Efficient Edge-swapping heuristics for the reload cost spanning tree problem

The reload cost spanning tree problem (RCSTP) is an NP-hard problem, where we are given a set of nonnegative pairwise demands between nodes, each edge is colored and a reload cost is incurred when a color change occurs on the path between a pair of demand nodes. The goal is to find a spanning tree with minimum reload cost. We propose a tree-nontree edge swap neighborhood for the RCSTP and an efficient way to search this neighborhood using preprocessed information. We then embed this edge swap neighborhood within a local search and a tabu search heuristic. We also discuss an initial solution procedure that is used by the local search and tabu search heuristic in a multi-start framework. On a test set of 630 instances (that includes benchmark instances from Gamvros et al., 2012), the local search solution improves upon the initial solution in 416 instances by an average of 23.62%, and the tabu search solution improves upon the local search solution in 364 instances by an average of 35.79%. Out of 495 test instances from this set that we know the optimal solution for, the initial solution is optimal 113 times, the local search solution is optimal 224 times, and the tabu search solution is optimal 481 times. On a second set of benchmark instances from Khalil and Singh (2010) the tabu search solution improves upon the best known solution in 32 out of 44 instances.