A genetic algorithm for shortest path routing problem and the sizing of populations

• Published in: IEEE transactions on evolutionary computation Vol. 6; no. 6; pp. 566 - 579
• Main Authors: Chang Wook Ahn, Ramakrishna, R.S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2002; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Biological and medical sciences; Biological cells; Chromosomes; Computer networks; Crossovers; Delay estimation; Equations; Exact sciences and technology; Flows in networks. Combinatorial problems; Fundamental and applied biological sciences. Psychology; General aspects; Genetic algorithms; Genetic mutations; Mathematical analysis; Mathematical models; Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects); Mobile ad hoc networks; Mobile communication; Mutation; Network topology; Operational research and scientific management; Operational research. Management science; Populations; Quality of service; Radiocommunications; Routing; Routing (telecommunications); Studies; Telecommunications; Telecommunications and information theory; Computer simulation; Algorithmics; Shortest path; shortest path routing problem; Chromosome; Routing; genetic algorithms; Population genetics; population size; Routing algorithm; Gene; Genetic algorithm; Character string; Gambler's ruin model; Ad hoc network
• ISSN: 1089-778X; 1941-0026
• DOI: 10.1109/TEVC.2002.804323

This paper presents a genetic algorithmic approach to the shortest path (SP) routing problem. Variable-length chromosomes (strings) and their genes (parameters) have been used for encoding the problem. The crossover operation exchanges partial chromosomes (partial routes) at positionally independent crossing sites and the mutation operation maintains the genetic diversity of the population. The proposed algorithm can cure all the infeasible chromosomes with a simple repair function. Crossover and mutation together provide a search capability that results in improved quality of solution and enhanced rate of convergence. This paper also develops a population-sizing equation that facilitates a solution with desired quality. It is based on the gambler ruin model; the equation has been further enhanced and generalized. The equation relates the size of the population, quality of solution, cardinality of the alphabet, and other parameters of the proposed algorithm. Computer simulations show that the proposed algorithm exhibits a much better quality of solution (route optimality) and a much higher rate of convergence than other algorithms. The results are relatively independent of problem types for almost all source-destination pairs. Furthermore, simulation studies emphasize the usefulness of the population-sizing equation. The equation scales to larger networks. It is felt that it can be used for determining an adequate population size in the SP routing problem.