A two-level self-adaptive variable neighborhood search algorithm for the prize-collecting vehicle routing problem

This paper investigates the prize-collecting vehicle routing problem (PCVRP), which has a strong background in practical industries. In the PCVRP, the capacities of all available vehicles are not sufficient to satisfy the demands of all customers. Consequently it is not a compulsory requirement that all customers should be visited. However, a prize can be collected once a customer is visited. In addition, it is required that the total demands of visited customers should reach a pre-specified value at least. The objective is to establish a schedule of vehicle routes so as to minimize the total transportation cost and at the same time maximize the prize collected by all vehicles. The total transportation cost consists of the total distance of vehicle routes and the sum of vehicles used in the schedule. To solve the PCVRP, a two-level self-adaptive variable neighborhood search (TLSAVNS) algorithm is developed according to the two levels of decisions in the PCVRP, namely the selection of customers to visit and the visiting sequence of selected customers in each vehicle route. The proposed TLSAVNS algorithm is self-adaptive because the neighborhoods and their search sequence are determined automatically by the algorithm itself based on the analysis of its search history. In addition, a graph extension method is adopted to obtain the lower bound for PCVRP by transforming the proposed mixed integer programming model of PCVRP into an equivalent traveling salesman problem (TSP) model, and the obtained lower bound is used to evaluate the proposed TLSAVNS algorithm. Computational results on benchmark problems show that the proposed TLSAVNS algorithm is efficient for PCVRP.     

层次分析法在择校问题中的应用

数学无处不在,比如小升初择校问题.公立学校升学率低、但校园环境好、私立学校升学率高、但其他条件却无法与公立学校相比,到底应该如何选择？使用层次分析法来指导家长择校,首先选取一些比较准则,如升学率、环境等,给出在家长心目中的权重,然后根据每一准则对学校进行排序,结合两层的排序得到总排序,排在第一位的学校就是最理想的学校.     

酚醛泡沫在建筑保温防火中的应用现状和前景

通过对酚醛泡沫在建筑中保温防火的性能研究,并阐述其在国内外的发展历程和现状,指出酚醛泡沫兼具防火、保温、环保等多重优点,在中国建筑保温领域具有广阔的应用前景。     

基于能见度图的元胞疏散最短路径模型研究

近年来发生的火灾多在人员密集场所,当突发事件发生时,人员疏散往往特别困难,因此,规划行人在大型公众聚集建筑物中的疏散路径非常重要。基于能见度图建构的元胞疏散最短路径模型可直接用于实际的紧急疏散指示路径的规划,避免设置大量逃生指示装置致使工程成本过高及视觉不美观,并且也解决了有限制逃生指示装置数量当作限制条件的最大涵盖面积的求解复杂、空间大的问题。     

考虑侧向支撑刚度影响的蜂窝钢梁临界弯矩计算研究

钢梁可通过设置侧向支撑并控制间距避免其发生整体弯扭屈曲,支撑刚度会对钢梁的临界弯矩产生影响。利用有限元方法研究了不同侧向支撑刚度下蜂窝钢梁临界弯矩。研究结果表明,随着侧向支撑刚度的增加,蜂窝钢梁临界弯矩亦逐渐增加;但当支撑刚度达到临界支撑刚度后,随着侧向支撑刚度的增加钢梁临界弯矩不变。根据参数分析结果,提出了根据支撑间距确定临界支撑刚度的简化计算公式。     

八辊轧机板形预报模型及应用

在分析八辊轧机结构特点的基础上,结合八辊轧机的设备与工艺特点,对金属塑性变形模型和辊系弹性变形模型两个模型进行耦合,开发了一套适合于八辊冷轧机组的板形预报模型,给出了相应的板形计算流程图,并将模型应用到某冷轧厂1450八辊冷轧机组的生产实践中,开发出了相应的板形预报软件。现场使用效果表明：预报软件预报效果良好,能够较大幅度地降低板形封闭率,给企业带来较大的经济效益。     

氢氧化钠羰基化合成甲酸钠工艺深入研究

通过热力学计算证明一氧化碳水合反应无法进行,同时对氢氧化钠羰基合成甲酸钠反应机理进一步探讨。对甲酸钠合成的化学反应焓变进行理论计算,为-90.131 kJ/mol。在此理论基础上,围绕优化甲酸钠反应条件开展研究,摸索出了生产中预热器温度控制的适宜范围(145~155℃)。通过实验发现:一氧化碳压力越高,反应速度越快,反应时间越短;在一氧化碳分压一定的情况下,氮气分压高低对甲酸钠的合成反应速度和转化率都没有影响。     

Syntheses,structures and field-dependent slow magnetic relaxation of saddle-like Cu4 and reverse “U” shape Mn3 complexes

Three novel complexes [Cu₄(ccsa)₄(Py)₈] (1), [Mn₃(ccsa)₄(Py)₆(H₂O)₂]·2Py·H₂O (2) and [MnFe₂(ccsa)₄(Py)₆(H₂O)₂] (3) (H₂ccsa = 3-carboxy-5-chloro-salicylald-ehyde) have been synthesized and characterized by elemental analysis, power X-ray diffraction (PXRD), Infrared (IR) spectrum and X-ray single-crystal diffraction. Complex 1 shows a rare 16-MC-4 macrocycle framework with [Cu-O-C-O] repeating unit, and four Cu ions connected by the carboxy groups from four ligands. Complexes 2 and 3 are isostructural and the metal ions exhibit reverse “U” shape arrangement. Magnetic studies reveal unexpected ferromagnetic coupling and field-dependent slow magnetic relaxation in complex 1.     

Preparation of a novel Cd2Ta2O7 photocatalyst and its photocatalytic activity in water splitting

Cd₂Ta₂O₇, which showed high photocatalytic activity for overall water splitting, was synthesized by sol–gel method. Its maximum activity increased from 46.2 μmol-H₂/h and 23.0 μmol-O₂/h into 173.0 μmol-H₂/h and 86.3 μmol-O₂/h when 0.2 wt.% NiO was loaded as co-catalyst. The band structure of Cd₂Ta₂O₇ was calculated by a plane-wave-based density functional theory (DFT). The valence band is mainly formed by O 2p AO's, and the conduction band predominantly consists of Ta 5d, O 2p and Cd 5s5p AO's. Cd atoms endue new features different from other tantalates, and its effect on the band structure of Cd₂Ta₂O₇ was discussed.