基于不同条件的旅游路线规划问题研究

运用2015年全国研究生数学建模竞赛F题的数据资料,针对旅游路线合理规划问题的第一问展开研究.以F题的问题一为起点进行了分析研究,是因为第一问的完成是解决后续问题的关键.首先通过地图搜集并补全了缺失数据并对数据进行合理的处理,然后采用将旅游年数最少目标转化为该最小生成树的"最少圈覆盖"方法来进行对问题一的求解,也可以理解为一个广义的多旅行商问题,以旅行商的人数(即年数)最少为目标.采用Dijkstra算法、最少圈覆盖法、智能算法和图论聚类等方法,通过这些方法建立了单目标优化模型,并运用旅行商问题和模型之间的转换来对问题进行分析与求解.     

Multi-objective optimization of inverse planning for accurate radiotherapy

The multi-objective optimization of inverse planning based on the Pareto solution set, according to the multi-objective character of inverse planning in accurate radiotherapy, was studied in this paper. Firstly,the clinical requirements of a treatment plan were transformed into a multi-objective optimization problem with multiple constraints. Then, the fast and elitist multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-Ⅱ)was introduced to optimize the problem. A clinical example was tested using this method. The results show that an obtained set of non-dominated solutions were uniformly distributed and the corresponding dose distribution of each solution not only approached the expected dose distribution, but also met the dosevolume constraints. It was indicated that the clinical requirements were better satisfied using the method and the planner could select the optimal treatment plan from the non-dominated solution set.     

Metric inequalities for routings on direct connections with application to line planning

We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems.     

Li2MnO3 content effects on thermal,structural, electrical and electrochemical properties of xLi2MnO3-(1-x)LiNi0.9Zn0.1O2 cathode materials

xLi₂MnO₃-(1-x)LiNi_0.9Zn_0.1O₂ (x = 0.1, 0.2 and 0.3) cathodes were prepared by two steps solid-state reaction method. Layered crystalline phases (space groups of C2/m for Li₂MnO₃ and R3m for LiNi_0.9Zn_0.1O₂) were detected in all cathodes. FTIR study also revealed the formation of the layered-type structures of all cathodes. The structural parameters were greatly influenced by the contents of Li₂MnO₃ in xLi₂MnO₃-(1-x)LiNi_0.9Zn_0.1O₂. The electrical conductivities were found in the range of 1.2 × 10^?6 to 2.7 × 10^?6 S/cm. The dielectric spectra revealed the interfacial polarization Maxwell–Wagner type dielectric dispersion existing in all samples. The cathodes delivered the discharge capacities of 149 (x = 0.1), 151 (x = 0.2) and 157 mAh/g (x = 0.3) with capacity retention between 94.6 and 96.8% when they were cycled from 3.0 to 4.5 V under 0.1C rate. The x = 0.3 cathode exhibited the highest cyclic performance (96.8%) after 10 cycles due to its lower cations disorder.     

MODELING HARVEST SCHEDULING IN MULTIFUNCTIONAL PLANNING OF FORESTS FOR LONGTERM WATER YIELD OPTIMIZATION

In this study, wood production and hydrologic functions of forests were accommodated within a planning procedure for separate working circles (areas dedicated to certain forest functions) that were delineated according to an Ecosystem‐Based Functional Planning approach. Mixed integer goal programming was used as the optimization technique. The timing and scheduling of a maintenance cutting (partial harvest) was the decision variable in the modeling effort, and an original formulation was developed as a multiobjective planning procedure. Four sample planning strategies were developed and model outputs were evaluated according to these strategies. Spatial characteristics of stands were considered, and used to prohibit the regeneration of adjacent stands during the same time period. Because of the positive relationship between qualified water production and standing timber volume in the forest, the model attempts to maximize qualified water production levels by increasing standing volume stocks in the forest through the delay of regeneration activities.     

Joint distributions of random sets and their relation to copulas

Random sets are set-valued random variables. They have been applied in various fields like stochastic geometry, statistics, economics, engineering or computer science, and are often used for modeling uncertainty. In an earlier paper the author has defined joint capacity and joint containment functionals which are multivariate set functions describing the joint distribution of random sets. This paper is concerned with the question how copulas can be used to describe or model the dependence of random sets. It is demonstrated that a joint containment functional can be related to its margins by a family of copulas. Furthermore, the paper provides a first insight how copulas can be used to define joint containment functionals.     

