Minimum Spanning Trees with neighborhoods: Mathematical programming formulations and solution methods

作者：Blanco Victor^*; Fernandez Elena; Puerto Justo

来源：European Journal of Operational Research, 2017, 262(3): 863-878.

DOI：10.1016/j.ejor.2017.04.023

• Combinatorial Optimization
• Minimum Spanning Trees
• Neighborhoods
• Mixed Integer Non Linear Programming
• Second order cone programming

This paper studies Minimum Spanning Trees under incomplete information assuming that it is only known that vertices belong to some neighborhoods that are second order cone representable and distances are measured with a l(q)-norm. Two Mixed Integer Non Linear mathematical programming formulations are presented, based on alternative representations of subtour elimination constraints. A solution scheme is also proposed, resulting from a reformulation suitable for a Benders-like decomposition, which is embedded within an exact branch-and-cut framework. Furthermore, a mathheuristic is developed, which alternates in solving convex subproblems in different solution spaces, and is able to solve larger instances. The results of extensive computational experiments are reported and analyzed.

• 出版日期2017-11-1