Scheduling tasks on unrelated machines: Large neighborhood improvement procedures

Two approximation algorithms are presented for minimizing the makespan of independent tasks assigned on unrelated machines. The first one is based upon a partial and heuristical exploration of a search tree, which is used not only to build a solution but also to improve it thanks to a post-optimization procedure. The second implements a new large neighborhood improvement procedure to an already existing algorithm. Computational experiments show that their efficiency is equivalent to the best local search heuristics.