基于资源参数分解的一类大系统优化模型最优解的性质

Properties of Optimal Solution of a Large-scale System Optimization Model Based on Resource Parameters Decomposition

以具有梯形结构大系统目标规划模型的"双向分解"为基础,在纵向垂直分解子问题(Pi)所包含的两个子问题(Pii)和(Pii+1)最优集相交非空的条件下,针对资源参数的不同情况证明了只要在横向第二层对资源参数进行适当分解,那么纵向垂直分解子问题(Pi)的最优解构成大系统目标规划模型(P)的最优解.通过讨论,将求解具有梯形结构的大系统目标规划问题(P)转化为求解子问题(Pi),从而为研究这类大系统问题的求解算法提供了理论依据.

According to the different situation of resource parameters, the paper demonstrates that if the resource parameters in thc horizontal second layer are decomposed properly, the optimal solutions of the subproblem（Pi ） will constitute the ones of the large scale system goal programming model（P）, The conclusion depends on the ＂two-way decomposition＂ of the large scale system goal programming model with trapezoidal structure. It is obtained under the condition of the non-empty intersecIion of their optimal set of the two subproblems （Pi）and（P_i^i＋1 ） which are contained in the longitudinal decomposition subproblem（Pi ）. By means of the discus sion, the solution of the large scale system goal programming model（P） is transformed into that of the subproblem（Pi）. It provides a theoretical basis for the algorithm of the kind of the large scale problem.