A Memetic Approach to Golomb Rulers

Abstract

Abstract. 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.

Performance comparison of five metaheuristic nature-inspired algorithms to find near-OGRs for WDM systems

“…the proposed algorithms can explore new search space by the mutation and random walk. A fundamental benefit of using mutation and Lévy flight strategies with nature-inspired algorithms in this paper is their ability to improve its solutions over time, which does not seem in the existing algorithms (Cotta et al 2006;Soliday et al 1995;Robinson 2000;Ayari et al 2010;Dotú and Hentenryck 2005;Bansal 2014Bansal , 2017Bansal and Sharma 2017) to find near-OGRs. Erol and Eksin (2006), inspired by the theories of the evolution of universe; namely, the Big bang and Big crunch theory, developed a metaheuristic algorithm called Big bang-big crunch (BB-BC) optimization algorithm.…”

“…Golomb rulers realized from 10-to 16-marks by TS (Cotta et al 2006), maximum Popsize set was 190. The hybrid approach proposed in (Ayari et al 2010) to find Golomb rulers from 11-to 23-marks, the Popsize was set between 20 and 2000.…”

“…In literatures (Cotta et al 2006) and (Ayari et al 2010), the maximum numbers of iterations (Maxiter) for TS algorithm to find Golomb rulers were set to 10000 and 30000 respectively. The hybrid approach proposed in (Ayari et al 2010) to find Golomb rulers the maximum number of iterations set were 100000.…”

“…For higher order marks, the exhaustive computer search (Robinson 1979;Shearer 1990) of such problems is difficult. Numerous algorithms (Robinson 1979;Shearer 1990;Galinier et al 2001;Leitao 2004;Rankin 1993;Cotta et al 2006) have been proposed to tackle Golomb ruler problem. To date, no efficient algorithm is known for finding the shortest length ruler.…”

“…To date, no efficient algorithm is known for finding the shortest length ruler. The realization of nature-inspired metaheuristic optimization algorithms such as Tabu search (TS) (Cotta et al 2006), Memetic approach (Cotta et al 2006), Genetic algorithms (GAs) (Soliday et al 1995;Robinson 2000;Ayari et al 2010;Dotú and Hentenryck 2005) and its hybridizations (HGA) (Ayari et al 2010), hybrid evolutionary (HE) algorithms (Dotú and Hentenryck 2005), Biogeography based optimization (BBO) (Bansal 2014) and Big bang-big crunch (BB-BC) (Bansal 2017;Bansal and Sharma 2017) in finding relatively good solutions to such NP-complete problems provides a good starting point for algorithms of finding near-OGRs. Therefore, nature-inspired algorithms seem to be very effective solutions for such NP-complete problems.…”