摘要
运筹学中的线性目标规划和线性规划问题一直分别采用修正单纯形法和单纯形法求解.当变量稍多时计算还是有些繁琐、费时,最近作者通过研究发现,可应用人工智能-代数方法求得这两类问题的解,而且具有相当广泛的适用性.若干例题说明,本法的结果和传统方法的结果由于传统算法在计算中发生的错误,除少数例外大都是一致的.本文的一个重要目的是希望和广大读者一起研究该方法是否具有通用性.
So far the modified simplex method and simplex method have been used for the solution of the linear goal programming and linear programming respectively.Of course,these methods are effective and successful,but they are some what trouble and time-consuming when the scale of problem is larger.Recently author discovered that and artificial intelligence-algebraic algorithm can be used for solving this two kinds of problem. The main idea of this algorithm is that based on the practical background of the problem man＇s wisdom is used to analyse which of the inequality constraints should be equalties to make the optimized goal function or the objective function optimum.Asuming that there are m＇ of equalities in m inequality constraints,in which only n decision variables are included and so there are n-m＇ of decision variables should be zeros to make the optimized goal function or the objective function optimum.The optimality condition is used to determine which of decision variables equal to zeros.At last,the optimum solution or the satistactory solution can be solved from the m＇ equality equations including m＇ decision variables.Many examples we collected show that this algorithm is very simple,rapid and effective and the results obtained by this algorithm and by the traditional simplex method are almost all consistent,exception of a few examples due to mistakes happened in the calculation of simplex methods.And so this algorithm posseses considerably wide applicability.But the universal applicability didn＇t be proved theretically yet.Therefore an important aim of this paper is to attract readers to investigate with us the problem of whether this algorithm posseses universal applicability.
出处
《运筹学学报》
CSCD
2010年第4期101-111,120,共12页
Operations Research Transactions
基金
大连理工大学211工程建设项目资助
关键词
运筹学
线性目标规划
线性规划
单纯形法
人工智能-代数解法
Operations research
linear goal programming
linear programming
simplex method
artificial intelligence
algebraic algorithm
