一类非线性动力系统的稳定性及周期运动

根据“库仑扭秤”实验的原理提出了一个非线性动力系统模型,分析了其稳定性及其周期运动．     

时程积分过程中结构运动参数的协调

通过在时程积分过程中补充一个能量方程,并借助原时程积分方法的过程数据,提出一种协调时间步长内结构计算位移、速度和加速度的方法,该方法蕴涵了对原时程积分方法计算假设条件的修正,使之更符合实际,以Wilson-θ法为例,加入协调过程后,提高了计算精度和减弱计算结果的超越现象,算例结果表明时间步长内结构的计算运动参数不协调,是时程积分结果误差的一个主要原因。     

航天光学遥感器像移速度矢计算数学模型

随着地面影像分辨力愈来愈高的要求,航天光学遥感器实时精确补偿摄影时地物产生的像移,已成为必需解决的关键技术之一。论述了航天光学遥感器在对星下点摄影时,通过建立从地面景物到像面的七个坐标系,进行14次线性变换,获得了具有15个参量的像面位置方程、像面速度方程,推导出像面上像移速度矢的计算公式,对影响像移速度矢的11个参量进行误差分配,以及应用蒙特卡罗法(统计试验法)进行误差综合。该理论方法已得到了实际应用,从获得的遥感图像达到的分辨力、奈奎斯特(Nyquist)频率处的传递函数、信噪比和平均灰度层次均充分证明了该研究结果的正确性。     

基于红外图像编码的运动预测相关算法

针对运动预测过程中单一匹配准则的不足提出了一种联合匹配准则,能较好地处理小目标的灰度渐变。基于运动预测过程中不断进行的像素块匹配运算提出了一种新的像素抽样算法,该算法使得运算量大大减少,匹配精度逼近全像素匹配算法。这两种技术的综合应用使得整个运动预测效率有较大改善。     

Sorting Using Complete Subintervals and the Maximum Number of Runs in a Randomly Evolving Sequence

We study the space requirements of a sorting algorithm where only items that at the end will be adjacent are kept together. This is equivalent to the following combinatorial problem: Consider a string of fixed length n that starts as a string of 0’s, and then evolves by changing each 0 to 1, with the n changes done in random order. What is the maximal number of runs of 1’s? We give asymptotic results for the distribution and mean. It turns out that, as in many problems involving a maximum, the maximum is asymptotically normal, with fluctuations of order n ^1/2, and to the first order well approximated by the number of runs at the instance when the expectation is maximized, in this case when half the elements have changed to 1; there is also a second order term of order n ^1/3. We also treat some variations, including priority queues and sock-sorting. The proofs use methods originally developed for random graphs.     

Optimal policy for a two-facility inventory problem with storage constraints and two freight modes

This paper considers a two-facility supply chain for a single product in which facility 1 orders the product from facility 2 and facility 2 orders the product from a supplier in each period. The orders placed by each facility are delivered in two possible nonnegative integer numbers of periods. The difference between them is one period. Random demands in each period arise only at facility 1. There are physical storage constraints at both facilities in each period. The objective of the supply chain is to find an ordering policy that minimizes the expected cost over a finite horizon and the discounted stationary expected cost over an infinite horizon. We characterize the structure of the minimum expected cost and the optimal ordering policy for both the finite and the discounted stationary infinite horizon problems.     

Competitive facility location on decentralized supply chains

This paper addresses a novel competitive facility location problem about a firm that intends to enter an existing decentralized supply chain comprised of three tiers of players with competition: manufacturers, retailers and consumers. It first proposes a variational inequality for the supply chain network equilibrium model with production capacity constraints, and then employs the logarithmic-quadratic proximal prediction–correction method as a solution algorithm. Based on this model, this paper develops a generic mathematical program with equilibrium constraints for the competitive facility location problem, which can simultaneously determine facility locations of the entering firm and the production levels of these facilities so as to optimize an objective. Subsequently, a hybrid genetic algorithm that incorporates with the logarithmic-quadratic proximal prediction–correction method is developed for solving the proposed mathematical program with an equilibrium constraint. Finally, this paper carries out some numerical examples to evaluate proposed models and solution algorithms.     

An approximate dynamic programming approach for the vehicle routing problem with stochastic demands

This paper examines approximate dynamic programming algorithms for the single-vehicle routing problem with stochastic demands from a dynamic or reoptimization perspective. The methods extend the rollout algorithm by implementing different base sequences (i.e. a priori solutions), look-ahead policies, and pruning schemes. The paper also considers computing the cost-to-go with Monte Carlo simulation in addition to direct approaches. The best new method found is a two-step lookahead rollout started with a stochastic base sequence. The routing cost is about 4.8% less than the one-step rollout algorithm started with a deterministic sequence. Results also show that Monte Carlo cost-to-go estimation reduces computation time 65% in large instances with little or no loss in solution quality. Moreover, the paper compares results to the perfect information case from solving exact a posteriori solutions for sampled vehicle routing problems. The confidence interval for the overall mean difference is (3.56%, 4.11%).     

Rough set approach to multiple criteria classification with imprecise evaluations and assignments

Dominance-based Rough Set Approach (DRSA) has been introduced to deal with multiple criteria classification (also called multiple criteria sorting, or ordinal classification with monotonicity constraints), where assignments of objects may be inconsistent with respect to dominance principle. In this paper, we consider an extension of DRSA to the context of imprecise evaluations of objects on condition criteria and imprecise assignments of objects to decision classes. The imprecisions are given in the form of intervals of possible values. In order to solve the problem, we reformulate the dominance principle and introduce second-order rough approximations. The presented methodology preserves well-known properties of rough approximations, such as rough inclusion, complementarity, identity of boundaries and precisiation. Moreover, the meaning of the precisiation property is extended to the considered case. The paper presents also a way to reduce decision tables and to induce decision rules from rough approximations.     

A Guided Tabu Search for the Vehicle Routing Problem with two-dimensional loading constraints

We present a metaheuristic methodology for the Capacitated Vehicle Routing Problem with two-dimensional loading constraints (2L-CVRP). 2L-CVRP is a generalisation of the Capacitated Vehicle Routing Problem, in which customer demand is formed by a set of two-dimensional, rectangular, weighted items. The purpose of this problem is to produce the minimum cost routes, starting and terminating at a central depot, to satisfy the customer demand. Furthermore, the transported items must be feasibly packed into the loading surfaces of the vehicles. We propose a metaheuristic algorithm which incorporates the rationale of Tabu Search and Guided Local Search. The loading aspects of the problem are tackled using a collection of packing heuristics. To accelerate the search process, we reduce the neighbourhoods explored, and employ a memory structure to record the loading feasibility information. Extensive experiments were conducted to calibrate the algorithmic parameters. The effectiveness of the proposed metaheuristic algorithm was tested on benchmark instances and led to several new best solutions.