ON ALTERNATIVE OPTIMAL SOLUTIONS TO QUASIMONOTONIC PROGRAMMING WITH LINEAR CONSTRAINTS

In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.

Multiple optimal solutions to a sort of nonlinear optimization problem

The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.

Higher-order Optimality Conditions for Henig Effcient Solution in Set-valued Optimization under Cone-convexlike Maps

This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.

Bad-scenario-set Robust Optimization Framework With Two Objectives for Uncertain Scheduling Systems

This paper proposes a robust optimization framework generally for scheduling systems subject to uncertain input data, which is described by discrete scenarios. The goal of robust optimization is to hedge against the risk of system performance degradation on a set of bad scenarios while maintaining an excellent expected system performance. The robustness is evaluated by a penalty function on the bad-scenario set. The bad-scenario set is identified for current solution by a threshold, which is restricted on a reasonable-value interval. The robust optimization framework is formulated by an optimization problem with two conflicting objectives. One objective is to minimize the reasonable value of threshold, and another is to minimize the measured penalty on the bad-scenario set. An approximate solution framework with two dependent stages is developed to surrogate the biobjective robust optimization problem. The approximation degree of the surrogate framework is analyzed. Finally, the proposed bad-scenario-set robust optimization framework is applied to a scenario job-shop scheduling system. An extensive computational experiment was conducted to demonstrate the effectiveness and the approximation degree of the framework. The computational results testified that the robust optimization framework can provide multiple selections of robust solutions for the decision maker. The robust scheduling framework studied in this paper can provide a unique paradigm for formulating and solving robust discrete optimization problems. © 2014 Chinese Association of Automation.

考虑土体参数不确定性的基桩多目标优化算法

为得到满足可靠性要求的基桩最佳设计方案,在有效控制基桩沉降量的情况下,尽可能降低基桩造价。以中国尊大厦基桩为例,考虑土体极限阻力不确定性,采用非支配排序遗传算法-II(NSGA-II),针对种群中的个体进行非支配解选择排序和拥挤距离比较。将桩径和桩长视为优化设计变量,以基桩承载力的目标可靠指标作为约束条件,工程造价和单桩沉降量的最小值为目标函数,得到Pareto最优解集。该算法解决了传统多目标优化方法在缺乏经验的情况下优化效果不佳与速度慢的问题。采用基于熵权理论的TOPSIS法对Pareto最优解集中的每一个解进行赋权后,筛选出相对贴近度最大的方案。结果表明:最优方案在造价和单桩沉降量上均优于原设计方案,证明基桩优化设计方法具有可行性。

海外油气效益产量“二步决策法”研究及应用

海外油气项目具有投入大、风险大、回收期长等特点,开展效益产量决策方法研究对提升石油公司整体经营实力、提高抗风险能力举足轻重.本文旨在建立一套系统全面的效益产量经营决策方法,通过抓准项目效益影响因素,构建基于全局满意解集的效益产量“二步决策法”,实现一套“可全面可聚焦”的系统决策优选技术模型,最终以优选出的组合作为效益产量推荐方案,助推海外油气资产保值增值.本文创建的海外油气效益产量“二步决策法”,在国内某石油公司海外业务板块近4年的油气资产生产经营中取得了较好的应用效果,为该石油公司海外油气资产提效增效和高质量发展提供了可靠的技术支持.该方法也同样适用于国内上游油气开发板块效益产量优化决策,值得借鉴及推广.

