Multiobjective mathematical programming via the Multiplex model and algorithm

The increased interest in the existence and consideration of multiple objectives has made itself evident in the significant growth in the development and implementation of multiobjective mathematical programming. Unfortunately, it is our opinion that this field is now characterized by such a diversity of philosophies, models, approaches and terminology that any unifying theme is obscured. In fact, rather than stressing the (substantial) degree of inherent commonality between multiobjective models and methods, most presentations seem to focus on their real, or imagined, differences. We believe that such treatment can be counterproductive and thus propose, herein, what we hope is a more unified treatment of multiobjective mathematical programming via the use of the multiphase simplex, or Multiplex model and algorithm. While none of the components and concepts of the Multiplex method are, in themselves, new, we do believe that the specific arrangement of these ideas, in the form presented, does serve to clarify the close relationships between the models and (simplex based) algorithms for most forms of multiobjective mathematical programming (and, in turn, their relationship to ‘conventional,’ single objective programming).