求解群体多目标决策问题的一种方法

引进了群体多目标决策问题的一种新的最优解概念──s-最优平衡解,它的实际意义是对于每个决策者而言在每个目标下都给出一个让步值.证明了求解s-最优平衡解等价于求解一个对应的单目标优化问题,并在一定条件下s-最优平衡解总是存在的.讨论了具有不同让步值的s-最优平衡解.数值例子表明这个方法对解决群体多目标决策问题具有一定的有效性.     

SENSITIVITY ANALYSIS IN BILEVEL LINEAR PROGRAMMING

1.IntroductionMultilevelprogrammingmodelsdescribesdecisionmakingsituationswhereahierarchyexists.Inabilevelsystem,thedecisionofthehigherlevel(leader)mayaffectthechoiceofstrategyavailabletothelowerlevel(follower)whoattemptstooptimizehisobjectivefunction.Inthissystem,theleaderalsoconsidersthefollower'sresponsewhichisbasedonoptimizingthefollower'sobjectivefunction,forinstance,see[1].Asanextensionandavariationofmathematicalprogramming,multilevelprogrammingwasfirstintroducedbyCandlerandTownsley[2].…     

New Implicit Enumeration Method for Polynomial 0-1 Programming

A new implicit enumeration method for polynomial zero-one programming is proposed in this article. By adopting the p-norm surrogate constraint method, a polynomial zero-one programming problem with multiple constraints can be converted into an equivalent polynomial zero-one programming problem with a single surrogate constraint. A new solution scheme is then devised to take the advantage of this prominent feature in carrying out the “fathoming” procedure and the “backtrack” procedure in a searching process of an implicit enumeration. We demonstrate the efficiency of this new algorithm by some promising computational results. Finally, we conclude by proposing certain topics for future research.     

伪凸二次规划的最优解集

寻找数学规划问题的多个最优解乃至最优解集是一项有理论价值和实践意义的工作,因为决策者可以从多个最优解中挑选其满意的最佳方案。然而,目前有关寻求非线性规划问题多个最优解的研究还比较少见且存在局限性。研究了伪凸目标函数的二次规划问题,首先提出和证明了最优解集的特征,然后借助于求解带有人工变量的辅助线性规划全部最优解的方法,提出了伪凸二次规划有唯一最优解的条件,并在不满足该条件的情况下,通过寻找辅助线性规划的最优解集以获得伪凸二次规划的最优解集。最后给出了两个算例以说明方法的有效性。     

多项式0-1规划中隐枚举算法的改进及应用

提出了一个求解多项式0-1规划问题的隐枚举算法.通过应用p次范数约束划归,多项式0-1规划问题的多个约束可以被一单一等价约束来替代.利用这一显著特性,新算法在搜寻最优解过程中,能改进探寻(fathoming)和折返(backtrack)策略以提高隐枚举法的计算效率.通过一个算例说明这个新算法的计算步骤并对随机产生的问题进行了测试,得到了较好的结果.     

A branch-and-cut approach to portfolio selection with marginal risk control in a linear conic programming framework

Marginal risk represents the risk contribution of an individual asset to the risk of the entire portfolio In this paper, we investigate the portfolio selection problem with direct marginal risk control in a linear conic programming framework. ＇The optimization model involved is a nonconvex quadratically constrained quadratic programming （QCQP） problem. We first transform the QCQP problem into a linear conic programming problem, and then approximate the problem by semidefinite programming （SDP） relaxation problems over some subrectangles. In order to improve the lower bounds obtained from the SDP relaxation problems, linear and quadratic polar cuts are introduced for designing a branch-and-cut algorithm, that may yield an e -optimal global solution （with respect to feasibility and optimality） in a finite number of iterations. By exploring the special structure of the SDP relaxation problems, an adaptive branch-and-cut rule is employed to speed up the computation. The proposed algorithm is tested and compared with a known method in the literature for portfolio selection problems with hundreds of assets and tens of marginal risk control constraints.     

