大型多目标线性规划解法研究

A Solution Method for the Large-Scale Multi Objective Linear Programming

对多维的多目标线性规划问题,研究了非劣解的特性和非劣解生成的"最小减优率法"。由于所提非劣解生成方法具有理论上的严格性和解的完整性,计算工作量亦相对不大,因此可以作为与其他现行方法进行对比和检验的手段;其理论、思路也适用于大型多目标二次规划的严格求解。另外研究了多维多目标线性规划问题的一种既保持解的严格性,又方便于实际问题求解选用的对话式求解方法,以及用折线迫近法解多目标凸规划的例子。

Multiobjective linear programming (MOLP) is one of the foundamental topics in studying the general multiobjective programming. The current adopted methods for solving such a problem seem not so effective, and sometimes not so strict theoretically. For example, the well-known weighting method is time-consuming and also easy to leave out some part of total non-inferior solution set. While other analytical methods like the multiobjective Simplex Method require usually a lot of computation work. In this paper we present an analytical method (called the least reduction rate method) for solving a large scale multiobjective linear programming, which not only gives a strict and complete solution set, but also requires relatively much less computational work. The proposed method may be applied to solve strictly the large-scale, multiobjective quadratic program equally well.