Estimation of Distribution Algorithms (EDAs) are a set of algorithms that belong to the field of Evolutionary Computation. In EDAs there are neither crossover nor mutation operators. Instead, the new population of individuals is sampled from a probability distribution, which is estimated from a database that contains the selected individuals from the previous generation. Thus, the interrelations between the different variables that represent the individuals may be explicitly expressed through the joint probability distribution associated with the individuals selected at each generation.
Accurately defining the radiation scope of the logistics park is the basis of the rational planning of the logistics park as well as further improvement of the regional logistics efficiency, but currently there is still a lack of scientific and systematical theory focusing on the research of defining the radiation scope of the logistics park. Therefore the concept of ‘hinterland’ was introduced into the research of the radiation scope of the logistics park, and the concept of ‘logistics park hinterland’ was particularly proposed. Subsequently, based on the Voronoi diagram theory in computational geometry which reflects the advantage of the continuity of space division, and by introducing the ‘scale’ parameter in the breaking-point model into weighted Voronoi diagram, the model based on weighted Voronoi diagram to define the logistics park hinterland was built. Finally, this model was practically applied to the planning example of ‘Four logistics centers’ of Chengdu, and also by means of GIS software the respective hinterlands of ‘Four logistics centers’ of Chengdu were defined. It practically proves that this model overcomes the shortcomings existing in the conventional single space division theories and methods such as the breaking-point model and the ordinary Voronoi diagram theory, which makes the definition of the logistics park hinterland more reasonable and scientific.
The study conducted in this paper is mainly driven by the topological characteristics of the structures that the interactions among the variables of the problems provide. Taking as reference the emergent field of complex networks, we generate a wide spectrum of networks that will serve as problem structures. Then, the impact that the topological characteristics of those networks have, both in the hardness of the optimization problem and in the behavior of the EDA, is analyzed. This reveals a relationship among the topology of the problem structure, the difficulty of the problems and the dependences that the algorithm needs to learn in order to solve the problems.
In this paper, we study the ability limit of EDAs to effectively solve problems in relation to the number of interactions among the variables. More in particular, we numerically analyze the learning limits that different EDA implementations encounter to solve problems on a sequence of additively decomposable functions (ADFs) in which new sub-functions are progressively added. The study is carried out in a worst-case scenario where the sub-functions are defined as deceptive functions. We argue that the limits for this type of algorithm are mainly imposed by the probabilistic model they rely on. Beyond the limitations of the approximate learning methods, the results suggest that, in general, the use of bayesian networks can entail strong computational restrictions to overcome the limits of applicability.
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