有效性．     

The Method of Artificial Space Dilation in Problems of Optimal Packing of Geometric Objects

The problem of optimal packing of geometric objects with specified shape and physical-metric parameters is considered. The combinatorial structure of the problem is defined. An equivalent problem is formulated based on the artificial expansion of space dimension with physical-metric parameters being independent variables. The proposed approach is illustrated by the solution of balanced circular packing problem.     

Solution of the laminated plate discrete design problem

The design problem of laminated plate possessing the required stiffnesses is analyzed under the condition that a given finite set of materials may be used to manufacture the plate. The mathematical formulation of the problem represents the convex combinations problem with the condition that the solution belongs to a finite set. This problem is called a discrete convex combinations problem. The algorithm for constructing the general solution (the set of all possible solutions) of the problem is proposed. The algorithm can be used for a numerical solution of the problem.     

Optimal control of switching systems

This paper considers an optimal control problem for a switching system. For solving this problem we do not make any assumptions about the number of switches nor about the mode sequence, they are determined by the solution of the problem. The switching system is embedded into a larger family of systems and the optimization problem is formulated for the latter. It is shown that the set of trajectories of the switching system is dense in the set of trajectories of the embedded system. The relationship between the two sets of trajectories (1) motivates the shift of focus from the original problem to the more general one and (2) underlies the engineering relevance of the study of the second problem. Sufficient and necessary conditions for optimality are formulated for the second optimization problem. If they exist, bang-bang-type solutions of the embedded optimal control problem are solutions of the original problem. Otherwise, suboptimal solutions are obtained via the Chattering Lemma.     

On the problem of spacing of oil wells and control of their production rates

A statement and a numerical solution of the optimization problem for sites of spacing of wells (well clusters) and modes of their operation in an oil field are presented. The mathematical problem represents a parametric problem of optimal control of the distributed system with concentrated sources, which is described by partial differential equations. Similar problems arise in the development and control of technological processes of various assignments and the design of control systems of technical objects. For its numerical solution, the initial problem is reduced to a finite-dimensional optimization problem with constraints of special features. Formulas of a gradient of the functional of the reduced problem are derived. Results of the solution of control problems are given.     

MPEC问题的精确罚函数法收敛性

应用精确罚函数方法,将MPEC问题转化为目标函数含有罚项的一般约束优化问题。当罚因子足够大时,该约束优化问题的极小点收敛于原问题的极小点。     

On the characterization of noninferior solutions of the vector optimization problem

This paper treats three familiar characterizations of noninferior solutions of the vector optimization problem in terms of solutions of (i) the -constraint problem; (ii) the weighting problem; and (iii) the Langrangian problem. Interrelationships among the above characterizations are emphasized by means of a unified treatment of various known results found in the literature. In addition to summarizing existing results, we propose necessary and sufficient conditions for proper noninferiority expressed in terms of the positivity of optimal Lagrange multipliers in the -constraint problem.     

A method of network programming in problems of nonlinear optimization

A method of network programming for solving problems of nonlinear optimization is used. A notion of dual problem is introduced. It is proved that a dual problem is a problem of convex programming. Necessary and sufficient conditions for optimality of dual problem of integer linear programming are obtained.     

排课表问题的闭环DNA计算模型的算法

排课表问题是NP-完全问题。基于闭环DNA计算模型引入多种生化实验得出求解排课表问题的DNA算法。本算法采用两部编码方式产生初始数据池,引入批删除实验解决了教师和班级的冲突问题和同班课问题;引入批分离实验解决了正常合班课问题和教师时间要求问题;引入电泳实验解决了排课的均衡分配问题;引入标记实验得到了排课表问题的全局最优解集,并给出了算法的生化实现过程。最后,对算法的正确性进行了证明,并讨论了算法的复杂性。     

Specification and analysis of real-time problem solvers

The authors provide a method for the specification of real-time artificial intelligence (AI) problem solvers. Using this method, a formal specification of a real-time problem is presented. In addition, a method for analyzing real-time AI problem solvers is examined using a case study of two real-time problem solvers, namely DYNORAII and RTA* for the real-time path planning problem. New results on worst-case and average-case complexity of the problem, and of the algorithms that solve it, and an experimental evaluation of DYNORAII and RTA* for deadline compliance and response-time minimization are provided     

The Restoration of Input Parameters of an Exterior Ballistic Solution by the Results of Body Movement Trajectory Measurement

Analyzing the results of ballistic experiments often brings up the problem of restoring the input computation parameters of the exterior ballistics of a body (the ballistic coefficient, the initial velocity, the environment temperature, the pressure, etc.) by the results of trajectory measurements (the reverse problem of exterior ballistics). It is found that without a priori information on unknown parameters, the problem in question cannot have a unique solution. We propose a procedure of solving the reverse problem with a priori information at hand; this procedure rests on the least-squares method and the maximum-likelihood method. An algorithm for solving the reverse problem is described in detail (the described algorithm implements the proposed procedure). We consider applying this procedure to the problem of restoring the initial departure conditions and atmospheric parameters, as well as to the problem of simultaneously determining the initial velocity of the body and its ballistic coefficient.     

Methods to develop a solution to the modified knapsack problem for purposes of information support of the Honorarium automated system

When developing information support for the Honorarium automated system, one of the problems involving mathematical methods was the problem of forming a so-called payroll register. This problem is classified as an NP-complete problem. The factorization of this problem enabled us to consider it as a particular case of the knapsack problem. Two methods of solution were proposed regarding the peculiarities of the problem. The computational complexity for all of these is estimated, the scope is indicated, and features of the development are described.     

Some elements of a Galois theory of the structure and complexity of the tree automorphism problem

Engeler's generalization of Galois theory is applied to the tree automorphism problem. We compute the Galois group of each instance of this problem. The group yields information on four aspects of problem difficulty: lower bounds for the time complexity of different solution approaches, ‘hard’ instances of the problem, dependence of problem difficulty on structural parameters of the input and relative solvability. In addition we show that an approximation of this information can be obtained from the group of the problem of finding ‘approximate’ tree automorphisms.