基于粒子群算法的变循环发动机部件法建模及优化

针对变循环发动机部件法建模及优化问题,首先使用部件法对变循环发动机进行建模,列出发动机各部件匹配工作时,受制约的7个平衡方程;然后,根据发动机工作时的已知条件以及发动机的部件法数学模型,推导出以7个平衡方程为基础的非线性方程组,并使用粒子群算法求解非线性方程组,实现变循环发动机部件法建模及优化;最后,对模型进行了评价并提出了改进方法.结果表明,粒子群算法对于求解变循环发动机非线性方程组具有较好的收敛性     

变循环发动机部件法建模及优化述评

叙述了2013年全国研究生数学建模竞赛A题"变循环发动机部件法建模及优化"的命题背景和目的,分析了本赛题的建模及求解思路,总结了参赛队的一些好的做法和评阅过程中发现的一些问题,最后叙述了本赛题还需要继续思考的问题.     

基于双层博弈模型的民用航空产业链研究

本文针对民用航空市场中的大飞机制造商及航空发动机制造商建立双层博弈模型。在上层模型中,大飞机制造商以市场利润为目标决定其产量及对各发动机供应商的采购量;在下层模型中,航空发动机供应商通过求解一个优化问题决定其自身产量。在求解过程中,将下层优化问题转化为KKT条件,并作为上层优化问题的约束条件,使用分布式迭代算法(Distributed iterative algorithm),进行编程求解。本文通过求解波音-空客双寡头格局下的市场均衡对模型的有效性进行验证,并进一步分析国产大飞机C919量产后市场均衡的变化。     

变循环发动机模型的求解算法研究

采用部件法建立了变循环发动机的多维非线性隐式方程组模型,模型具有隐式性,因而求解过程复杂,收敛困难.针对上述问题,采用遗传算法和牛顿-拉夫逊法进行模型求解,提出了算法的有效性评价指标:初值敏感性、收敛性和稳定性.对两种算法进行有效性评价.针对发动机工作性能最优化问题,建立了多目标模型,用遗传算法进行求解,并分析了相关变量随马赫数变化的规律.结果可为变循环发动机模型求解算法的选择与设计提供参考.     

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.     

一种多参数谱三项共轭梯度法

通过求解带有罚参数的优化问题设计共轭梯度法是一种新思路.基于Fatemi的优化问题求解,通过估计步长和选择合适的罚参数建立一个谱三项共轭梯度法,为证得算法的全局收敛性对谱参数进行修正.在标准Wolfe线搜索下证明了该谱三项共轭梯度算法的充分下降性以及全局收敛性.最后,在选取相同算例的多个算法测试结果中表明新方法数值试验性能表现良好.     

基于配点GA-SQP算法的月球软着陆轨道优化设计

月球软着陆是月球探测中的一项关键技术.针对这项技术,提出基于直接配点法和GA-SQP法的月球软着陆轨道优化算法.算法通过建立月球软着陆动力学模型并进行归一化处理,利用直接配点法将月球软着陆轨道优化问题离散为非线性规划问题,应用SQP方法可求解该优化问题.同时考虑到SQP方法对初值敏感、收敛半径小及容易陷入局部极值等不足,提出了应用GA为SQP方法提供迭代初值的算法,提高了算法的稳定性.最后给出了相关的仿真结果.     

考虑n中连续取k失效准则的树状系统可靠性求解方法

树状网络系统在管道运输,网络通信中较为常见,对其进行可靠性评估对系统设计及优化具有重要意义。针对树状冗余系统,在n中连续取k失效准则下,通过有限马尔可夫嵌入法并对其进行变形,研究了树状系统可靠性求解方法。本文对树状系统建模加以定义,提出了基于层数参数,层-节点向量,父-子节点矩阵三元参数的树状系统表示方法,研究了变形有限马尔可夫嵌入法的树状系统n中连续取k失效准则下的可靠性求解方法,给出了三个数值算例应用并分析了算法的运算复杂度。最后,本文对比讨论了基于概率母函数法的树状系统在n中连续取k准则下系统可靠性求解方法的研究,得出结论本文算法针对树状冗余系统n中连续取k失效准则下系统可靠性求解应用范围更广,求解效率较高。     

考虑车载容量的多区型仓库拣货路径优化研究

拣货作业是仓库核心作业之一,占据仓库运营大量的时间成本和资金成本.针对多区型仓库拣货路径优化问题,对多区型仓库布局、货位坐标、路径等问题进行了定义,构建了多区型仓库拣货路径优化建模,接着通过大量实验确定了人工鱼群算法在求解拣货路径问题时的最优算法参数组合,通过演示性实验验证了模型与算法的有效性,最后从波次订单对实验结果的影响、车载容量对实验结果的影响和算法对比分析3个方面验证了人工鱼群算法的实用性和优越性.结果表明,所建立的多区型仓库拣货路径优化的模型及其求解方法,能够有效提高仓储拣货作业效率.     

基于拟态物理学的约束多目标共轭梯度混合算法

在拟态物理学优化算法APO的基础上,将一种基于序值的无约束多目标算法RMOAPO的思想引入到约束多目标优化领域中.提出一种基于拟态物理学的约束多目标共轭梯度混合算法CGRMOAPA.算法采取外点罚函数法作为约束问题处理技术,并借鉴聚集函数法的思想,将约束多目标优化问题转化为单目标无约束优化问题,最终利用共轭梯度法进行求解.通过与CRMOAPO、MOGA、NSGA-II的实验对比,表明了算法CGRMOAPA具有较好的分布性能,也为约束多目标优化问题的求解提供了一种新的思路.     

