Efficient lower and upper bounds for the weight-constrained minimum spanning tree problem using simple Lagrangian based algorithms

The weight-constrained minimum spanning tree problem (WMST) is a combinatorial optimization problem for which simple but effective Lagrangian based algorithms have been used to compute lower and upper bounds. In this work we present several Lagrangian based algorithms for the WMST and propose two new algorithms, one incorporates cover inequalities. A uniform framework for deriving approximate solutions to the WMST is presented. We undertake an extensive computational experience comparing these Lagrangian based algorithms and show that these algorithms are fast and present small integrality gap values. The two proposed algorithms obtain good upper bounds and one of the proposed algorithms obtains the best lower bounds to the WMST.