A Hybrid GRASP - Evolutionary Algorithm Approach to Golomb Ruler Search

We consider the problem of finding small Golomb rulers, a hard combinatorial optimization task. This problem is here tackled by means of a hybrid evolutionary algorithm (EA). This EA incorporates ideas from greedy randomized adaptive search procedures (GRASP) in order to perform the genotype-to-phenotype mapping. As it will be shown, this hybrid approach can provide high quality results, better than those of reactive GRASP and other EAs.

[1]  Celso C. Ribeiro,et al.  Reactive GRASP: An Application to a Matrix Decomposition Problem in TDMA Traffic Assignment , 2000, INFORMS J. Comput..

[2]  William T. Rankin,et al.  Optimal Golomb Rulers: An Exhaustive Parallel Search Implementation , 1993 .

[3]  Celso C. Ribeiro,et al.  Greedy Randomized Adaptive Search Procedures , 2003, Handbook of Metaheuristics.

[4]  Christophe G. Giraud-Carrier,et al.  Unifying Learning with Evolution Through Baldwinian Evolution and Lamarckism , 2000, Advances in Computational Intelligence and Learning.

[5]  Abdollah Homaifar,et al.  Genetic Algorithm Approach to the Search for Golomb Rulers , 1995, ICGA.

[6]  W. C. Babcock.  Intermodulation interference in radio systems frequency of occurrence and control by channel selection , 1953 .

[7]  Ernesto Costa,et al.  Golomb Rulers: The Advantage of Evolution , 2003, EPIA.

[8]  Torleiv Kløve.  Bounds and construction for difference triangle sets , 1989, IEEE Trans. Inf. Theory.

[9]  Nicholas J. Radcliffe,et al.  Equivalence Class Analysis of Genetic Algorithms , 1991, Complex Syst..

[10]  Mauricio G. C. Resende,et al.  Greedy Randomized Adaptive Search Procedures , 1995, J. Glob. Optim..

[11]  Bryant A. Julstrom.  Comparing Darwinian, Baldwinian, and Lamarckian Search in a Genetic Algorithm for the 4-Cycle Proble , 1999 .

[12]  Bhaba R. Sarker,et al.  Discrete location theory , 1991 .

[13]  Said Salhi,et al.  Discrete Location Theory , 1991 .

[14]  James C. Bean,et al.  Genetic Algorithms and Random Keys for Sequencing and Optimization , 1994, INFORMS J. Comput..

[15]  Ernesto Costa,et al.  Understanding the role of insertion and correction in the evolution of Golomb rulers , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[16]  James B. Shearer,et al.  Some new optimum Golomb rulers , 1990, IEEE Trans. Inf. Theory.

[17]  James R. Wilson,et al.  Empirical Investigation of the Benefits of Partial Lamarckianism , 1997, Evolutionary Computation.

[18]  G.S. Bloom,et al.  Applications of numbered undirected graphs , 1977, Proceedings of the IEEE.

[19]  Pablo Moscato,et al.  Memetic algorithms: a short introduction , 1999 .