Browsing by Subject "Cauchy distribution"

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    Randomized and rank based differential evolution
    (IEEE, 2009-12) Urfalıoğlu, Onay; Arıkan, Orhan
    Many real world problems which can be assigned to the machine learning domain are inverse problems. The available data is often noisy and may contain outliers, which requires the application of global optimization. Evolutionary Algorithms (EA's) are one class of possible global optimization methods for solving such problems. Within population based EA's, Differential Evolution (DE) is a widely used and successful algorithm. However, due to its differential update nature, given a current population, the set of possible new populations is finite and a true subset of the cost function domain. Furthermore, the update formula of DE does not use any information about the fitnesses of the population. This paper presents a novel extension of DE called Randomized and Rank based Differential Evolution (R2DE) to improve robustness and global convergence speed on multimodal problems by introducing two multiplicative terms in the DE update formula. The first term is based on a random variate of a Cauchy distribution, which leads to a randomization. The second term is based on ranking of individuals, so that R2DE exploits additional information provided by the fitnesses. In experiments including non-linear dimension reduction by autoencoders, it is shown that R2DE improves robustness and speed of global convergence. © 2009 IEEE.
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    Self-adaptive randomized and rank-based differential evolution for multimodal problems
    (Springer, 2011-01-15) Urfalioglu, O.; Arıkan, Orhan
    Differential Evolution (DE) is a widely used successful evolutionary algorithm (EA) based on a population of individuals, which is especially well suited to solve problems that have non-linear, multimodal cost functions. However, for a given population, the set of possible new populations is finite and a true subset of the cost function domain. Furthermore, the update formula of DE does not use any information about the fitness of the population. This paper presents a novel extension of DE called Randomized and Rank-based Differential Evolution (R2DE) and its self-adaptive version SAR2DE to improve robustness and global convergence speed on multimodal problems by introducing two multiplicative terms in the DE update formula. The first term is based on a random variate of a Cauchy distribution, which leads to a randomization. The second term is based on ranking of individuals, so that R2DE exploits additional information provided by the population fitness. In extensive experiments conducted with a wide range of complexity settings, we show that the proposed heuristics lead to an overall improvement in robustness and speed of convergence compared to several global optimization techniques, including DE, Opposition based Differential Evolution (ODE), DE with Random Scale Factor (DERSF) and the self-adaptive Cauchy distribution based DE (NSDE).