【作者】 刘莉；

【导师】 王海明；

【作者基本信息】 兰州大学 ， 运筹学与控制论， 2007， 硕士

【摘要】 目标规划是一种解决实际生活中多目标问题的有效方法，它作为一个强大而实用的工具，近几年来一直是国际学术界研究的热门话题，特别是对那些具有众多而相互矛盾的目标，以及软硬约束共存的问题，在理论和应用方面都取得了很大的进展．但是，对这类问题用常规的方法进行求解时，通常都要作许多简化的(往往是有一定问题的)假定，这使得有些问题失去了原来的实际应用意义．本文结合线性目标规划自身的特点，将基线算法和对偶基线算法推广到了线性目标规划问题，构造了基线算法和对偶基线算法中所没有的检验数行，将目标函数按照优先因素多阶段化，形成了目标规划的多阶段基线算法和多阶段对偶基线算法，并解决了带有软硬约束条件的目标规划问题，给出了寻找初始可行基的可行的方法．文中给出了这两种算法的计算步骤并讨论了他们的收敛性，通过编程与目标规划的单纯形法进行了比较．数值实验表明，多阶段基线算法和多阶段对偶基线算法较通常的单纯形法更易操作、迭代次数更少、数值稳定性更强．更多还原

【Abstract】 The Objective Programming is an effective method to solve multi-objective optimization problem in our daily life. As a powerful and practical tool, it has been attracting more and more attentions and becoming a hot-discussed topic in the whole global academe over the recent years. It has gained much important progress in both of the theoretical research and its application, especially in solving the problems which contain multiple but self-contradictory objections and problems including both soft and hard restriction. However, applying conventional method to solve such kind of problem is always based on many assumptions (Usually, some of which are probably incorrect), which made the model loose its practical value.In this paper, combined with the characteristic of the Linear Objective Programming, the Basic Line Algorithm (BLA) and the Dual Basic Line Algorithm (DBLA) were extended into solving the Linear Objective Programming. The concept of test number array which didn’ t used in BLA and DBLA was constructed. Through dividing the objective function into different stages according to their priority factors, a Multi-stage BLA and a Multi-stage DBLA for the objective programming problem were formed. The objective programming problem with soft and hard restriction was also solved and a way to find out the initial feasible basis of it was given; finally, the procedures and the convergence of the Multi-stage BLA and the Multi-stage DBLA were also discussed respectively. By comparing with the simplex method in Objective Programming, the numeric experiment displayed that the Multi-stage BLA and the Multi-stage DBLA are much more easily to operate, and need less iterative steps, and the numeric stability are showed better.更多还原