Díez's algorithm for the noisy MAX is very efficient for polytrees, but when the network has loops, it has to be combined with local conditioning, a suboptimal propagation algorithm. Other algorithms, based on several factorizations of the conditional probability of the noisy MAX, are not as efficient for polytrees but can be combined with general propagation algorithms such as clustering or variable elimination, which are more efficient for networks with loops. In this article we propose a new factorization of the noisy MAX that amounts to Díez's algorithm in the case of polytrees and at the same time is more efficient than previous factorizations when combined with either variable elimination or clustering.

Crowding is a technique used in genetic algorithms to preserve diversity in the population and to prevent premature convergence to local optima. It consists of pairing each offspring with a similar individual in the current population (pairing phase) and deciding which of the two will remain in the population (replacement phase). The present work focuses on the replacement phase of crowding, which usually has been carried out by one of the following three approaches: Deterministic, Probabilistic, and Simulated Annealing. These approaches present some limitations regarding the way replacement is conducted. On the one hand, the first two apply the same selective pressure regardless of the problem being solved or the stage of the genetic algorithm. On the other hand, the third does not apply a uniform selective pressure over all the individuals in the population, which makes the control of selective pressure over the generations somewhat difficult. This work presents a Generalized Crowding approach that allows selective pressure to be controlled in a simple way in the replacement phase of crowding, thus overcoming limitations of the other approaches. Furthermore, the understanding of existing approaches is greatly improved, since both Deterministic and Probabilistic Crowding turn out to be special cases of Generalized Crowding. In addition, the temperature parameter used in Simulated Annealing is replaced by a parameter called scaling factor that controls the selective pressure applied. Theoretical analysis using Markov chains and empirical evaluation using Bayesian networks demonstrate the potential of this novel Generalized Crowding approach.

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Genetic algorithms typically use crossover, which relies on mating a set of selected parents. As part of crossover, random mating is often carried out. A novel approach to parent mating is presented in this work. Our novel approach can be applied in combination with a traditional similarity-based criterion to measure distance between individuals or with a fitness-based criterion. We introduce a parameter called the mating index that allows different mating strategies to be developed within a uniform framework: an exploitative strategy called best-first, an explorative strategy called best-last, and an adaptive strategy called self-adaptive. Self-adaptive mating is defined in the context of the novel algorithm, and aims to achieve a balance between exploitation and exploration in a domain-independent manner. The present work formally defines the novel mating approach, analyzes its behavior, and conducts an extensive experimental study to quantitatively determine its benefits. In the domain of real function optimization, the experiments show that, as the degree of multimodality of the function at hand grows, increasing the mating index improves performance. In the case of the self-adaptive mating strategy, the experiments give strong results for several case studies.

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