利用算符分析的问题求解

将状态空间的问题求解过程变换为逐步缩小与目标状态的差异过程是一种问题的分解方式．求解差异的顺序可通过分析算符对状态的影响而作出规划，规划的原则是最大限度地在不改变最近已实现子目标的条件下实现下一子目标．为此，在问题分解时各层子目标选择的依据是让各算符有最大的可利用率，即以状态对算符最小约束传播的原则选择各层子目标；最后生成一个子目标规划层次集．问题求解过程就表现为从初始状态开始实现层次集中的某一子目标序列，其间可能涉及子目标回溯．     

求解二层规划的混合微粒群算法

对于二层规划问题有许多经典的求解方法，如极点搜索法、分支定界法和罚函数法等。文中给出了基于微粒群算法的二层规划的一种新的求解方法。提出了分别先用单纯形法和内部映射牛顿法的子空间置信域法求解下层规划，然后用微粒群算法求解上层规划的求解方法，这两种混合微粒群算法分别用于求解线性二层规划和非线性二层规划。并结合实例的对比分析，说明了这两种混合微粒群算法求解二层规划的可行性和有效性。     

不确定性数据的超球支持向量机分类方法

针对区间不确定性数据的分类问题,提出一种基于超球支持向量机的多分类方法。采用超椭球凸集模型描述数据的不确定性信息;建立超球支持向量机的不确定约束规划模型,将其转化为两层嵌套约束规划问题;通过上下两层子优化交替迭代寻优的方法求解最优超球面,利用泰勒展开法,直接推导下层子优化线性近似问题的最优解,以降低计算复杂度。实验结果表明,该方法具有较高的分类精度及较好的抗噪性和鲁棒性,适合解决区间不确定性数据多分类问题。     

基于递阶嵌套GA 的空-地武器靶场效能大规模总体优化

针对大规模优化问题，其大系统分解协调算法存在收敛速度慢、计算时间长、易导致组合爆炸等不足，以空-地制导武器大规模火力规划问题为背景，提出一种递阶嵌套GA．其基本思想是通过分层降低计算复杂性，从而有效解决大规模火力规划问题求解的可计算性问题．递阶嵌套GA由内外两层构成。内层GA实现对各子模型的求解，并将求解结果传送给外层GA；外层GA则通过遗传操作对内层GA发生干预．仿真算例验证了算法的有效性．     

基于观测器的受扰非线性系统近似最优跟踪控制

研究一类受扰非线性系统的最优输出跟踪控制问题.给出了有限时域最优输出跟踪控制律的近似设计算法.首先将求解受扰非线性系统最优跟踪控制问题转换为求解状态向量与伴随向量耦合的非线性两点边值问题,然后利用逐次逼近方法构造序列将其转化为求解两个解耦的线性微分方程序列问题.通过迭代求解伴随向量的序列,可得到由解析的线性前馈-反馈控制部分和伴随向量的极限形式的非线性补偿部分组成的最优输出跟踪控制律.利用参考输入降维观测器和扰动降维观测器,解决了前馈控制的物理可实现问题.最后仿真结果表明了该方法的有效性.     

一类非线性连续大系统的三层递阶最优控制算法

非线性连续大系统的最优控制问题，应用线性化和预估方法，非线性问题可转化为一系列一性子系统问题，利用共态预估方法从而在低层并行地求解低维子系统的最优化问题，而上两层分别连续地副近所指定为量及共态向量和拉格朗日乘子，直到达到各自的最估值，最后得到全局问题解的三层递阶控制算法，其主要优点是明显地减少了计算时间。     

求解二层规划的混合微粒群算法

对于二层规划问题有许多经典的求解方法,如极点搜索法、分支定界法和罚函数法等。文中给出了基于微粒群算法的二层规划的一种新的求解方法。提出了分别先用单纯形法和内部映射牛顿法的子空间置信域法求解下层规划,然后用微粒群算法求解上层规划的求解方法,这两种混合微粒群算法分别用于求解线性二层规划和非线性二层规划。并结合实例的对比分析,说明了这两种混合微粒群算法求解二层规划的可行性和有效性。     

