A hybrid differential evolution algorithm to vehicle routing problem with fuzzy demands

In this paper, the vehicle routing problem with fuzzy demands (VRPFD) is considered, and a fuzzy chance constrained program model is designed, based on fuzzy credibility theory. Then stochastic simulation and differential evolution algorithm are integrated to design a hybrid intelligent algorithm to solve the fuzzy chance constrained program model. Moreover, the influence of the dispatcher preference index on the final objective of the problem is discussed using stochastic simulation, and the best value of the dispatcher preference index is obtained.     

Mathematical modeling and efficient optimization methods for the distance-dependent rearrangement clustering problem

In this article we present a computational study for solving the distance-dependent rearrangement clustering problem using mixed-integer linear programming (MILP). To address sparse data sets, we present an objective function for evaluating the pair-wise interactions between two elements as a function of the distance between them in the final ordering. The physical permutations of the rows and columns of the data matrix can be modeled using mixed-integer linear programming and we present three models based on (1) the relative ordering of elements, (2) the assignment of elements to a final position, and (3) the assignment of a distance between a pair of elements. These models can be augmented with the use of cutting planes and heuristic methods to increase computational efficiency. The performance of the models is compared for three distinct re-ordering problems corresponding to glass transition temperature data for polymers and two drug inhibition data matrices. The results of the comparative study suggest that the assignment model is the most effective for identifying the optimal re-ordering of rows and columns of sparse data matrices.     

Calculus of variations and descriptive set theory

If X is a locally compact Polish space, then LSC(X, ?) denotes the compact Polish space of lower semi‐continuous real‐valued functions on X equipped with the topology of epi‐convergence. Our purpose in this article is to prove the following: if –∞ < α < β < ∞ and –∞ < a < b < ∞, while r ∈ ? \ {0}, then the set CV of all f ∈ LSC([α, β ] × [a, b ] × ?, ?) for which there is u ∈ C^r ([α, β ], [a, b ]) such that for any v ∈ C^r ([α, β ], [a, b ]) we have that ∫_α^β f (x, u (x), v ′(x))dx ≥ ∫_α^β f (x, v (x), v (x))dx is not Borel (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

直线Cantor集的Hausdorff中心测度

设K是由直线上迭代函数系统{φ1,φ2,…,φm}生成的吸引子,其中φi(z)=ρix+bi,i=1,2,…,m.称K为直线Cantor集.在压缩参数满足一定条件时,本文得到了K的Hausdorff中心测度精确值的计算公式.     

Global attracting sets and stability of neutral stochastic functional differential equations driven by Rosenblatt process

We are concerned with a class of neutral stochastic partial differential equations driven by Rosenblatt process in a Hilbert space. By combining some stochastic analysis techniques, tools from semigroup theory, and stochastic integral inequalities, we identify the global attracting sets of this kind of equations. Especially, some sufficient conditions ensuring the exponent p-stability of mild solutions to the stochastic systems under investigation are obtained. Last, an example is given to illustrate the theory in the work.     

An explicit algorithm for imbedding solid boundaries in Cartesian grids for the reactive Euler equations

We present a local and point-wise scheme for imposing reflective boundary conditions to stationary internal boundaries for solving the reactive Euler equations on Cartesian grids. The scheme is presented in two and three dimensions and can run efficiently on parallel machines while still maintaining the same advantages over other methods for enforcing internal boundary conditions. Level sets are used to represent internal solid regions along with a new local node sorting algorithm that decouples internal boundary nodes by establishing their connectivity to other internal boundary nodes. This approach allows us to enforce boundary conditions via a direct procedure, removing the need to solve a coupled system of equations numerically. We examine the accuracy and fidelity of our internal boundary algorithm by simulating flows past various solid boundaries in two and three dimensions, showing good agreement between our numerical results and experimental data.     

Transition sets analysis based parametrical design of nonlinear metal rubber isolator

This research proposes the parametrical design of Metal Rubber (MR) isolation platform based on the investigation of nonlinear vibration properties under different types of excitation. Based on the mechanical model established by experiments, the restoring force of the isolation platform is proposed as a nonlinear function in consideration of the stiffness nonlinearity and Coulomb friction of metal wires. Then, the perturbation method is utilized to solve the steady states whose local stability is studied by singularity theory. The main results obtained by singularity theory show that there are five different types of vibration property, and the critical conditions for the transformation of different vibration properties are defined by transition sets. For impact excitation, the optimum structural parameters are obtained based on the vibration dissipation time via nonlinear backbone analysis; for periodic excitation, the optimum structural parameters are determined according to multiple standards including the bandwidth for effective isolation, bandwidth for multi-steady states, resonance peak and displacement transmissibility in high frequency band etc. The vibration performances for optimum structural parameters are verified by dynamical experiments. In conclusion, this paper carries out a novel sight of choosing optimum parameters, and therefore provides the guidance for the utilization of MR isolation platform for different types of excitation in engineering practices.     

基于改进的局部表面凸性算法三维点云分割

点云分割是点云分类、识别以及三维重建等处理的基础,分割结果对后续应用影响巨大。本文提出利用连通点集改进局部表面凸性算法中邻近点关系的方法,解决目前激光三维成像系统点云分割算法在处理复杂环境散乱点云时存在分割过度及分割不充分的问题,通过主顶点与周围点构成连通集,作为分割判断局部子点集,形成有效分割区域。该方法解决了常用点云分割方法无法对形状不规则物体进行有效分割的问题,提高了分割精度。算法实验结果表明,相比于最小切割算法和区域生长算法,基于连通点集的改进局部表面凸性算法对实际路面环境信息的分割效果更好,并能在一定程度上避免分割过度和分割不充分的情况,证明该方法适用于复杂环境散乱点云数据分割。     

区间集上非交换剩余格<∈,∈∪Q>-fuzzy滤子的构造

以区间集和滤子理论作为研究区间集上非交换剩余格<∈,∈∪Q>-fuzzy滤子的工具,通过引入区间集上非交换剩余格<∈,∈∪Q>-fuzzy滤子的概念,讨论了生成<∈,∈∪Q>-fuzzy滤子的几种方法,彰显模糊逻辑推演系统被视为代数滤子的镜像.