Finite time exergoeconomic performance for six endoreversible heat engine cycles: Unified description

The operation of a universal steady flow endoreversible heat engine cycle model consisting of two constant thermal-capacity heating branches, a constant thermal-capacity cooling branch and two adiabatic branches is viewed as a production process with exergy as its output. The finite time exergoeconomic performance optimization of the universal endoreversible heat engine cycle is investigated by taking profit optimization criterion as the objective. The analytical formulae for power, efficiency and profit rate function of the universal endoreversible heat engine cycle with heat resistance loss are derived. The focus of this paper is to search the compromised optimization between economics (profit) and the utilization factor (efficiency) for endoreversible cycles. Moreover, analysis and optimization of the model are carried out in order to investigate the effect of cycle process on the performance of the universal endoreversible heat engine cycle using numerical examples. The results obtained herein include the performance characteristics of six endoreversible heat engines, including Carnot, Diesel, Otto, Atkinson, Brayton and Dual cycles.     

基于混沌量子算法和MAGTD的多目标FJSP求解策略

针对多目标环境下柔性作业车间的调度问题,以最小化最大完工时间和惩罚值为目标,建立调度问题的数学模型,提出了基于混沌理论的量子粒子群算法。针对实际生产交货期不确定的特点,在量子粒子群算法基础上,提出引入混沌机制建立初始群的方法;利用混沌机制的遍历性,提出混沌局部优化策略;为获取最优调度方案提出了引入多指标加权灰靶选择策略。通过典型基准算例和对比测试,验证了所提出的算法获得最满意调度方案的可行性和求解多目标柔性作业车间调度问题的有效性。     

An exact parallel method for a bi-objective permutation flowshop problem

In this paper, we propose a parallel exact method to solve bi-objective combinatorial optimization problems. This method has been inspired by the two-phase method which is a very general scheme to optimally solve bi-objective combinatorial optimization problems. Here, we first show that applying such a method to a particular problem allows improvements. Secondly, we propose a parallel model to speed up the search. Experiments have been carried out on a bi-objective permutation flowshop problem for which we also propose a new lower bound.     

一种连续的谱聚类优化模型

聚类与图的划分问题在大数据分析中有着重要的应用.这类问题一般被描述为组合优化问题,因此较难快速求解.本文设计了一种新的连续优化模型,并提出了一种块坐标下降算法,数值实验显示我们的新方法在求解聚类与图的划分问题上很有潜力.我们还更进一步分析了我们的连续优化模型和组合优化模型的关系.     

Optimization technique in solving laminar boundary layer problems with temperature dependent viscosity

In this paper, a novel numerical method is proposed to solve specific third order ODE on semi-infinite interval. These kinds of problems often occur in laminar boundary layer with temperature dependent viscosity. Runge-Kutta method incorporating with optimization techniques is used to solve the problem. First, the semi-infinite interval is transformed into a finite interval. Second, by converting the boundary value problem, with some initial and distributed unknowns, into an optimization problem, solving the original problem is limited to solving a multiobjective optimization problem. Third, we use shooting-Newton’s method for solving this optimization problem. It is shown that the Falkner-Skan problem with constant surface temperature, that arise during the solution for the laminar forced convection heat transfer from wedges to flow, can be solved accurately and simultaneously by this strategy. Numerical results for different values of wedge angle and Prandtl number are presented, which are in good agreement with some of the successful provided solutions in the literature.     

GasTurbnLab: a multidisciplinary problem solving environment for gas turbine engine design on a network of nonhomogeneous machines

Gas turbine engines are very complex (with 20–40,000 parts) and have extreme operating conditions. The important physical phenomena take place on scales from 10–100 microns to meters. A complete and accurate dynamic simulation of an entire engine is enormously demanding. Designing a complex system, like a gas turbine engine, will require fast, accurate simulations of computational models from multiple engineering disciplines along with sophisticated optimization techniques to help guide the design process. In this paper, we describe the architecture of an agent-based software framework for the simulation of various aspects of a gas turbine engine, utilizing a “network” of collaborating numerical objects through a set of interfaces among the engine parts. Moreover, we present its implementation using the Grasshopper agent middleware and provide simulation results that show the feasibility of the computational paradigm implemented.     

油田注水系统拓扑布局优化的混合遗传算法

以投资最小为目标函数,建立了注水系统拓扑布局优化数学模型.根据模型特点,将优化问题分为两层,分别采用遗传算法和非线性优化方法进行求解.并对遗传算法的操作过程进行了改进,调整了适应函数,改进了交叉和变异操作,结合了模拟退火算法,在操作过程中使约束条件得到满足,减少了不可行解的产生,使遗传算法的优化性能得到了提高.优化算例说明了该方法的有效性.     

Scheduling open shops with parallel machines to minimize total completion time

This paper explores scheduling a realistic variant of open shops with parallel machines per working stage. Since real production floors seldom employ a single machine for each operation, the regular open shop problem is very often in practice extended with a set of parallel machines at each stage. The purpose of duplicating machines in parallel is to either eliminate or to reduce the impact of bottleneck stages on the overall shop efficiency. The objective is to find the sequence which minimizes total completion times of jobs. We first formulate the problem as an effective mixed integer linear programming model, and then we employ memetic algorithms to solve the problem. We employ Taguchi method to evaluate the effects of different operators and parameters on the performance of memetic algorithm. To further enhance the memetic algorithm, we hybridize it with a simple form of simulated annealing as its local search engine. To assess the performance of the model and algorithms, we establish two computational experiments. The first one is small-sized instances by which the model and general performance of the algorithms are evaluated. The second one consists of large-sized instances by which we further evaluate the algorithms.