一种连续型不确定性复杂系统博弈理论及算法研究

当前对于不确定性复杂系统博弈的研究,通常情况下有关策略集是离散的,而非连续和随机的。而在复杂经济社会系统中,常常会遇到连续性随机博弈问题,以及系统中数据的确权问题。在此背景下,提出了一种随机博弈的概念,给出连续策略集下N人非合作随机博弈模型均衡解存在性定理,以及复杂信息系统随机博弈模型的构建及其纳什均衡解算法。给出连续策略下不确定性N人非合作随机博弈概念,建立以局中人的最大收益为目标函数的N人非合作随机博弈模型,提出了均衡解的存在性定理;构建了Wasserstein模糊集,之后融合分布鲁棒优化方法以及投资组合优化方法将该模型转化为有限凸规划,并运用遗传算法求解局中人的近似混合策略,最后构建了基于回归分析的纳什均衡求解算法并将纳什均衡解归一化进行确权。实证分析表明,所构建的理论与算法是有效可行的。

多目标粒子群优化算法及其应用研究综述

现有研究较少涵盖最先进的多目标粒子群优化(MOPSO)算法.本研究介绍了多目标优化问题(MOPs)的研究背景,阐述了MOPSO的基本理论.根据特征将其分为基于Pareto支配、基于分解和基于指标的3类MOPSO算法,介绍了现有的经典算法.介绍相关评价指标,并选取7个有代表性的算法进行性能分析.实验结果展示了传统MOPSO和3类改进的MOPSO算法各自的优势与不足,其中,基于指标的MOPSO在收敛性和多样性方面表现较优.对MOPSO算法在生产调度、图像处理和电力系统等领域的应用进行简要介绍.并探讨了MOPSO算法用于求解复杂优化问题的局限性及未来的研究方向.

基于多粒度犹豫模糊语言术语集的TOPSIS决策方法研究

为了解决在实际决策时,由于知识背景不同决策者采用不同粒度语言术语集来表达而导致决策结果不准确的问题,本文提出了一种基于多粒度犹豫模糊语言术语集的逼近理想解排序(technique for order preference by similarity to ideal solution,TOPSIS)决策方法。首先选用各术语集中的最大粒度作为标准粒度,通过转换算法将每个决策者的语言术语集转换到同一标准粒度下进行集结,得出相应的隶属度语言术语集;然后结合TOPSIS方法,计算每个备选方案与正、负理想点距离,以相对贴近度的大小排序实现最优方案的选择;最后,通过一个实例,验证该方法的可行性和优越性。本文所提方法可应用于最优方案的选择问题中,提升决策结果准确度。

梯度蜂窝力学行为及其多目标优化设计

梯度蜂窝因具有优异的力学性能及耐撞性受到了广泛的关注。以蜂窝的耐撞性指标为优化目标,在梯度蜂窝的设计空间内,直接采用多目标优化算法确定梯度蜂窝每层的具体参数。采用多目标优化设计方法将会得到多组最优的蜂窝梯度参数,这些参数形成一个解集,根据蜂窝不同的应用场景,可以选取合适的梯度参数。以正六边形蜂窝为研究对象,将均质蜂窝分成4层进行梯度优化设计。将NSGA⁃Ⅱ算法推荐的梯度蜂窝与均质蜂窝进行对比研究,结果表明,梯度蜂窝可以在小幅提高总吸能(EEA)与比吸能(SSEA)的同时大幅改善初始峰值力(PPCF),最大的改善程度达到7851%,证明了采用这种方法进行梯度设计的优势。

基于帕累托解集的水资源优化模型及应用

【目的】为解决需水预测中信息缺失,忽略目标之间博弈过程等问题,研发了考虑水资源与城市发展之间相互联系与博弈特征的非线性多目标水资源优化模型。【方法】模型以用水总量最低和万元增加值用水量最小为目标,基于“四水四定”原则,对不同年份、不同产业的水资源需求进行联合优化。针对传统的定额预测法忽视了目标间竞争过程的问题,使用遗传算法求解此非线性多目标模型的帕累托解集,生成一系列符合目标要求的水资源优化方案。【结果】模型应用于江苏省苏州市吴江区,得到100组非劣的水资源优化方案。结果显示:帕累托解集上的优化方案在区域用水总量上较定额法低6%~16%,万元增加值用水量较定额法降低19%~31%,优化效果显著。【结论】结果表明:帕累托解集可以全面展现出水与城市发展之间的竞争状态。该模型统筹考虑了水资源与人口、土地、城市、产业之间的关系,将其内在复杂的竞争关系清晰地展现出来,可以为实际应用提供更丰富的决策支持信息。

