线性一二次双层规划问题

本文利用对偶理论和Kuhn-Tucker条件来研究线性一二次双层规划问题, 给出一些二层规划解的最优性条件和一个求解二层规划解的算法。这些最优性条件丰富了非线性多层规划的理论, 而其求解算法为求解实际问题提供了有力的工具。一些数值试验结果将在本文未给出, 这些结果表明算法对于小规模问题的求解是相当有效的。     

求解多目标规划问题的Pareto多目标遗传算法

针对传统的多目标优化方法的局限性，提出用于多目标规划问题求解的Pareto多目标遗传算法。实验结果表明，该算法是可行有效的，而且能为决策者提供满意解。     

求解双层规划模型的粒子群优化算法

首先对粒子群优化算法作了改进,然后提出采用改进的粒子群优化算法并借助分层迭代的思想来求解双层规划模型,进而提出并描述了求解双层规划模型的一种通用的有效算法.最后,通过实验研究和对比分析验证了文中算法的有效性.     

求解非线性双层规划问题的混合变邻域粒子群算法

针对非线性双层规划难以获得全局最优的问题,汲取粒子群算法的快速搜索能力及变邻域搜索算法的全局搜索优势,提出了求解非线性双层规划问题的混合变邻域粒子群算法.首先利用Kuhn-Tucker条件,将非线性双层规划转化为一个单层规划问题,然后由粒子群算法得到一个较优的群体,通过审敛因子判断陷入局部最优的粒子,并进一步利用变邻域搜索算法的全局搜索能力对陷入局部最优的粒子进行优化,从而得到全局最优.测试函数的仿真实验对比分析证明了该算法的有效性.     

一种多损失条件风险值的双层规划模型及应用

在两级供应链中制造商与零售商之间的多产品定价与订购问题, 是一个多损失的双层风险决策问题, 可以建立双层规划模型解决. 本文研究了一种多损失条件风险值的双层规划模型, 对于多个损失函数和对应的权值水平, 在给定的置信水平下, 定义了不超过给定损失值的最小风险值(即VaR值)和对应的累积期望损失值(即CVaR损失值) 概念, 然后建立了一个多损失条件风险值的双层规划模型, 该模型的目标是求上下层的多损失CVaR值达最小的最优策略, 我们证明了它可以通过另一个较容易求解的双层规划模型获得最优解. 最后, 给出了两级供应链中多产品的定价与订购的双层条件风险值模型, 通过对2种面包产品销售数据进行计算, 获得了面包制造商的最优批发价和最优回购策略, 及零售商最优订购量.     

基于双层规划的攻击无人机协同目标分配优化

针对攻击无人机编队协同作战的背景,提出了基于双层规划的攻击无人机协同目标分配模型。分别以打击效果最大化和飞行航线最短作为模型的上下层目标,并贴近战场环境将目标优先程度、目标打击效果上下限以及打击时间窗口等因素作为模型约束。利用直觉模糊双层规划(intuitionistic fuzzy bilevel programming, IFBLP)理论对构建的协同目标分配双层混合整数规划模型进行了转化,并采用粒子群优化(particle swarm optimization, PSO)方法对其进行求解,给出了具体求解步骤。算例结果证明IFBLP理论能够有效解决所构建的双层混合整数规划模型。     

几类非线性双层规划问题的混合遗传算法

针对几类具有特殊下层结构的非线性双层规划问题,提出了一种混合遗传算法。首先利用单纯形法的思想设计了新的杂交算子,使杂交个体与种群中好的个体组杂交,从而产生尽可能好的杂交后代;其次对每个相对固定的上层变量值x,通过计算下层最优解y来提高种群个体的可行性,并分析了下层最优解的计算误差对算法性能的影响;最后对于下层存在多个最优解的情况,通过求解一个单层规划,给出了下层最优解的选择方法。数值结果表明该算法是有效的。     

基于层次遗传算法的非线性双层规划问题求解策略

双层规划是解决层次决策问题的运筹学工具。当前基于传统的优化思想已经提出了很多算法解决搜索空间已知的双层规划问题。但在双层规划领域仍然存在许多问题无法利用现有算法求解。本文基于进化博弈和多目标优化非支配排序的思想,设计了层次遗传算法并利用其求解非线性双层规划问题。最后通过测试函数验证算法的有效性。     

线性分式—二次双层规划的一个充要条件

利用已有的强对偶定理 ,给出线性分式—二次双层规划的一个充要条件.     

