会议筹备问题的多目标最优化模型

利用2009年全国大学生数学建模竞赛D题的会议筹备问题,通过预测与会代表总人数和合理的住宿安排方案,建立预订宾馆客房的多目标最优化模型;在租借会议室和租用客车上采用等可能假设,并给出费用的最优化模型。最后利用LING09．0得出会议筹备总费用的全局最优解。     

基于ε支配的MOGA在0／1背包问题中的应用

多目标遗传算法NSGA—Ⅱ是解决0／1背包问题^[1]的有效算法,但是它还存在一定的缺陷,当0／1背包问题的规模较大时,这种方法很难收敛到Pareto最优边界,因此解的分布性不是很好,解集也很难收敛。针对此问题,提出基于ε支配的MOGA来求解0／1背包问题,通过实验验证该算法在求解分布性上优于NSGA-Ⅱ。     

贫困山区县级土地利用结构调整模型研究

本文从农业生态经济系统和土地资源二个层次的分析入手,揭示了贫困山区县农业生态经济系统功能退化和土地资源利用不合理等普遍性问题。确立了以重建良性农业生态经济系统为总目标的土地利用结构调整基本方向,对用地矛盾众多的贫困山区县,运用多目标规划方法建立了土地利用结构调整模型,为贫困山区县级土地利用结构调整提供了一种可借鉴的思路和方法。     

Multi-objective optimization of water supply network rehabilitation with non-dominated sorting Genetic Algorithm-Ⅱ

Through the transformation of hydraulic constraints into the objective functions associated with a water supply network rehabilitation problem, a non-dominated sorting Genetic Aigorithm-Ⅱ (NSGA-Ⅱ) can be used to solve the altered multi-objective optimization model. The introduction of NSGA-Ⅱ into water supply network optimal rehabilitation problem solves the conflict between one fitness value of standard genetic algorithm (SGA) and multi-objectives of rehabilitation problem. And the uncertainties brought by using weight coefficients or punish functions in conventional methods are controlled. And also by introduction of artificial inducement mutation (AIM) operation, the convergence speed of population is accelerated; this operation not only improves the convergence speed, but also improves the rationality and feasibility of solutions.     

Multi-objective optimization of water supply network rehabilitation with non-dominated sorting Genetic Algorithm-II

Through the transformation of hydraulic constraints into the objective functions associated with a water supply network rehabilitation problem, a non-dominated sorting Genetic Algorithm-II （NSGA-II） can be used to solve the altered multi-objective optimization model. The introduction of NSGA-II into water supply network optimal rehabilitation problem solves the conflict between one fitness value of standard genetic algorithm （SGA） and multi-objectives of rehabilitation problem. And the uncertainties brought by using weight coefficients or punish functions in conventional methods are controlled. And also by in- troduction of artificial inducement mutation （AIM） operation, the convergence speed of population is accelerated; this operation not only improves the convergence speed, but also improves the rationality and feasibility of solutions.     

基于遗传算法的电梯群控研究

针对电梯群控系统的特点,设计出一种更适合的梯群控制的遗传算法.本算法中采用了整数编码和可进行种群竞争的双种群机制,设计了以候梯时间、乘梯时间、系统能耗为群控目标的多目标适应度函数.并在选择操作中引入个体最优选择策略,在交叉操作中构造了与遗传代的数目、预交叉个体本身特点相结合的交叉方式,在变异操作中应用了两点对换和位点变异相结合的变异方法,并设计了从最优解集合中选择最优解的评价函数.经过模拟仿真,运行实验结果表明了此方案的可行性和优越性.     

基于粗糙集的多目标类Bayes粗糙集模型

介绍了两个目标类的决策信息系统中各目标类的Bayes粗糙集模型,并将这一模型推广到具有多目标类的情形.最后讨论了该模型的相关性质,计算实例表明该模型是有效的.     

Optimum allocation of FACTS devices in Fars Regional Electric Network using genetic algorithm based goal attainment

This paper presents a novel approach to find optimum locations and capacity of flexible alternating current transmission system （FACTS） devices in a power system using a multi-objective optimization function. Thyristor controlled series compensators （TCSCs） and static var compensators （SVCs） are the utilized FACTS devices. Our objectives are active power loss reduction, newly introduced FACTS devices cost reduction, voltage deviation reduction, and increase on the robustness of the security margin against voltage collapse. The operational and controlling constraints, as well as load constraints, were considered in the optimum allocation. A goal attainment method based on the genetic algorithm （GA） was used to approach the global optimum. The estimated annual load profile was utilized in a sequential quadratic programming （SQP） optimization sub-problem to the optimum siting and sizing of FACTS devices. Fars Regional Electric Network was selected as a practical system to validate the performance and effectiveness of the proposed method. The entire investment of the FACTS devices was paid offand an additional 2.4% savings was made. The cost reduction of peak point power generation implies that power plant expansion can be postponed.     

多目标线性规划的若干解法及Lingo实现

多目标线性规划是优化问题的一种,求解多目标线性规划的基本思想大都是将多目标问题转化为单目标规划。介绍了理想点法、线性加权和法、模糊偏差解法,最后对每种解法给出例子,并用Lingo软件中多个子模型的一个程序加以实现。程序编写原理简单易懂,适合在建模竞赛时采用。     

基于聚集密度的协同进化多目标优化算法

为了改善协同进化多目标优化算法性能,引入了聚集密度对超级个体集合进行更新。其基本思想是：首先计算种群中各个体的聚集密度,再定义一个偏序集,然后根据一定的比例依次从偏序集中选择个体更新。根据数值试验和量化指标测试了新算法的收敛性与分布性。结果表明,新算法在收敛性方面与常规协同进化多目标算法相当,但其分布性获得了一定程度的改善。