The genomic median problem aims at finding the organization of the chromosome of a common ancestor to multiple living species. The problem is often formulated as searching for a genome that minimizes some distance measure among given genomes. In our previous research, we have proposed a new stochastic local search algorithm for this problem that combined elements of tabu search, iterated local search, and a reactive search mechanism for adapting crucial parameters while solving an instance. In this talk, we will report on several improvements upon the initial algorithm and additional computational results including comparisons to current state-of-the-art algorithms for the genomic median problem.