供需失衡背景下非正式绿地更新潜力及策略研究——以福州市鼓台中心区为例

我国经济社会发展步入新常态,城市发展开启存量更新模式。居民绿地需求与绿地空间不足之间的矛盾日益凸显,已有研究证明,非正式绿地在城市建成环境中具有良好适应性,能够有效解决城市面临的一系列社会和生态问题,具备较大发展潜力。聚焦于绿地低供高需的城市区域,以福州市鼓台中心区为例,通过实地调研挖掘供需失衡区范围内可利用的非正式绿地资源。从时、空间可用潜力两个维度确定影响非正式绿地发展潜力的评价指标,建立多目标优化模型;引入帕累托前沿理论,利用Matlab中非支配排序遗传算法求解得出调研区域内对非正式绿地进行更新改造的多个解集的优先层级。最后基于综合评估结果和三种不同的场地类型提出非正式绿地的更新策略,为高密度老旧城区绿地的存量更新发展提供借鉴。

基于粗糙集最优解山区公路边坡防护效果评价

为系统有效评估不同边坡防护技术的护坡效果,通过调查大量护坡技术对边坡沿线生态环境、边坡特性等的影响,以粗糙集理论和条件信息熵为基础,分析护坡效果与稳定性、抗侵蚀性等因素的相互关系,结合最优解优化评价指标重要度,提出了一种适用于山区公路边坡防护效果的指标权重确定方法。构建了边坡防护效果评价体系。运用模糊理论和模糊综合评价理论,建立了山区公路边坡防护效果模糊综合评价方法。依托某山区实体边坡对常见的11种护坡技术分析得到:生态混凝土护坡技术和土工网植草防护技术的护坡效果最优。对生态混凝土和土工网植草组合防护技术进行仿真计算,得到边坡水平最大位移和最大剪应变分别降低66.21%和90.17%,边坡稳定性系数从1.252提高到1.351,符合规范要求,为山区公路边坡防护技术的优选提供了新的思路。

改进偏好多目标优化算法在直流偏磁抑制装置优化配置中的应用

基于偏好的多目标优化算法能够定向搜索符合决策者需求的Pareto解集,是多目标优化算法与工程实际联系最为紧密的方法之一。为准确地将决策者偏好需求反映到最终Pareto解集,提出一种偏好映射点动态更新策略,通过动态更新偏好映射点来降低算法对初始参考点位置的依赖。为实现输出Pareto解数目可调可控,引入偏好解集过滤器,使得算法能够得到解集数目符合决策者要求、分布均匀的Pareto解。最后,利用所提算法求解ZDT系列测试函数和浙北区域直流偏磁抑制装置优化配置问题。结果表明,所提算法能有效收敛至决策者偏好对应的Pareto解集,可以为直流偏磁抑制装置优化配置工程实际问题提供符合决策者需求的优秀候选方案。

基于SPEA-Ⅱ算法的网络多层次安全访问控制方法

当前网络技术迅猛发展,网络安全问题日益突出,尤其是访问控制安全性;为了解决目前网络系统中存在的威胁检测精度和安全访问控制问题,引入SPEA-Ⅱ算法,提出一种新的网络多层次安全访问控制方法;深入分析网络多层次访问控制机制原理,明确安全访问控制目标;结合网络边界区域、传输信道区域及移动终端设备区域,建立边界访问控制目标函数、安全威胁检测目标函数、用户身份认证目标函数,提高网络系统安全威胁检测精度;利用SPEA-Ⅱ算法对联合目标函数进行求解,获取网络多层次安全访问控制机制最佳方案;通过迭代逐渐接近近似最优解集,建立最优安全策略组合,计算攻击流量因子完成网络多层次安全访问控制;实验结果表明,所提方法的网络多层次威胁检测精度为94%,安全评估为0.96;由此证明,所提方法的网络多层次安全访问控制效果较好,具有较强的安全性和适应性,能够为中移互联网领域的网络安全策略提供技术支持。

