Abstract
We focus on the Golomb ruler problem, a hard constrained combinatorial optimization problem. Two alternative encodings are considered, one based on the direct representation of solutions, and one based on the use of an auxiliary decoder. The properties of the corresponding fitness landscapes are analyzed. It turns out that the landscape for the direct encoding is highly irregular, causing drift to low-fitness regions. On the contrary, the landscape for the indirect representation is regular, and exhibits comparable fitness-distance correlation to that of the former landscape. These findings are validated in the context of variable neighborhood search.
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References
Fang, R., Sandrin, W.: Carrier frequency assignment for non-linear repeaters. Comsat Technical Review 7, 227–245 (1977)
Babcock, W.: Intermodulation interference in radio systems. Bell Systems Technical Journal, 63–73 (1953)
Bloom, G., Golomb, S.: Aplications of numbered undirected graphs. Proceedings of the IEEE 65, 562–570 (1977)
Robbins, J., Gagliardi, R., Taylor, H.: Acquisition sequences in PPM communications. IEEE Transactions on Information Theory 33, 738–744 (1987)
Klove, T.: Bounds and construction for difference triangle sets. IEEE Transactions on Information Theory 35, 879–886 (1989)
Robinson, J., Bernstein, A.: A class of binary recurrent codes with limited error propagation. IEEE Transactions on Information Theory 13, 106–113 (1967)
Feeney, B.: Determining optimum and near-optimum Golomb rulers using genetic algorithms. Master thesis, Computer Science, University College Cork (2003)
Rankin, W.: Optimal Golomb rulers: An exhaustive parallel search implementation. Master thesis, Duke University Electrical Engineering Dept., Durham, NC (1993)
Dollas, A., Rankin, W.T., McCracken, D.: A new algorithm for Golomb ruler derivation and proof of the 19 mark ruler. IEEE Transactions on Information Theory 44, 379–382 (1998)
OGR project (on-going since September 14, 1998), http://www.distributed.net/ogr/
Mirchandani, P., Francis, R.: Discrete Location Theory. Wiley-Interscience, Hoboken (1990)
Dewdney, A.: Computer recreations. Scientific American, 14–21 (1986)
McCracken, D.: Minimum redundancy linear arrays. Senior thesis, Duke University, Durham, NC (1991)
Shearer, J.B.: Golomb ruler table. Mathematics Department, IBM Research (2001), http://www.research.ibm.com/people/s/shearer/grtab.html
Shearer, J.: Some new optimum Golomb rulers. IEEE Transactions on Information Theory 36, 183–184 (1990)
Garry, M., Vanderschel, D., et al.: Search of the optimal 20, 21 & 22 mark Golomb rulers. GVANT project (1999), http://members.aol.com/golomb20/index.html
Smith, B., Walsh, T.: Modelling the Golomb ruler problem. In: Workshop on non-binary constraints (IJCAI 1999), Stockholm (1999)
Galinier, P., Jaumard, B., Morales, R., Pesant, G.: A constraint-based approach to the Golomb ruler problem. In: 3rd International Workshop on Integration of AI and OR Techniques, CP-AI-OR 2001 (2001)
Koziel, S., Michalewicz, Z.: A decoder-based evolutionary algorithm for constrained parameter optimization problems. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 231–240. Springer, Heidelberg (1998)
Soliday, S., Homaifar, A., Lebby, G.: Genetic algorithm approach to the search for Golomb rulers. In: Eshelman, L. (ed.) 6th International Conference on Genetic Algorithms (ICGA 1995), Pittsburgh, PA, USA, pp. 528–535. Morgan Kaufmann, San Francisco (1995)
Pereira, F., Tavares, J., Costa, E.: Golomb rulers: The advantage of evolution. In: Pires, F.M., Abreu, S.P. (eds.) EPIA 2003. LNCS (LNAI), vol. 2902, pp. 29–42. Springer, Heidelberg (2003)
Bean, J.: Genetic algorithms and random keys for sequencing and optimization. ORSA Journal on Computing 6, 154–160 (1994)
Cotta, C., Fernández, A.J.: A hybrid GRASP – evolutionary algorithm approach to golomb ruler search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 481–490. Springer, Heidelberg (2004)
Resende, M., Ribeiro, C.: Greedy randomized adaptive search procedures. In: Glover, F., Kochenberger, G. (eds.) Handbook of Metaheuristics, pp. 219–249. Kluwer Academic Publishers, Boston (2003)
Radcliffe, N.: Equivalence class analysis of genetic algorithms. Complex Systems 5, 183–205 (1991)
Wright, S.: The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: Jones, D. (ed.) 6th Intenational Congress on Genetics, vol. 1, pp. 356–366 (1932)
Diaz, D., Codognet, P.: GNU Prolog: beyond compiling Prolog to C. In: Pontelli, E., Santos Costa, V. (eds.) PADL 2000. LNCS, vol. 1753, pp. 81–92. Springer, Heidelberg (2000)
Barták, R.: Practical constraints: A tutorial on modelling with constraints. In: Figwer, J. (ed.) 5th Workshop on Constraint Programming for Decision and Control, Gliwice, Poland, pp. 7–17 (2003)
Bierwirth, C., Mattfeld, D., Watson, J.P.: Landscape regularity and random walks for the job shop scheduling problem. In: Gottlieb, J., Raidl, G.R. (eds.) EvoCOP 2004. LNCS, vol. 3004, pp. 21–30. Springer, Heidelberg (2004)
Jones, T.: Evolutionary Algorithms, Fitness Landscapes and Search. Phd thesis, Santa Fe Institute, University of New Mexico, Alburquerque (1995)
Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Eshelman, L. (ed.) Proceedings of the 6th International Conference on Genetic Algorithms, pp. 184–192. Morgan Kaufmann Publishers, San Francisco (1995)
Reeves, C.: Landscapes, operators and heuristic search. Annals of Operational Research 86, 473–490 (1999)
Boese, K., Kahng, A., Muddu, S.: A new adaptive multi-start technique for combinatorial global optimizations. Operations Research Letters 16, 101–113 (1994)
Mladenović, N., Hansen, P.: Variable neighborhood search. Computers and Operations Research 24, 1097–1100 (1997)
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Cotta, C., Fernández, A.J. (2005). Analyzing Fitness Landscapes for the Optimal Golomb Ruler Problem. In: Raidl, G.R., Gottlieb, J. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2005. Lecture Notes in Computer Science, vol 3448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31996-2_7
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DOI: https://doi.org/10.1007/978-3-540-31996-2_7
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