PGAs求解双层规划及其在分销系统优化设计中的应用

研究并行基因算法求解双层规划问题及其在供应链物流分销系统优化设计中的应用.利用下层优化问题的KKT条件把双层规划问题转化为等价的单层规划问题,再利用并行基因算法对得到的单层规划问题进行全局优化,从而得到双层规划问题的全局最优解,最后,通过具体案例研究了上述算法在供应链物流分销系统优化设计中的应用.结果表明,并行基因算法求解双层规划,充分利用了现有计算环境的并行能力,加快了收敛速度,改善了基因算法的全局收敛性能,算法达到了实用化的规模,是一种很有应用前景的计算方法.     

A penalty function method for solving ill-posed bilevel programming problem via weighted summation

For ill-posed bilevel programming problem, the optimistic solution is always the best decision for the upper level but it is not always the best choice for both levels if the authors consider the model＇s satisfactory degree in application. To acquire a more satisfying solution than the optimistic one to realize the two levels＇ most profits, this paper considers both levels＇ satisfactory degree and constructs a minimization problem of the two objective functions by weighted summation. Then, using the duality gap of the lower level as the penalty function, the authors transfer these two levels problem to a single one and propose a corresponding algorithm. Finally, the authors give an example to show a more satisfying solution than the optimistic solution can be achieved by this algorithm.     

基于二层规划的委托代理协调问题

考虑不对称信息条件下的委托代理问题,结合不适定二层规划的理论,给出了不适定委托代理问题的定义. 针对后者的乐观模型,利用一种模糊交互式协调算法进行求解,最终获得了一个委托人与代理人均可以接受的满意契约,从而达到了双方共赢的目的. 最后通过一个算例说明了所设计算法的合理性与可操作性.     

二层线性规划的有效解

在容许集有界且二层线性规划存在最优解是相应双目标规划有效解的假设下,证明了有效最优解可在容许集的顶点达到。给出了二层线性规划的解的更为合理的有效化方法,并用算例对各种有效化方法所得的有效解进行了比较。     

Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems

Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.     

Global convergent algorithm for the bilevel linear fractional-linear programming based on modified convex simplex method

A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming,which is a special class of bilevel programming.In our algorithm,replacing the lower level problem by its dual gap equaling to zero,the bilevel linear fractional-linear programming is transformed into a traditional single level programming problem,which can be transformed into a series of linear fractional programming problem.Thus,the modified convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming.Finally,an example demonstrates the feasibility of the proposed algorithm.     

New partial cooperation model for bilevel programming problems

Partial cooperation models are studied for many years to solve the bilevel programming problems where the follower’s optimal reaction is not unique. However, in these existed models, the follower’s cooperation level does not depend on the leader’s decision. A new model is proposed to solve this deficiency. It is proved the feasibility of the new model when the reaction set of the lower level is lower semicontinuous. And the numerical results show that the new model has optimal solutions when the reaction set of the lower level is discrete, lower semi-continuous and non-lower semi-continuous.     

A quadratic objective penalty function for bilevel programming

The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to find an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at lower level problems, a quadratic objective penalty function without lower level problems is defined and is proved equal to the original bilevel programming.     

基于递阶优化算法的一类两层规划问题的解法

提出一种基于分解协调的两级递阶结构优化算法来求解两层规划问题。通过设计解耦变量,两层规划问题被分解成若干相互独立的易于在结构的第一级求解的子问题。而结构的第二级是调整解耦变量使各子问题的解得以改善。算法以一种迭代的方式使第一级求得的子问题的解不断协调,最终达到两层规划的解。算例表明该算法是可行且有效的     

基于正交遗传算法的非线性两层规划问题解法

对于一类非线性两层规划问题,将下层规划分解成几个并列且独立的子问题。对于上层的每一个决策变量,求出下层各子问题的Karush-Kuhn-Tucker(K-K-T)稳定点,作为对上层决策的反应。针对上层问题,设计了自适应的正交遗传算法,并给出其全局收敛性证明。最后数值模拟验证了该算法的高效性及鲁棒性。