等式约束的凸非线性规划问题降维算法

对等式约束的凸非线性规划问题的非线性方程组算法进行了研究.从一般等式约束问题的最优性条件出发,构造一个非线性方程组,解此方程组便可求得非线性规划问题的最优解.     

A Note on Relations between Linear Bilevel Programming and Linear Bicriteria Programming

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基于PEV准则的I-UMOP问题求解方法

针对传统方法在求解不确定多目标规划问题过程中存在的不足,提出了该问题在新准则下的求解方法。首先,提出了求解方法的基本框架,并通过引入不确定变量之间的序关系定义了不确定多目标规划的帕累托有效解;其次,根据线性加权或理想点法将原问题转化为不确定单目标规划问题,再利用期望方差准则将不确定单目标规划问题转化为确定的单目标规划问题;再次,通过相关理论推导证明了在该准则下转化后的问题求得的最优解是原不确定问题的帕累托有效解;最后,设计了决策变量分别为连续型和离散型的数值算例对该方法的有效性加以说明,考虑算例的复杂度,分别采用遗传粒子群算法和二进制狼群算法进行了求解。     

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.     

含直觉模糊弹性约束的模糊线性规划求解

本文基于模糊结构元方法构建并讨论了一类含有直觉模糊弹性约束的新型模糊线性规划问题. 通过引入模糊数的加权特征数, 定义了一种序关系并拓展了Verdegay的模糊线性规划方法, 将新型模糊线性规划问题转化成两个等价的含参数约束条件的清晰线性规划模型, 给出了此类线性规划模型对比最优可行解的求法. 最后通过一个数值实例来说明此类问题的一般求解方法.     

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.     

CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS

In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C     

允许缺货和转包的受限批量模型的多项式算法

有效组织带转包的采购计划对企业提高竞争力和参与全球产业分工有重要意义.研究了一个新的非减库存能力约束下的允许缺货和转包的企业采购计划模型,提出了一个基于动态规划的多项式算法.引入子计划概念,将问题归结为有效计算子计划;依据最优解的性质设计了求解子计划的多项式算法;再通过动态规划算法以多项式时间枚举所有可能子计划组合,得到问题的最优解.数值试验显示了该算法的有效性及高效性.     

一类新型的指派问题的多目标模型

针对传统的指派问题在实际应用中的局限性，提出了一类新型的指派问题，基于其特殊性建立了相应的多目标模型，并通过化为单目标问题而获得的有效解，同时，模型学考虑了给被分配者有多次选择机会的情形，最后给出实例分析。     

解非线性两层规划问题的新的遗传算法及全局收敛性

针对两层规划问题本质上的非凸性和不可微性给其数值求解带来极大困难,特别是求非线性两层规划问题的全局最优解,而遗传算法不受这些因素的限制,设计了一种新的有效的遗传算法来解决非线性两层规划问题.该算法充分考虑了两层规划问题的结构特点,使遗传算子更加有效,并且易于产生好的后代.     

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。     

D运输问题

提出一类要求货物尽量在某一给定时间以前如数运抵目的地的运输问题。这是一类含离散目标约束的目标规划问题，我们把它称为D运输问题。建立D运输问题的数学模型，引入可实施解、最优解、解对预警时间的偏差等概念，给出D运输问题的求解方法和一个计算例子。     

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.     

COMPARISON OF MAX—MIN APPROACH AND NN METHOD FOR RELIABILITY OPTIMIZATION OF SERIES—PARALLEL SYSTEM

Two heuristics, the max-min approach and the Nakagawa and Nakashima method, are consideredfor the redundancy allocation problem with series-parallel structure. The max-min approach canformulate the problem as an integer linear programming problem instead of an integer nonlinearproblem. This paper presents a comparison between those methods from the standpoint of solutionquality and computational complexity. The experimental results show that the max-min approach issuperior to the Nakagawa and Nakashima method in terms of solution quality in small-scale problems,but analysis of computational complexity shows that the max-min approach is inferior to other greedyheuristics.