Convergent Aspiration Based Interior Point Method (CAIN) for Multiple Objective Linear Programming (MOLP).

摘要

This report describes a new convergent aspiration based algorithm (CAIN--Convergent Aspiration based INterior method) for solving the multiple objective linear programming (MOLP) problem. Initial motivation for the research was provided by a recently developed methodology for the discrete multiple criteria decision making problem called AIM (Aspiration-Level Interactive model). Although CAIN uses many of the features implemented in AIM, the continuous MOLP provides for an entirely different domain of research. As part of CAIN, an innovative decision maker (DM) interaction technique called ALaRM (Aspiration Level Range Method) was concurrently developed. Using ALaRM, an interior point strategy for converging to efficient solutions is employed based upon DM levels of aspiration for the objectives. This technique, the Algorithm of Centers, has been shown to converge in polynomial time (unlike many simplex based strategies). CAIN is shown to be simple and practical from a DM standpoint, and is believed to represent an improvement over existing aspiration based MOLP techniques.