Numerical Procedures in Multiobjective Optimization with Variable Ordering Structures

Multiobjective optimization problems with a variable ordering structure, instead of a partial ordering, have recently gained interest due to several applications. In the previous years, a basic theory has been developed for such problems. The binary relations of a variable ordering structure are defined by a cone-valued map that associates, with each element of the linear space ℝm, a pointed convex cone of dominated or preferred directions. The difficulty in the study of the variable ordering structures arises from the fact that the binary relations are in general not transitive.