基于定制内点法的多无人机协同轨迹规划

为提高多无人机(Unmanned aerial vehicles, UAV)协同轨迹规划(Cooperative trajectory planning, CTP)效率,在解耦序列凸优化(Sequential convex programming, SCP)方法基础上,提出一种高效求解凸优化子问题的定制内点法.首先引入松弛变量,构建子问题的等价描述形式,并推导该形式下的子问题最优性条件.然后在预测-校正原对偶内点法的框架下,构建一套高效求解最优性条件方程组的计算流程以降低子问题计算复杂度,并利用约束矩阵特征提出一种快速计算原对偶搜索方向的方法以提高规划效率.仿真结果表明,在解耦序列凸优化框架下,定制内点法可将协同轨迹规划耗时降低一个数量级,达到秒级.     

共轭梯度型支撑向量机

求解支撑向量机的二次规划有不同的变形.对于线性问题,从一个变形出发,利用Lagrangian对偶技巧,将特征空间的高维二次规划问题转化为输入空间的低维无约束、可微凸的对偶规划.针对目标函数的分片二次特征,结合快速精确的一维搜索技术,提出共轭梯度型支撑向量机来求解该问题.利用Cholesky分解或非完全(incomplete)Cholesky分解方法分解核矩阵,在算法复杂度增加很少的条件下可实现基于核函数的非线性分类.该算法可以在普通计算机上快速求解上百万规模的线性训练问题和较大规模的非线性训练问题.大量数据实验和复杂度分析表明,该算法与同类算法如ASVM、LSVM相比是有效的.     

基于聚类分解的WCDMA基站布局规划算法

针对大规模WCDMA无线网络基站布局规划问题，提出一种基于聚类分解的分层算法．在聚类分解中，以测试点信号增益矩阵构造聚类分解数据，并给出了收敛判定函数和相似度计算方法．在分层算法中，首先用K均值聚类将原问题分解为K个子规划问题，然后对各子问题求解整数规划问题，最后对各子问题的基站布局结果进行全局调整．仿真计算验证了该算法的有效性．     

灰色二层多目标线性规划问题及其解法

针对二层多目标线性规划问题,结合灰色系统的特性,提出了一般灰色二层多目标线性规划问题,并给出了模型的相关定义和定理.针对漂移型灰色二层多目标线性规划问题,提出一种具有全局收敛性质的求解算法.首先通过线性加权模理想点法把多目标转化为单目标;然后当可行域为非空紧集时,利用库恩塔克条件把双层转化为单层,再利用粒子群算法搜索单目标单层线性规划即可得到原问题的解;最后通过算例表明了该算法的有效性.     

两层多目标规划的罚函数法

研究了一类非线性两层多目标规划问题.在下层多目标规划问题的目标函数是严格凸函 数、决策变量约束集是凸集的假设下,通过将两层多目标规划问题转化成一系列单层多目标规划 问题,建立了两层多目标规划的罚函数理论,并进行了收敛性分析.从而丰富了两层多目标规划的 理论,为解决实际中的两层多目标决策问题提供了有力的工具.     

A study on the use of heuristics to solve a bilevel programming problem

The bilevel programming problem is characterized as an optimization problem that has another optimization problem in its constraints. The leader in the upper level and the follower in the lower level are hierarchically related where the leader's decisions affect both the follower's payoff function and allowable actions, and vice versa. One difficulty that arises in solving bilevel problems is that unless a solution is optimal for the lower level problem, it cannot be feasible for the overall problem. This suggests that approximate methods could not be used for solving the lower level problem, as they do not guarantee that the optimal solution is actually found. However, from the practical point of view near‐optimal solutions are often acceptable, especially when the lower level problem is too costly to be exactly solved thus rendering the use of exact methods impractical. In this paper, we study the impact of using an approximate method in the lower level problem, discussing how near‐optimal solutions on the lower level can affect the upper level objective function values. This study considers a bilevel production‐distribution planning problem that is solved by two intelligent heuristics hierarchically related: ant colony optimization for solving the upper level problem, and differential evolution method to solve the lower level problem.     

An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn–Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.     

