Finally, an algorithm for nonlinear multiobjective programming with linear equality constraints is offered . at first, multiobjective programming is transformed into a single-objective programming by using linear qualitied method; and then, a single-objective programming with equality constraints is transformed into a series of linear equation systems, an algorithm is obtained by applying the dimension-descending algorithm with equality constraints 最后,获得了具有线性等式约束的非线性多目标规划问题的一种新算法,首先利用线性加权和法将线性等式约束的非线性多目标规划问题转化为单目标规划问题,再将其转化为求解一系列线性方程组,从而用降维算法获得了该问题的一个算法。
Finally, an algorithm for nonlinear multiobjective programming with linear equality constraints is offered . at first, multiobjective programming is transformed into a single-objective programming by using linear qualitied method; and then, a single-objective programming with equality constraints is transformed into a series of linear equation systems, an algorithm is obtained by applying the dimension-descending algorithm with equality constraints 最后,获得了具有线性等式约束的非线性多目标规划问题的一种新算法,首先利用线性加权和法将线性等式约束的非线性多目标规划问题转化为单目标规划问题,再将其转化为求解一系列线性方程组,从而用降维算法获得了该问题的一个算法。
According to order relations defined between fuzzy numbers, the pareto less optimal solution and the pareto optimal solution are defined, then a fuzzy evaluation function is introduced into a multiobjective programming problem, this method results in a multiobjective programming problem been converted into a one objective programming problem, accordingly the solution by this method is the pareto less optimal solution to the primitive problem, which is given proof a multiobjective problem with general fuzzy number coefficients is also further discussed, by _ cutset of fuzzy sets a multiobjective problem can be transformed into a interval linear programming problem, and using the method of the previous chapter, we can obtain the pareto less optimal solution 从模糊数之间的序关系出发,分别定义了弱较优解和较优解,然后对模糊多目标问题引入模糊评价函数,将多目标化为单目标,在此也证明了求得的解为原问题的弱较优解。还讨论了系数为一般模糊数的多目标问题,通过模糊集的水平集可将多目标问题转化为区间数线性规划问题,并利用上一章所讲的方法,得到原问题的弱较优解。最后,对变量为模糊数的线性规划问题也进行了讨论。
Here the operations research, economics and related knowledge are used to analyze this issue . the author firstly elaborates such issues as : finance decision-making, investment environment analysis, decision making evaluation index, and investment risk analysis, and then a dynamic multi objective programming model is set up . there are three objectives in the model, which are npv, value and opportunity loss 本文针对我国航运企业的经营特点及其所面临的问题,运用运筹学中的多目标规划法,在分析阐述融资决策、投资环境、投资决策评价指标及投资风险分析的基础上,提出并建立了船舶投资决策多目标规划模型,在船舶运营经济效果、决策者效用值、机会损失等方面,对各种投资方案的不同特点进行了比较选优。
Abstract : the main techniques in multiple objectives decision-making is discussed in this paper, and the difficulties for them to solve problems for harmonious objectives are analyzed . a technique by introducing the ideas of decision-maker, making multiple steps of single objective programming, and ruminating over the projects, to optimize all the objectives within the satisfied ranges is proposed . finally, the programs for interactive decision for harmonious objectives are given 文摘:概述了各种主要的多目标决策方法,指出了其在处理协调型目标决策中的困难.提出了将决策者意见引入分析过程,通过多步单目标规划反复尝试,使各个目标在满意范围内均达到优化的方法,并给出了协调型目标的交互决策程序.最后通过一个简化实例予以说明
Data procession and analyzing, the paper first use regression analysis model to analyze the relationship between economic benefit and land use structure, ecological benefit and land use structure . then, the paper based on the results, use mathematical of multi-objective programming to determine the land use structure in the hilly countryside of sichuan . lastly, the paper analyzed the laws of land use structure optimization in the different relevance of economic county 本文以四川丘陵区各典型丘陵区县为例,在土地利用结构最优思想的指导下,通过数据的收集、整理与分析,首先采用回归分析的方法,分析了该区的经济、生态效益与土地利用结构的相关性,然后以回归分析所得的回归系数为效益系数,在不同经济发达程度的区域,各选取三个区县,以经济、生态效益最优为目标,以社会条件为约束条件,建立多目标规划模型,得出该区县的土地利用优化结构。
First, in this paper, a multi-objective programming model on the development of high-tech industry in hainan province is established, and then simulated caculation is made according to historical data, and finally some suggestions on the future development of high-tech industry in the province is brought out 本文运用系统工程学的多目标决策分析方法对海南省高新技术产业的发展建立了多目标规划模型,而后利用历史数据进行仿真运算;在此基础上,对海南省未来高新技术产业的发展提出了可行性建议。