Abstract : using the definitions of semi - locally star shaped set and generalized convexity for vector functions . we discuss the existence of efficient solutions for generalized multiobjective programming 文摘:本文利用1中的半局部星状集和向量函数的广义凸性，讨论了一类广义多目标规划有效解的存在性。
We solved multiobject nonconvex programming by means of homotopy - interior method and got the minimum weak effect solution under quasi - normal cone condition ; meanwhile we proved the convergence of this method 摘要利用同伦内点算法求解多目标非凸规划在拟锥条件下的最小弱有效解，并证明了算法的大范围收敛性。
By computing valid path to evaluate individuals and cumulate local advantage modules in the procedure of genetic operations , invalid individuals can be processed and formed valid individuals at last 通过计算个体的有效路径，评价个体，并在遗传操作中不断累积局部优势模式，可以对无效解进行遗传操作并最终生成有效解。
4 . the technical decision of ground improvement is a multi - object fuzzy mathematics programming problem . fuzzy similar preferred ratio decision method can solve this problem and take the best ground improvement project 4 .软基处理方案决策是一个多目标的模糊数学规划问题，用模糊相似优先比决策法可以解决多目标函数中有效解模糊关系的问题。
In all , from above research , this paper concluded as follow : ( 1 ) making out the four kinds solution ’ s definition , and in the basis putting out the existence theorem of pareto efficient solution on blmop found . ( 2 ) giving out the algorithm of blmop based on the genetic algorithm 总体说来,通过以上研究,本文主要得出以下结论: ( 1 )给出了二层多目标规划四种类型的解的定义,并在此基础上提出并证明了二层多目标规划问题的pareto有效解存在的充分性和必要性条件。
Motivated by the above results , the third part of this paper considers the equivalence problems that every stationary point or kuhn - tucker point is an efficient solution . we define i - quasi - invex vector function . , i - strictly quasi - invex vector function and kt - i - strictly quasi invex vector function , and derive the above equivalent condition for unconstrained or constrained multiobjective programming 于是，在本文的第三部分，我们定义了类不变拟凸、类严格不变拟凸、 kt -类严格不变拟凸的向量值函数，并且在无约束或约束多目标规划中，获得了每个驻点(或k - t点)是有效解的等价条件。
In conclusion , the algorithm of removing pseudo elements can reduce the number of face loops generated and the searching space of the decision - making . compared with former methods , our method can reduce the execute - time mostly , and also can delete pseudo elements generated by the broken lines in more cases . the decision - making algorithm can efficiently get a solution satisfying orthographic views and truly deal with multi - solutions 本文所做的工作与以前方法相比,假元删除算法不仅在线框模型中执行次数减少,假元删除的效率得到明显提高,而且能删除更多情况下虚线边所产生的假元;决策求解算法真正做到快速并有效地得到所有满足投影视图的有效解。
In this paper , a concept of strictly efficient solution of the optimization problem for a set - valued mapping is introduced . it is proved that strictly efficient point set of the objective space is connected when objective function is cone convex - like , and that if objective function is cone convex set - valued mapping , then strictly efficient solution set is also connected . as an interesting application of the results in this paper , the connectedness of super efficient solution sets is discussed 本文对集值映射最优化问题引入严有效解的概念.证明了当目标函数为锥类凸的集值映射时，其目标空间里的严有效点集是连通的；若目标函数为锥凸的集值映射时，其严有效解集也是连通的.作为应用，讨论了超有效解集的连通性
Two methods are brought forward to obtain the optimal solution after gained the efficient solution : one is letting the non - discrimination of specific investor and the efficient borderline have a common tangent at a point , and this point is the optimal solution ; the other gains optimal solution basing on safety - first method 在得到有效解后，本文提出采用两种方法来获取最优解：第一种方法是采用特定投资者的无差异曲线与有效边界相切的方法得到最优解；第二种方法是采用安全第一方法来获得最优解。
In normed space , the theorem of existence of lagrangian multipliers is proved , and - super saddle point is defined , and the relations between - super saddle point and existence of - super efficient solution are discuss . based on these , lagrange - super dual results of set - valued optimization problem are given , including weak duality , strong duality , converse duality etc 在赋范空间中，证明了lagrangian乘子存在性定理，定义了-超鞍点的概念，探讨了-超鞍点与-超有效解存在性之间的关系。