A NEW METHOD FOR FINDING MAJOR EFFICIENT SOLUTIONS AND MAJOR OPTIMAL SOLUTIONS OFDISCRETE MULTIOBJECTIVE PROGRAMMING

Major efficiency is an efficiency theory of multiobjective programming, whichis based on the law of majority. For the case that the feasible region is a finite set, paper [3]gave a comparison-number method for finding major efficient solutions and major optimalsolutions.This paper represents a new method to solve the same problem. The new method isbased on a concept of efficient equivalence point set. We give the definition of efficientequivalence point set, discuss the relationship between it and major efficiency, and presenta new approach to find major efficient (optimal) solutions.

Multicriteria Optimization of Cellular Networks

When designing modern cellular networks, it is challenging to account for many contradictory criteria and constantly changing external conditions of the networks (e.g., traffic). We need to solve multicriteria problems with high-dimensional vectors of parameters. A prerequisite to solution of these problems is correct determination of the feasible solution set, which is directly related to the statement of optimization problem. This is a major challenge in all multicriteria engineering optimization problems and represents significant difficulties for the expert. In this paper, we show how to define the feasible solution set for cellular network optimal design problems and thus answer the fundamental question of where to search for optimal solutions in such problems. We use the Parameter Space Investigation (PSI) method implemented in the Multicriteria Optimization and Vector Identification (MOVI) software system and apply it to a mathematical model of cellular network. In addition to developing methodology for stating and solving the problem of multicriteria optimization of cellular network, we have found that 1) defining the feasible solution set is directly related to the correct statement of the optimization problem, 2) once the feasible solution set has been determined, the criteria convolution can be applied to find the optimal solution in the feasible solution set, 3) it is possible to perform online tuning of the cellular network parameters.

Solution set calculation of the Sun-perturbed optimal two-impulse trans-lunar orbits using continuation theory

The solution set of the Sun-perturbed optimal two-impulse trans-lunar orbit is helpful for overall optimization of the lunar exploration mission.A model for computing the two-impulse trans-lunar orbit,which strictly satisfies the boundary constraints,is established.The solution set is computed first with a circular restricted three-body model using a generalized local gradient optimization algorithm and the strategy of design variable initial continuation.By taking the solution set of a circular restricted three-body model as the initial values of the design variables,the Sun-perturbed solution set is calculated based on the dynamic model continuation theory and traversal search methodology.A comparative analysis shows that the fuel cost may be reduced to some extent by considering the Sun’s perturbation and choosing an appropriate transfer window.Moreover,there are several optimal two-impulse trans-lunar methods for supporting a lunar mission to select a scenario with a certain ground measurement and to control the time cost.A fitted linear dependence relationship between the Sun’s befitting phase and the trans-lunar duration could thus provide a reference to select a low-fuel-cost trans-lunar injection window in an engineering project.

Optimization Model on Quadratic Programming Problem with Fuzzy

In this paper, the authors propose a computational procedure by using fuzzy approach to fred the optimal solution of quadratic programming problems. The authors divide the calculation of the optimal solution into two stages. In the first stage the authors determine the unconstrained minimization and check its feasibility. The second stage, the authors explore the feasible region from initial point to another point until the authors get the optimal point by using Lagrange multiplier. A numerical example is included to support as illustration of the paper.

向量集值优化问题f-有效解的最优性条件

利用分离定理并借助集值映射的余切上图导数、Y-上图导数、径向上图导数和Clarke正切上图导数给出了向量集值优化问题,取得f-有效解的4个最优性条件。