Genetic algorithms for communications network design - an empirical study of the factors that influence performance

We explore the use of GAs for solving a network optimization problem, the degree-constrained minimum spanning tree problem. We also examine the impact of encoding, crossover, and mutation on the performance of the GA. A specialized repair heuristic is used to improve performance. An experimental design with 48 cells and ten data points in each cell is used to examine the impact of two encoding methods, three crossover methods, two mutation methods, and four networks of varying node sizes. Two performance measures, solution quality and computation time, are used to evaluate the performance. The results obtained indicate that encoding has the greatest effect on solution quality, followed by mutation and crossover. Among the various options, the combination of determinant encoding, exchange mutation, and uniform crossover more often provides better results for solution quality than other combinations. For computation time, the combination of determinant encoding, exchange mutation, and one-point crossover provides better results.

[1]  Fred W. Glover,et al.  Using tabu search to solve the Steiner tree-star problem in telecommunications network design , 1996, Telecommun. Syst..

[2]  Monica Cuppini,et al.  A genetic algorithm for channel assignment problems , 2010, Eur. Trans. Telecommun..

[3]  Charles C. Palmer,et al.  An approach to a problem in network design using genetic algorithms , 1994, Networks.

[4]  Ravindra K. Ahuja,et al.  Developing Fitter Genetic Algorithms , 1997, INFORMS J. Comput..

[5]  Aaron Kershenbaum When Genetic Algorithms Work Best , 1997, INFORMS J. Comput..

[6]  Lawrence Davis,et al.  Genetic Algorithms and Communication Link Speed Design: Constraints and Operators , 1987, ICGA.

[7]  David S. Johnson The NP-Completeness Column: An Ongoing Guide , 1986, J. Algorithms.

[8]  Vassilios Petridis,et al.  Varying fitness functions in genetic algorithm constrained optimization: the cutting stock and unit commitment problems , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Mitsuo Gen,et al.  Genetic algorithms and engineering design , 1997 .

[10]  Derek Smith,et al.  Bin Packing with Adaptive Search , 1985, ICGA.

[11]  Pierre Chardaire,et al.  Applications of Genetic Algorithms in Telecommunications , 1995 .

[12]  John J. Grefenstette,et al.  Optimization of Control Parameters for Genetic Algorithms , 1986, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  R. Prim Shortest connection networks and some generalizations , 1957 .

[14]  J. Reed,et al.  Simulation of biological evolution and machine learning. I. Selection of self-reproducing numeric patterns by data processing machines, effects of hereditary control, mutation type and crossing. , 1967, Journal of theoretical biology.

[15]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[16]  John J. Grefenstette,et al.  Multilevel Credit Assignment in a Genetic Learning System , 1987, International Conference on Genetic Algorithms.

[17]  Henrik Esbensen,et al.  Computing near-optimal solutions to the steiner problem in a graph using a genetic algorithm , 1995, Networks.

[18]  Colin R. Reeves,et al.  Genetic Algorithms for the Operations Researcher , 1997, INFORMS J. Comput..

[19]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[20]  Alex Karel Obruca Spanning Tree Manipulation and the Travelling Salesman Problem , 1968, Comput. J..

[21]  M. Gen,et al.  A note on genetic algorithms for degree‐constrained spanning tree problems , 1997 .

[22]  Alice E. Smith,et al.  Local search genetic algorithm for optimal design of reliable networks , 1997, IEEE Trans. Evol. Comput..

[23]  Martin W. P. Savelsbergh,et al.  Edge exchanges in the degree-constrained minimum spanning tree problem , 1985, Comput. Oper. Res..

[24]  James E. Baker,et al.  Adaptive Selection Methods for Genetic Algorithms , 1985, International Conference on Genetic Algorithms.

[25]  David E. Goldberg,et al.  Alleles, loci and the traveling salesman problem , 1985 .

[26]  Gilbert Syswerda,et al.  Uniform Crossover in Genetic Algorithms , 1989, ICGA.

[27]  G. D. Smith,et al.  Solving the Graphical Steiner Tree Problem Using Genetic Algorithms , 1993 .

[28]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[29]  Subhash C. Narula,et al.  Degree-constrained minimum spanning tree , 1980, Comput. Oper. Res..

[30]  Roger L. Wainwright,et al.  Determinant Factorization: A New Encoding Scheme for Spanning Trees Applied to the Probabilistic Minimum Spanning Tree Problem , 1995, ICGA.

[31]  J. Kruskal On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[32]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[33]  John J. Grefenstette,et al.  Genetic Search with Approximate Function Evaluation , 1985, ICGA.

[34]  John P. Hayes,et al.  Edge fault tolerance in graphs , 1993, Networks.

[35]  P. W. Poon,et al.  Genetic algorithm crossover operators for ordering applications , 1995, Comput. Oper. Res..

[36]  K. Dejong,et al.  An analysis of the behavior of a class of genetic adaptive systems , 1975 .

[37]  David W. Coit,et al.  Adaptive Penalty Methods for Genetic Optimization of Constrained Combinatorial Problems , 1996, INFORMS J. Comput..

[38]  Lawrence Davis,et al.  Adapting Operator Probabilities in Genetic Algorithms , 1989, ICGA.

[39]  M. Savelsbergh,et al.  Edge exchanges in the degree-constrained spanning tree problem , 1985 .

[40]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[41]  Zbigniew Michalewicz,et al.  Handbook of Evolutionary Computation , 1997 .

[42]  Colin R. Reeves,et al.  A genetic algorithm for flowshop sequencing , 1995, Comput. Oper. Res..

[43]  John P. Hayes,et al.  Optimally edge fault-tolerant trees , 1996 .

[44]  Ronald L. Graham,et al.  On the History of the Minimum Spanning Tree Problem , 1985, Annals of the History of Computing.