基于Pareto支配的双目标优化求解非线性双层规划问题

双层规划问题是一类具有双层递阶结构的系统优化问题。采用Pareto支配的双目标优化策略求解非线性双层规划问题。利用K-T条件把双层规划问题等价转化单层规划问题,进而结合约束部分建立可行性度量目标形成双目标规划问题。在基本的差分进化算法框架中融入非负的最小二乘曲线拟合判断候选解的可行性,构造基于动态概率的Pareto支配选择策略挑选下一代个体,解决种群容易陷入局部最优的缺陷。15个标准函数的测试结果对比显示,该算法在求解非线性双层规划问题中具有较好的全局寻优能力、较低的计算复杂度、较强的稳定性和适用性,可以获得全局最优解。     

计算甘油代谢目标函数的一种新算法

通量平衡分析是代谢工程研究中能够定量预测细胞内通量分布情况的有效工具,然而其预测准确性的前提是需要设计合理的代谢目标函数。研究了克雷伯氏杆菌歧化甘油生产1,3-丙二醇的代谢目标函数计算问题。该问题的数学形式是一个双层规划模型,首先应用线性规划的对偶理论将其转化为等价的单层非线性优化问题,然后采用非线性优化算法对其进行求解。与已有的研究结果相比,所提方法获得了克雷伯氏杆菌歧化甘油代谢的全局最优通量分布情况。     

一类区间系数二次双层规划问题的遗传算法

针对上下层均含区间系数的二次双层规划,提出了一种基于两个适应度评估的遗传算法。将下层目标系数区间作为遗传算法的搜索空间,对于每一个确定的个体,下层问题不含区间系数;利用二次规划的最优性条件,将个体所对应的问题转化为两个确定的二次规划;利用基枚举方法求解这两个二次规划问题,相应的最优值作为个体的两个适应度。算法通过两个适应度的比较,获得问题的最好最优解和最差最优解。数值仿真结果表明,该算法是可行有效的。     

An approximate programming method based on the simplex method for bilevel programming problem

Many real problems can be modeled to the problems with a hierarchical structure, and bilevel programming is a useful tool to solve the hierarchical optimization problems. So the bilevel programming is widely applied, and numerous methods have been proposed to solve this programming. In this paper, we propose an approximate programming algorithm to solve bilevel nonlinear programming problem. Finally, the example illustrates the feasibility of the proposed algorithm.     

Topology optimization with displacement constraints: a bilevel programming approach

We consider the minimum-compliance formulation of the truss topology problem with additional linear constraints on the displacements: the so-called displacement constraints. We propose a new bilevel programming approach to this problem. Our primal goal (upper-level) is to satisfy the displacement constraint as well as possible — we minimize the gap between the actual and prescribed displacement. Our second goal (lower level) is to minimize the compliance — we still want to find the stiffest structure satisfying the displacement constraints. On the lower level we solve a standard truss topology problem and hence we can solve it in the formulation suitable for the fast interior point alogrithms. The overall bilevel problem is solved by means of the so-called implicit programming approach. This approach leads to a nonsmooth optimization problem which is finally solved by a nonsmooth solver.     

PARTICLE SWARM OPTIMIZATION-BASED ALGORITHM FOR BILEVEL JOINT PRICING AND LOT-SIZING DECISIONS IN A SUPPLY CHAIN

This study considers joint pricing and lot-sizing policies in a single-manufacturer–single-retailer system. Because a supply chain is a hierarchical system, we adopt a bilevel programming technique to establish a bilevel joint pricing and lot-sizing model guided by the manufacturer. The objective of the problem here is to respectively maximize the manufacturer's and the retailer's net profits by determining the manufacturer's and retailer's lot size, the wholesale price and the retail price simultaneously. Following the properties of the bilevel programming problem (BLPP), we design a novel bilevel particle swarm optimization algorithm (BPSO), and it can solve BLPP without any assumed conditions of the problem. BPSO shows a good performance on eight benchmark bilevel problems. Then BPSO is employed to solve the proposed bilevel model, and the experimental data are used to analyze the features of the proposed bilevel model, and the results support the finding that BPSO is effective in optimizing BLPP.