On the Structure of the Non-dominated Set for Bicriteria Programmes

In multiple-objective programming, a knowledge of the structure of the non-dominated set can aid in generating efficient solutions. We present new concepts which allow for a better understanding of the structure of the set of non-dominated solutions for non-convex bicriteria programming problems. In particular, a means of determining whether or not this set is connected is examined. Both supersets and newly defined subsets of the non-dominated set are utilized in this investigation. Of additional value is the use of the lower envelope of the set of outcomes in classifying feasible points as (properly) non-dominated solutions.