A Memetic Approach to Golomb Rulers

Finding Golomb rulers is an extremely challenging optimization problem with many practical applications. This problem has been approached by a variety of search methods in recent years. We consider in this work a hybrid evolutionary algorithm that incorporates ideas from greedy randomized adaptive search procedures (GRASP), tabu-based local search methods (TS) and scatter search (SS). In particular, GRASP and TS are embedded into a SS algorithm to serve as initialization and restarting methods for the population and as improvement technique respectively. The resulting memetic algorithm significantly outperforms earlier approaches (including other hybrid EAs, as well as hybridizations of local search and constraint programming), finding optimal rulers where the mentioned techniques failed.