This paper proposes different strategies of parallelizing a multi-criteria GRASP (Greedy Randomized Adaptive Search Problem) algorithm. The parallel GRASP algorithm is applied to the multi-criteria minimum spanning tree problem, which is NP-hard. In this problem, a vector of costs is defined for each edge of the graph and the goal is to find all the efficient or Pareto optimal spanning trees (Pareto-optimal solutions). Each process finds a subset of efficient solutions. These subsets are joined using different strategies to obtain the final set of efficient solutions. The multi-criteria GRASP algorithm with the different parallel strategies are tested on complete graphs with n = 20, 30 and 50 nodes and r = 2 and 3 criteria. The computational results show that the proposed parallel algorithms reduce the execution time and the results obtained by the sequential version were improved.
Parallel GRASP algorithm; multi-criteria combinatorial optimization; minimum spanning tree
