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Final fitness value after generations for each operator line colour , as a function of the mutation rate, p m logarithmic scale , for each problem row and number of crossover points column. All other parameters were unchanged. We also observe that crossovers with low scores, which had very low performance at nominal mutation levels, can outperform the negative control and even other crossover methods when mutation rate is very low.
This may indicate that lowering the mutation rate leads to a regime where crossover is primarily responsible for creating new variation, rather than recombining existing variation. In other words, it suggests that non-homologous crossovers can partially replace mutation as a source of variation in an evolutionary process. Our work presents a new look at crossover in variable-length linear genomes, highlighting the dual importance of correctly exchanging homologous information, and recombining unique variations in the two parents.
We quantify these two goals by defining the homology and linkage score, which can be measured for any crossover operator and sequence divergence, and show that these two factors indeed explain the difference between crossover methods. The trade-off between linkage and homology is controlled in large part by the number of crossover points.
In the extreme case, we provide an approximation of uniform crossover for variable-length genomes by defining the near-uniform crossover. While both homology and linkage are important for successful recombination, our results show that, given a method that is reasonably effective at recognising homology, the most crucial factor for efficient evolution is choosing an appropriate correlation between the inheritance of genomic variations. The global alignment crossover allows the most flexible tuning of the linkage score by working with a wider range of crossover points.
In particular, it has the highest number of possible crossover points among the reliable methods, and its near-uniform variant approaches the uniform linkage score. In many cases, desirable crossovers do not only accelerate evolution, but are also easy to implement and fast to compute. We also propose a heuristic alternative to the Hirschberg algorithm for global alignment, which runs 3—4 times faster than the exact method in our experiments, with virtually no difference in performance for our scores and benchmarks.
There is likely more room for improvement for heuristic alignment methods that are optimised for use in evolutionary computation. Our work looks at crossover in evolutionary algorithms with linear genomes of variable length. In the future, it may be interesting to investigate the theoretical goals and practical implementation of crossover for genomes which may not only change in length, but also in structure, by allowing parts of the genome to be moved or copied.
We are grateful to Karl Fogelmark for interesting discussions and Carsten Peterson for comments and encouragement. Browse Subject Areas? Click through the PLOS taxonomy to find articles in your field. Abstract The use of variable-length genomes in evolutionary computation has applications in optimisation when the size of the search space is unknown, and provides a unique environment to study the evolutionary dynamics of genome structure.
Introduction Evolutionary algorithms are a family of computational methods that utilise natural selection for global optimisation on a wide range of problem types. Download: PPT. Fig 1. Illustration of crossover and homology and linkage scores with binary genomes. Alignment In practice, detailed information on the history of each genetic element is not available during an evolutionary process. Crossovers Below we review existing crossover methods for linear variable-length genomes. Global alignment crossover Hirschberg or Needleman-Wunsch.
Global alignment crossover Heuristic. One-gap alignment crossover. Messy crossover. Synapsing crossover. Near-uniform crossover The linkage score of a crossover methods increases naturally with the number n of crossover sites, as higher n makes it increasingly likely that any two bits are separated by an odd number of crossover points and thus end up on different genomes.
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Results and discussion We first analysed the recombination scores, followed by an analysis of performance in three different benchmark problems. Recombination scores In order to track the evolutionary history of each sequence element, we generate random genomes of length , and tag each bit with a unique identifier.
Fig 2. Homology and linkage scores for different crossover operators. Benchmarks To test the performance of each crossover operator, we performed three benchmark experiments with an evolutionary algorithm. The three benchmarks are designed to represent different alleged benefits of crossover. Benchmark 1: string match. Benchmark 2: substrings. Benchmark 3: RBF.
Fig 3. Benchmark performance and connection to recombination scores. Crossover accelerates evolution based on its recombination scores.
- From the Cell to the Cross.
- Homology (biology) - Wikipedia.
- 9.1.1 Homology Modeling Introduction.
Variable-length genomes evolve faster than fixed-length genomes. Effect of crossover on optimal mutation rate. Conclusions Our work presents a new look at crossover in variable-length linear genomes, highlighting the dual importance of correctly exchanging homologous information, and recombining unique variations in the two parents. Supporting information.
S1 Code. Crossover source code. Acknowledgments We are grateful to Karl Fogelmark for interesting discussions and Carsten Peterson for comments and encouragement. References 1. Eiben AE, Schoenauer M. Evolutionary computing. Information Processing Letters. View Article Google Scholar 2. Holland JH. Genetic Algorithms. Scientific American. View Article Google Scholar 3.
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