Mixed integer nonlinear optimizationmodels for the Euclidean Steiner tree problem in Rd

New mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in d-space (with d >= 3) will be presented in this work. All models feature a nonsmooth objective function but the continuous relaxations of their set of feasible solutions are convex. From these models, four convex mixed integer linear and nonlinear relaxations will be considered. Each relaxation has the same set of feasible solutions as the set of feasible solutions of the model from which it is derived. Finally, preliminary computational results highlighting the main features of the presented relaxations will be discussed.

Automated summary

This work introduces new mixed integer nonlinear optimization models for the Euclidean Steiner tree problem in high dimensions (d >= 3), featuring nonsmooth objective functions with convex continuous relaxations. Four convex mixed integer linear and nonlinear relaxations derived from these models are considered, each having the same feasible solutions as their respective original models. Preliminary computational results discussing the main features of these relaxations are presented.