Golomb Rulers: A fitness landscape analysis

Fitness landscape analysis techniques are used to better understand the influence of genetic representations and associated variation operators when solving a combinatorial optimization problem. Several representations for the optimal Golomb ruler problem are examined. Common mutation operators such as bit-flip mutation are employed to generate fitness landscapes to study the genetic representations. Furthermore, additional experiments are made to observe the effects of adding heuristics and local improvements to the encodings.

[1]  F. Biraud,et al.  On optimum synthetic linear arrays with application to radioastronomy , 1974 .

[2]  Pascal Van Hentenryck,et al.  A Memetic Approach to Golomb Rulers , 2006, PPSN.

[3]  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).

[4]  Bernard Manderick,et al.  The Genetic Algorithm and the Structure of the Fitness Landscape , 1991, ICGA.

[5]  Holger Becker,et al.  Collective Wisdom , 1998, American Scientist.

[6]  Carlos Cotta,et al.  Analyzing Fitness Landscapes for the Optimal Golomb Ruler Problem , 2005, EvoCOP.

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

[8]  Carol Bult,et al.  PERMUTATIONS , 1994 .

[9]  Günther R. Raidl,et al.  Empirical Analysis of Locality, Heritability and Heuristic Bias in Evolutionary Algorithms: A Case Study for the Multidimensional Knapsack Problem , 2005, Evolutionary Computation.

[10]  Apostolos Dollas,et al.  A New Algorithm for Golomb Ruler Derivation and Proof of the 19 Mark Ruler , 1998, IEEE Trans. Inf. Theory.

[11]  Tim Jones.  Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

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

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

[14]  Solomon W. Golomb,et al.  HOW TO NUMBER A GRAPH††This research was supported in part by the United States Air Force under Grant AFOSR-68-1555. , 1972 .

[15]  Franz Rothlauf,et al.  Network Random KeysA Tree Representation Scheme for Genetic and Evolutionary Algorithms , 2002, Evolutionary Computation.

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

[17]  Franz Rothlauf,et al.  Network Random Keys-A Tree Representation Scheme for Genetic and Evolutionary Algorithms , 2005 .

[18]  Franz Rothlauf,et al.  Representations for genetic and evolutionary algorithms , 2002, Studies in Fuzziness and Soft Computing.

[19]  Terry Jones,et al.  Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms , 1995, ICGA.

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

[21]  Kalyanmoy Deb,et al.  Introduction to representations , 2000 .

[22]  Bernhard Sendhoff,et al.  A Condition for the Genotype-Phenotype Mapping: Causality , 1997, ICGA.

[23]  Carlos Cotta,et al.  A Hybrid GRASP - Evolutionary Algorithm Approach to Golomb Ruler Search , 2004, PPSN.

[24]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[25]  Peter Merz,et al.  Memetic algorithms for combinatorial optimization problems : fitness landscapes and effective search strategies , 2006 .

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

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

[28]  Takeshi Yamada,et al.  Genetic Algorithms, Path Relinking, and the Flowshop Sequencing Problem , 1998, Evolutionary Computation.

[29]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[30]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .