Analysis of epistatic interactions and fitness landscapes using a new geometric approach

BACKGROUND: Understanding interactions between mutations and how they affect fitness is a central problem in evolutionary biology that bears on such fundamental issues as the structure of fitness landscapes and the evolution of sex. To date, analyses of fitness landscapes have focused either on the overall directional curvature of the fitness landscape or on the distribution of pairwise interactions. In this paper, we propose and employ a new mathematical approach that allows a more complete description of multi-way interactions and provides new insights into the structure of fitness landscapes. RESULTS: We apply the mathematical theory of gene interactions developed by Beerenwinkel et al. to a fitness landscape for Escherichia coli obtained by Elena and Lenski. The genotypes were constructed by introducing nine mutations into a wild-type strain and constructing a restricted set of 27 double mutants. Despite the absence of mutants higher than second order, our analysis of this genotypic space points to previously unappreciated gene interactions, in addition to the standard pairwise epistasis. Our analysis confirms Elena and Lenski's inference that the fitness landscape is complex, so that an overall measure of curvature obscures a diversity of interaction types. We also demonstrate that some mutations contribute disproportionately to this complexity. In particular, some mutations are systematically better than others at mixing with other mutations. We also find a strong correlation between epistasis and the average fitness loss caused by deleterious mutations. In particular, the epistatic deviations from multiplicative expectations tend toward more positive values in the context of more deleterious mutations, emphasizing that pairwise epistasis is a local property of the fitness landscape. Finally, we determine the geometry of the fitness landscape, which reflects many of these biologically interesting features. CONCLUSION: A full description of complex fitness landscapes requires more information than the average curvature or the distribution of independent pairwise interactions. We have proposed a mathematical approach that, in principle, allows a complete description and, in practice, can suggest new insights into the structure of real fitness landscapes. Our analysis emphasizes the value of non-independent genotypes for these inferences

Cellular Genetic Algorithms: Understanding the Behavior of Using Neighborhoods

In this paper, we analyze the neighborhood effect in the selection of parents on an evolutionary algorithm. In this line, we compare a cellular genetic algorithm (cGA), which intrinsically uses the neighbor notion in the mating process, with a modified genetic algorithm including the concept of neighborhood in the selection of parents. Additionally, we analyze the neighborhood size considered for the selection of parent, trying to discover if a quasi-optimal size exists. All the analysis is carried out from a traditional analytic sense to a theoretical point of view regarding evolvability measures. The experimental results suggest that the neighbor effect is important in the performance of an evolutionary algorithm and could provide the cGA with higher chances of success in well-known optimization problems. Regarding the neighborhood size, there is an evidence that a range of neighbors of six, plus/minus two, individuals leads to the cGA to perform more efficiently than other considered sizes.Fil: Salto, Carolina. Universidad Nacional de La Pampa. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Confluencia; ArgentinaFil: Alba, Enrique. Universidad de Málaga; Españ

Comparison of Different Approaches for Adapting Mutation Probabilities in Genetic Algorithms

Traditionally in Genetic Algorithms, the mutation probability parameter maintains a constant value during the search. However, an important difficulty is to determine a priori which probability value is the best suited for a given problem. In this paper we compare three different adaptive algorithms that include strategies to modify the mutation probability without external control. One adaptive strategy uses the genetic diversity present in the population to update the mutation probability. Other strategy is based on the ideas of reinforcement learning and the last one varies the probabilities of mutation depending on the fitness values of the solution. All these strategies eliminate a very expensive computational phase related to the pre-tuning of the algorithmic parameters. The empirical comparisons show that if the genetic algorithm uses the genetic diversity, as the strategy for adapting the mutation probability outperforms the other two strategies.XVII Workshop Agentes y Sistemas Inteligentes (WASI).Red de Universidades con Carreras en Informática (RedUNCI

Comparison of Different Approaches for Adapting Mutation Probabilities in Genetic Algorithms

Traditionally in Genetic Algorithms, the mutation probability parameter maintains a constant value during the search. However, an important difficulty is to determine a priori which probability value is the best suited for a given problem. In this paper we compare three different adaptive algorithms that include strategies to modify the mutation probability without external control. One adaptive strategy uses the genetic diversity present in the population to update the mutation probability. Other strategy is based on the ideas of reinforcement learning and the last one varies the probabilities of mutation depending on the fitness values of the solution. All these strategies eliminate a very expensive computational phase related to the pre-tuning of the algorithmic parameters. The empirical comparisons show that if the genetic algorithm uses the genetic diversity, as the strategy for adapting the mutation probability outperforms the other two strategies.XVII Workshop Agentes y Sistemas Inteligentes (WASI).Red de Universidades con Carreras en Informática (RedUNCI

When Hillclimbers Beat Genetic Algorithms in Multimodal Optimization

It has been shown in the past that a multistart hillclimbing strategy compares favourably to a standard genetic algorithm with respect to solving instances of the multimodal problem generator. We extend that work and verify if the utilization of diversity preservation techniques in the genetic algorithm changes the outcome of the comparison. We do so under two scenarios: (1) when the goal is to find the global optimum, (2) when the goal is to find all optima. A mathematical analysis is performed for the multistart hillclimbing algorithm and a through empirical study is conducted for solving instances of the multimodal problem generator with increasing number of optima, both with the hillclimbing strategy as well as with genetic algorithms with niching. Although niching improves the performance of the genetic algorithm, it is still inferior to the multistart hillclimbing strategy on this class of problems. An idealized niching strategy is also presented and it is argued that its performance should be close to a lower bound of what any evolutionary algorithm can do on this class of problems