Note—Finding Certain Weakly-Efficient Vertices in Multiple Objective Linear Fractional Programming
指出Kornbluth和Steuer算法中用于检测弱有效顶点(断点)的计算方法可能失败,并提出一种安全替代方法及计算测试结果。
Recently Kornbluth and Steuer have developed a simplex-based algorithm for finding all weakly-efficient vertices of an augmented feasible region of a multiple objective linear fractional programming problem. As part of this algorithm, they presented a method for detecting certain weakly-efficient vertices called break points. In this note we show that the procedure used by Kornbluth and Steuer in this method for computing the numbers needed to find these break points may sometimes fail. We also propose a fail-safe method for computing these numbers and give some computational results with this method.