Graphene/activated carbon supercapacitors with sulfonated-polyetheretherketone as solid-state electrolyte and multifunctional binder

Sulfonated polyetheretherketone (SPEEK) has been synthesised by sulphonation process and used as the solid-state electrolyte, binder and surfactant for supercapacitors. Reduced graphene dispersed by SPEEK is used as a high-efficiency conducting additive in solid-state supercapacitors. It is found that SPEEK can improve the stability of the reduced graphene dispersion significantly, and therefore, the solid-state supercapacitors show a large decrease in IR drop and charge-transfer resistance (R_ct), resulting in a higher rate capability. The solid-state supercapacitors with the activated carbon/reduced graphene/SPEEK/electrode can be operated from 1 to 8 A/g and exhibit capacity retention of 93%. The noteworthy is more than twice higher value for capacity retention by comparison with the solid-state supercapacitors using activated carbon/reduced graphene/PVDF electrode (capacity retention is 36%). The cell of reduced graphene with SPEEK can be cycled over 5000 times at 5 A/g with no capacitance fading.     

Carbon-coated Li3VO4 with optimized structure as high capacity anode material for lithium-ion capacitors

Due to the high capacity, moderate voltage platform, and stable structure, Li₃VO₄ (LVO) has attracted close attention as feasible anode material for lithium-ion capacitor. However, the intrinsic low electronic conductivity and sluggish kinetics of the Li⁺ insertion process severely impede its practical application in lithium-ion capacitors (LICs). Herein, a carbon-coated Li₃VO₄ (LVO/C) hierarchical structure was prepared by a facial one-step solid-state method. The synthesized LVO/C composite delivers an impressive capacity of 435 mAh/g at 0.07 A/g, remarkable rate capability, and nearly 100% capacity retention after 500 cycles at 0.5 A/g. The superior electrochemical properties of LVO/C composite materials are attributed to the improved conductivity of electron and stable carbon/LVO composite structures. Besides, the LIC device based on activated carbon (AC) cathode and optimal LVO/C as anode reveals a maximum energy density of 110 Wh/kg and long-term cycle life. These results provide a potential way for assembling the advanced hybrid lithium-ion capacitors.     

Li3V2（PO4）3/C正极材料在不同电压区间的电化学行为及容量衰减原因

采用溶胶-凝胶法制备锂离子电池正极材料Li3V2(PO4)3/C.通过恒电流充放电测试、循环伏安(CV)、电化学阻抗谱(EIS)等方法,研究了Li3V2(PO4)3/C在不同电压区间的电化学行为(3.0-4.5 V和3.0-4.8 V).结果表明,3.0-4.8 V电压区间的循环性能和倍率性能均不及3.0-4.5 V电压区间的.3.0-4.5 V区间0.1C (1C=150 mA?g-1)倍率首次放电比容量为127.0 mAh?g-1,循环50次后容量保持率为99.5%,而3.0-4.8 V区间的分别为168.2 mAh?g-1和78.5%.经过高倍率测试后再回到0.1C倍率充放电,3.0-4.5 V和3.0-4.8 V的放电比容量分别为初始0.1C倍率的99.0%和80.7%.经过3.0-4.8 V电压区间测试后,少部分第三个锂离子能够在低于4.5 V的电压脱出,使3.0-4.5 V电压区间的放电比容量提升了7.4%. CV结果表明3.0-4.8 V区间的容量损失主要表现为第一个锂离子的不可逆损失.极片的X射线衍射(XRD)和X射线光电子能谱(XPS)分析测试结果表明经过3.0-4.8 V测试后, Li3V2(PO4)3的结构发生了轻微的改变.电感耦合等离子体(ICP)测试结果表明循环后的电解液中含有少量的V.结构变形和V溶解可能是Li3V2(PO4)3在3.0-4.8 V区间容量衰减的主要原因.     

一类多体系统非完整运动最优规划的拟牛顿算法

研究带有非完整约束的一类多体系统运动规划问题。多体系统中的非完整约束通常是由不可积的速度约束或不可积的守恒律引起。在系统动量和动量矩守恒情况下,动力学方程降阶为非完整形式约束方程,系统的控制问题可转化为无漂移系统的非完整运动规划问题。文中首先导出具有多体开链系统的非完整运动模型。利用最优控制理论和最优化技术,采用输入参数化的方法将连续的最优控制问题转化为离散的最优控制问题,提出一种非完整多体系统运动规划的拟牛顿算法。最后将该方法用于自由漂浮的空间三连杆机构,仿真结果验证了该方法的有效性。