Decades after the potential of evolutionary inspirations in global optimization was acknowledged, there is still some confusion concerning the way the essential evolutionary operators act in basic adaptive situations. This is because the dynamics of evolving populations are quite complex and often counterintuitive. Therefore appropriate visualization programs might be really helpful in providing the required expertise. We present such a program together with a number of examples that illustrate some aspects of evolution of phenotypes in unlimited, multidimensional, real spaces under different kinds of selection.
Belief networks encode joint probability distribution functions and can be used as fitness functions in genetic algorithms. Individuals in the genetic algorithm's population then represent instantiations, or explanations, in the belief network. Computing the most probable explanations (belief revision) is thus cast as a genetic algorithm search in the joint probability distribution space. At any time, the best fit individual in the genetic algorithm population is an estimate of the most probable explanation. This paper argues that joint probability distribution functions represented by belief networks typically are multimodal and highly variable. Thus the genetic algorithm techniques known as sharing and scaling should be of help. It is shown empirically that this is indeed the case, in particular that niching combined with scaling significantly improves the quality of a genetic algorithm's estimate of the most probable explanations. A novel scaling approach, root scaling, is also introduced.
For function approximation using fuzzy if-then rules, Nomura et al. (1992) proposed a genetic algorithm-based method for adjusting the fuzzy partition of an input space. In this paper, we apply their method to pattern classification problems. We have already extended the coding method to the case where intervals and trapezoidal membership functions can be used for antecedent fuzzy sets (Ishibuchi & Murata, 1996). There are, however, two drawbacks in these methods. One is that the resolution of each axis on which the fuzzy partition is adjusted should be prespecified by a decision-maker. The other is that the number of fuzzy if-then rules exponentially increases as the number of attributes increases. To cope with these drawbacks, we propose a genetic algorithmbased fuzzy partition method that has the following advantages; We show the effectiveness of the proposed method by computer simulations on iris data with 4 attributes and wine data with 13 attributes.
The task of finding minimal elements of a partially ordered set is a generalization of the task of finding the global minimum of a real-valued function or of finding Pareto-optimal points of a multicriteria optimization problem. It is shown that evolutionary algorithms are able to converge to the set of minimal elements in finite time with probability one, provided that the search space is finite, the time-invariant variation operator is associated with a positive transition probability function and that the selection operator obeys the so-called ‘elite preservation strategy.’
This paper presents a new approach to evolutionary artificial neural networks, based on the integration of feedforward neural networks, messy genetic algorithms (GAs), and singular value decomposition (SVD). The set of competing hidden nodes with variable number of connections from the input layer represents an evolving neural network. Selection of hidden nodes is based on their estimation via SVD. The resulting singular values are used to determine significance of hidden nodes for the network's output. To represent connectivity of hidden nodes and to process the topology of connections between input and hidden layers, we employ the approach of messy GAs. This establishes a framework for processing strings of variable length which codes this topology and allows one to search for useful combinations of input variables. The proposed approach is tested using sonar data classification.
